The circumference of a particular circle is 18 cm. In square centimeters, what is the area of the circle? Express your answer as a common fraction in terms of $\pi$.

Answer:

False. He is not correct.

Step-by-step explanation:

To find the percent increase subtract  the old time from the new time then divide that number by the old time. 25-20=5. 5/20=.25. There was a 25% increase in time worked. Evan worked 125% of the original time but only worked 25% more time.

Answer:

10. 5556 discs per month

11. 3.33 hours; 0.196%

Step-by-step explanation:

I find "appropriate technology" for questions like these to be a graphing calculator.

10. Put the given function definitions into the formula for profit and look for the peak of the profit curve. It is found at x ≈ 5556.

___

11. The peak of the graph is found at t=3.333. The value of A(t) there is about 0.1962.

_____

If these are part of a calculus course, you can find the maximum values by differentiating the P(x) or A(t) functions and setting the derivative to zero. You get a linear equation in each case, so finding the independent variable value is not difficult:

10. 5 -.0009x = 0

11. (.16 -.048t)e^(-.3t) = 0

Answer: 18 gallons.

Step-by-step explanation:

Let's call the total gallons that the container can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{4}{9}x+4=\frac{2}{3}x[/tex]

Now, you must solve for x, as you can see below. Therefore, you obtain the following result:

[tex]\frac{4}{9}x+4=\frac{2}{3}x\\\\4=\frac{2}{3}x-\frac{4}{9}x\\\\4=\frac{2}{9}x\\\\4*9=2x\\\\36=2x\\\\x=18\ gallons[/tex]

To solve the container problem, we set up a proportion based on the given fill levels and found that the total capacity of the container is 18 gallons.

To solve how many gallons the container can hold, we need to set up a proportion based on the information given. The container was initially 4/9 full, and after adding 4 gallons of water, it became 2/3 full. We can use this ratio to find the total capacity of the container.

Therefore, the container's total capacity is 18 gallons.

Answer:

1/6

Step-by-step explanation:

Number of orange crayons = 2

Total number of crayons = 2 + 4 + 1 + 2 + 3 = 12

Probability is calculated as:

[tex]\frac{\text{Number of Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Here the favorable or desired outcome is picking up an orange crayon. So number of favorable outcomes will be 2 as 2 orange crayons are available.

Total number of outcomes is 12 which is the sum of all the crayons available.

So, the probability the crayon she pulls out will be orange = [tex]\frac{2}{12}=\frac{1}{6}[/tex]

The probability of Jill drawing an orange crayon from her bag is 1/6. This is calculated by dividing the number of desired outcomes (orange crayons) by the total number of outcomes (total crayons).

To solve this problem, we have to calculate the probability of picking an orange crayon from the bag. First, we calculate the total number of crayons Jill has in the bag. So Jill has 2 black, 4 blue, 1 yellow, 2 orange, and 3 purple crayons, which add up to a total of 12 crayons.

Probability is calculated by dividing the number of desired outcomes (in this case, drawing an orange crayon) by the total number of outcomes (the total number of crayons). Jill has 2 orange crayons, so the total number of desired outcomes is 2. As calculated earlier, the total number of outcomes is 12 crayons. So the probability of Jill drawing an orange crayon from her bag is 2 (orange crayons) divided by 12 (total crayons), or 1/6.

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  D. hypotenuse/opposite

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

You know that

  csc = 1/sin

so

  csc = 1/(opposite/hypotenuse) = hypotenuse/opposite . . . . matches D

The correct answer to the definition of the cosecant function in a right triangle is D. hypotenuse/opposite, which is the length of the hypotenuse divided by the length of the opposite side.

The right triangle definition of the cosecant function is the length of the hypotenuse divided by the length of the side opposite the angle in question. According to this definition, the correct answer to the student's question is D. hypotenuse/opposite.

In a right triangle, suppose we have an angle 0 (theta), which is not the 90-degree angle. The side opposite this angle is called the 'opposite side', and the side that is not the hypotenuse or the opposite side is called the 'adjacent side'. The hypotenuse is the longest side, opposite the right angle, denoted by c in the Pythagorean theorem, a2 + b2 = c2. Therefore, the cosecant of angle 0 is given by c / opposite side, where c is the hypotenuse.

A solid has 6 faces

Answer:

a) ±5

b) ±9

Step-by-step explanation:

In each case, the expression on the left is the square of the expression you're asked to find the value of. Then the value of your expression is the square root of the constant on the right. That square root can be either positive or negative.

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a) a^2 +2ab +b^2 = (a +b)^2 = 25

(a +b) = ±√25 = ±5

___

b) a^2 -8ab +16b^2 = (a -4b)^2 = 81

(a -4b) = ±√81 = ±9

Answer:

y = 5 + 2.50x

Step-by-step explanation:

If no apples are picked, the cost is 5 (dollars). For each pound of apples (x) the cost goes up by 2.50x (dollars). The sum of the entry and per-pound costs is the total cost:

y = 5 + 2.50x

Answer:

y=2.5x+5

Step-by-step explanation:

Answer:

15 rentals

Step-by-step explanation:

You can (and may be expected to) set up an equation that equates the total cost at one store to the total cost at the other store. When you work through the solution of this equation, you find that the "break even" number of rentals is the ratio of the difference in fixed cost (setup fee) to the difference in per-use cost (rental charge).

Here, that ratio is ...

(15.00 -7.50)/(2.25 -1.75) = 7.50/0.50 = 15

15 rentals will make the total costs the same.

so after 15 movie sales they will be equal

Answer:

[tex](-3, \frac{9}{5})[/tex]

Step-by-step explanation:

We have the equation [tex]2x + 5y-3 = 0[/tex].

The ordered pairs of this equation have the form [tex](x_0, y_0)[/tex]

Where x is the independent variable and y is the dependent variabe.

That is, the points belonging to the line [tex]2x + 5y-3 = 0[/tex] have the form [tex](x_0, f (x_0))[/tex]

For [tex]y = f(x)[/tex].

So, we need to find [tex]f(x_0)[/tex] for x_0 = -3.

Then we substitute x = -3 into the equation and clear the value of y.

[tex]2(-3) + 5y -3 = 0[/tex]

[tex]-6 + 5y = 3\\\\5y = 9\\\\y = \frac{9}{5}[/tex].

Then the ordered pair is:

[tex](-3, \frac{9}{5})[/tex]

the general term for the sequence m, -m, m, -m, . . . is

The correct option is (A).

The given sequence is: m, -m, m, -m, ...

Let's analyze the pattern:

1. For n = 1, the term is m.

2. For n = 2, the term is -m.

3. For n = 3, the term is m.

4. For n = 4, the term is -m.

5. And so on...

From the pattern, we can see that the sign alternates between positive and negative, and the term alternates between m and -m. This suggests that we can use [tex](-1)^(n-1)[/tex] to control the sign alternation and m to control the alternation between m and -m.

Now, let's check the options one by one:

A. [tex]m(-1)^(n-1)[/tex]

  Substituting n = 1, we get[tex]m * (-1)^(1-1) = m * (-1)^0 = m * 1 = m[/tex]

  Substituting n = 2, we get [tex]m * (-1)^(2-1) = m * (-1)^1 = m * -1 = -m[/tex]

  This matches our sequence. So, Option A seems correct.

B.[tex](-m)^n[/tex]

  This doesn't match our sequence because it would give us [tex](-m)^1 = -m,[/tex][tex](-m)^2 = m^2, (-m)^3 = -m^3[/tex], and so on, which doesn't alternate between m and -m.

C.[tex](-1)m^(n + 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 + 1) = (-1)m^2 = -m^2[/tex]

  Substituting n = 2, we get [tex](-1)m^(2 + 1) = (-1)m^3 = -m^3[/tex]

  This doesn't match our sequence because it doesn't alternate between m and -m.

D.[tex](-1)m^(n - 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 - 1) = (-1)m^0 = -1[/tex]

  Substituting n = 2, we get[tex](-1)m^(2 - 1) = (-1)m^1 = -m[/tex]

  This also doesn't match our sequence because it doesn't alternate between m and -m.

So, the correct answer is Option A:[tex]m(-1)^(n-1).[/tex]

Answer:

AC

Step-by-step explanation:

A chord is a line segment connecting two points on a circle.

Basically, it means that a chord is a line that has both endpoints on the edge of the circle.

Answer:

Step-by-step explanation:

a) Apparently, you're to put the given values into a table. The first 5 entries of the table below are the given values. The next few are the result of using the recursive formula. (The formula bar shows the formula that is in the selected cell.)

__

b) The first differences of the terms of this sequence are ...

These are not constant, so the sequence is not arithmetic. The ratios of terms are not constant (2/-1 ≠ 10/2), so the sequence is not geometric.

The second differences are ...

These are constant, which tells us the sequence is a polynomial sequence of 2nd degree (since 2nd differences are constant).

In terms of the differences and second differences we can write the expression for the n-th term

  first difference with term before: a[n] -a[n-1]

  first difference between previous two terms: a[n-1] -a[n-2]

The difference between these two differences is 5, so we can write ...

  (a[n] -a[n-1]) -(a[n-1] -a[n-2]) = 5

Solving for a[n], we get ...

  a[n] = 5 + 2·a[n-1] -a[n-2] . . . . . the desired recursive relation

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c) As indicated in part (b), this sequence is quadratic. As "proof", we offer that the sequence can be described by an explicit quadratic formula that can be derived from the first sequence term (d0) and the first and second differences (d1 and d2):

  f(n) = d0 + (n-1)(d1 +(n-2)/2·d2) = -1 +(n-1)(3 +(n-2)/2·5)

  f(n) = 5/2n² -9/2n +1

Answer:

  756 m²

Step-by-step explanation:

The ratio of areas is the square of the ratio of linear dimensions. Hence the area of the red solid is ...

  (6/4)²×336 m² = 756 m²

The absolute value |2x+7| simplifies differently depending on values of x. If x > -7/2, |2x+7|=2x+7. If x=-7/2, |2x+7|=0. If x<-7/2, |2x+7|= -(2x+7).

The absolute value |2x + 7| measures the distance of the value 2x + 7 from zero on the number line. To simplify the equation and determine for what values of x the absolute value results are positive, negative or zero, we must consider the following conditions:

In the first case, the inside of the absolute value is positive and thus its value is itself. In the second case, the inside of the absolute value equals to zero and the absolute value of zero is zero. In the third case, the inside of the absolute value is negative and thus its absolute value is the negation of it.

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You get extract [tex] 2i [/tex] objects out of 97 object in this number of ways:

[tex] \displaystyle \binom{97}{2i} = \dfrac{97!}{(2i)!(97-2i)!} [/tex]

So, the number of all possible subsets is

[tex]\displaystyle \binom{97}{0} + \binom{97}{2} + \ldots + \binom{97}{96} = \sum_{i=0}^{48}\binom{97}{2i} = 79228162514264337593543950336[/tex]

3(m + -2) + -5 = 8 + -2(m + -4)

Reorder the terms:

3(-2 + m) + -5 = 8 + -2(m + -4)

(-2 * 3 + m * 3) + -5 = 8 + -2(m + -4)

(-6 + 3m) + -5 = 8 + -2(m + -4)

Reorder the terms:

-6 + -5 + 3m = 8 + -2(m + -4)

Combine like terms: -6 + -5 = -11

-11 + 3m = 8 + -2(m + -4)

Reorder the terms:

-11 + 3m = 8 + -2(-4 + m)

-11 + 3m = 8 + (-4 * -2 + m * -2)

-11 + 3m = 8 + (8 + -2m)

Combine like terms: 8 + 8 = 16

-11 + 3m = 16 + -2m

Solving

-11 + 3m = 16 + -2m

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '2m' to each side of the equation.

-11 + 3m + 2m = 16 + -2m + 2m

Combine like terms: 3m + 2m = 5m

-11 + 5m = 16 + -2m + 2m

Combine like terms: -2m + 2m = 0

-11 + 5m = 16 + 0

-11 + 5m = 16

Add '11' to each side of the equation.

-11 + 11 + 5m = 16 + 11

Combine like terms: -11 + 11 = 0

0 + 5m = 16 + 11

5m = 16 + 11

Combine like terms: 16 + 11 = 27

5m = 27

Divide each side by '5'.

m = 5.4

Simplifying

m = 5.4

Equation:

Variable:

Answer:

Step-by-step explanation:

Answer:

Option B)

Step-by-step explanation:

The intersection of two sets M and N consists of all the elements that are in both M and N.

So if M = {5, 10, 15, 20, 25} and N ={10, 20, 30, 40, 50}, then M ∩ N = {10, 20}

Then, the union of two sets L and C is to add to L all the elements that are in C

Where: C = M ∩ N

So, if  L = {0, 20, 40, 80, 100} and  M ∩ N = {10, 20}, then:

L ∪ (M ∩ N) =  {0, 10, 20, 40, 80, 100}

Finally the correct option is B) {0, 10, 20, 40, 80, 100}

Answer:

B) {0, 10, 20, 40, 80, 100}

Step-by-step explanation:

The INTERSECTION of two sets is the set of elements which are in both sets.

The UNION of two sets is the set of elements which are in either set.

A)

recall that there are 180° in π radians.

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=10\\ r=5 \end{cases}\implies 10=5\theta \implies \cfrac{10}{5}=\theta \implies \stackrel{\textit{radians}}{2=\theta } \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ x&2 \end{array}\implies \cfrac{180}{x}=\cfrac{\pi }{2}\implies 360=x\pi \\\\\\ \cfrac{360}{\pi }=x\implies 114.59\approx x[/tex]

B)

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=5\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(5)^2}{2}\implies A=25[/tex]

A car's speed is a measure of velocity. One method for finding (final) velocity is using the formula v = u + at where u is initial velocity, a is acceleration, and t is time.

Answer:

  60 miles per hour

Step-by-step explanation:

Let s represent the speed in miles per hour during the first part of the trip. Then s-10 will be the speed during the last part of the trip.

For speed/time/distance problems, the appropriate relation is the one that is posted on every speed limit sign:

  speed = miles/hour = distance/time

Rearranging this relation gives you the expression for time:

  time = distance / speed

You are given time and distance and you need to find speed. The time you're given is the total for the two parts of the trip, so ...

  4 = 84/s + 130/(s-10) . . . . . . total time = time1 + time2

Multiplying by the product of the denominators, this becomes ...

  4s(s-10) = 84(s-10) +130s

  4s^2 -254s +840 = 0 . . . . . . subtract the right side to put in standard form

This can be solved using any of several methods for solving quadratic equations. Solutions are ...

  s = 60, s = 3.5 . . . . . only the first solution makes any sense in the problem

The speed during the first part of the trip is 60 miles per hour.

Answer:

Step-by-step explanation:

The answer is D)

Best regards

Answer:

Step-by-step explanation:

1. You have correctly written the relationship between the side lengths and the length of the hypotenuse for these isosceles right triangles.

For this problem, you simply need to multiply the side length by √2. The length of the hypotenuse is then ...

  x = 6√2

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2. The side length multiplied by √2 is √6. You know

  √6 = √(2·3) = (√2)(√3) = (√2) · (side length)

so we know that x = √3.

Answer: 52

Step-by-step explanation:

Answer:  [tex]52^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of a ll the angles of a quadrilateral is 360 degrees.

Then for the given trapezoid, applying the angle sum property of quadrilateral we get

[tex]\angle{A}+\angle{B}+\angle{C}+\angle{D}=360^{\circ}\\\\\Rightarrow\ 128^{\circ}+126^{\circ}+54^{\circ}\angle{D}=360^{\circ}\\\\\Rightarrow\ \angle{D}=360-128-126-54\\\\\Rightarrow\ \angle{D}=360-308\\\\\Rightarrow\ \angle{D}=52^{\circ}[/tex]

Hence, The measure of angle D = [tex]52^{\circ}[/tex]

Answer:

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr^2

where the radius (r) is half the diameter. For a circle with a diameter of 20 units, the radius is 10 units and the circle area is ...

  A = π·(10 units)^2 = 100π units^2 ≈ 314.16 square units

__

When there are 20 congruent sectors, each sector has an area of 1/20 of the circle area, so

  sector area = (1/20)·100π unit^2 = 5π units^2 ≈ 15.7 square units

16 ounces = 1 pound, 8 ounces is half of 16, so 8 ounces = 1/2 pound.

1 pound of salmon cost 17.98.

Divide the cost for one pound in half:

8 ounces cost: 17.98 / 2 = $8.99

y^2-14y+49

(y-7)(y-7)

Answer:

y^2-14y+49 I hope i can help you out

Answer:

z = 0.33

Step-by-step explanation:

Mean = u = 500

Standard Deviation = s = 60

Scores of Jake = x = 520

Step 1: Finding the z score

In order to find the percentage who scored below Jake first we have to convert the scores of Jake to z scores. The formula to find z value is:

[tex]z=\frac{x-u}{s}[/tex]

Using the given values in this formula, we get the z scores:

[tex]z=\frac{520-500}{60}=0.33[/tex]

Thus, rounded of to two decimal places, the z-value for Jake's score is 0.33

Step 2: Find probability from the z-table

In the given table, from first column we will find the value 0.3. In the row across 0.3 we will find the value directly below 0.03 as 0.3 + 0.03 = 0.33

This value comes out to be 0.6293

The image attached below shows this process of finding the probability.

Step 3: Converting the probability to percentage

In order to convert this probability to percentage simply multiply it be 100.

So, 0.6293 = 62.93 %

62.93% rounded to nearest whole number will be 63%

This tells us that approximately 63% students scored below Jake i.e. below 520.

Answer:

{1;-2}

Step-by-step explanation:

[tex]...=\left \{ {{x=2y+5} \atop {7x-3y=13}} \right. =\left \{ {{x=2y+5} \atop {14y+35-3y=13}} \right.=\left \{ {{x=2y+5} \atop {y=-2}} \right.=\left \{ {{x=1} \atop {y=-2}} \right.[/tex]

$135

First, change the mixed number to an improper fraction.

2 1/4 = 9/4

Next, change $60 to an improper fraction.

$60 = 60/1

Then, multiply straight across on both the top and bottom to get 540/4.

Finally, simplify and get 135.

Hope this helped :)

For this case we have to:

[tex]2 \frac {1} {4}[/tex]is a mixed number that equals:

[tex]\frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]

If the price of the original ticket is $ 60, then the current price is:

[tex]\frac {60 * 9} {4} =\\\frac {540} {4} =\\135[/tex]

So, the price of the ticket is $ 135

Answer:

$ 135