Write the standard equation of the circle shown.

Answer:

Part A) The height of the cylinder is [tex]7.8\ in[/tex]

Part B) The volume of one tennis ball is [tex]9.2\ in^{3}[/tex]

Part C) The volume of the cylinder is [tex]41.4\ in^{3}[/tex]

Part D) The volume of space in the cylinder not taken by the tennis balls is [tex]13.8\ in^{3}[/tex]

Step-by-step explanation:

Part A) Each tennis ball has a diameter of 2.6 inches

What is the height of the cylinder?

we know that

The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3

so

[tex]h=2.6*3=7.8\ in[/tex]

Part B)  Find the volume of one tennis ball

The volume of the sphere (one tennis ball) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=2.6/2=1.3\ in[/tex] ----> the radius is half the diameter

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(1.3)^{3}[/tex]

[tex]V=9.2\ in^{3}[/tex]

Part C) Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=2.6/2=1.3\ in[/tex] ----> the radius is half the diameter

[tex]\pi=3.14[/tex]

[tex]h=2.6*3=7.8\ in[/tex]

substitute

[tex]V=(3.14)(1.3)^{2} (7.8)[/tex]

[tex]V=41.4\ in^{3}[/tex]

Part D) What is the volume of space in the cylinder not taken by the tennis balls?

we know that

The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis

[tex]V=41.4-(3)*(9.2)=13.8\ in^{3}[/tex]

Answer:

Part A) The height of the cylinder is

Part B) The volume of one tennis ball is

Part C) The volume of the cylinder is

Part D) The volume of space in the cylinder not taken by the tennis balls is

Step-by-step explanation:

Part A) Each tennis ball has a diameter of 2.6 inches

What is the height of the cylinder?

we know that

The height of the cylinder is equal to the diameter of one ball of tennis multiplied by 3

so

Part B)  Find the volume of one tennis ball

The volume of the sphere (one tennis ball) is equal to

we have

----> the radius is half the diameter

substitute

Part C) Find the volume of the cylinder

The volume of the cylinder is equal to

we have

----> the radius is half the diameter

substitute

Part D) What is the volume of space in the cylinder not taken by the tennis balls?

we know that

The volume of space in the cylinder not taken by the tennis balls, is equal to the difference from the volume of the cylinder and the volume of three ball of tennis

Step-by-step explanation:

Answer:

A. 15

B. Scalene

Step-by-step explanation:

8x-10+6x+10x+10=360

24x=360

x=15

8x-10

8(15)-10=110

6x

6(15)=90

10x+10

10(15)+10=160

The triangle is scalene because none of the three sides are equal to each other.

Answer:

x = 6.6 cm

Step-by-step explanation:

The angle formed on the circle by the radius and the tangent is right.

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

Hypotenuse is (x + 8.45) and 2 sides are x and 13.5, thus

(x + 8.45)² = x² + 13.5² ← expand left side

x² + 16.9x + 71.4025 = x² + 182.25 ( subtract x² from both sides )

16.9x + 71.4025 = 182.25 ( subtract 71.4025 from both sides )

16.9x = 110.8475 ( divide both sides by 16.9 )

x ≈ 6.6 cm

a. Parameterize [tex]C[/tex] by

[tex]\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath[/tex]

with [tex]0\le t\le1[/tex].

b/c. The line integral of [tex]\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath[/tex] over [tex]C[/tex] is

[tex]\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt[/tex]

[tex]=\displaystyle10\int_0^1\mathrm dt=\boxed{10}[/tex]

d. Notice that we can write the line integral as

[tex]\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)[/tex]

By Green's theorem, the line integral is equivalent to

[tex]\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy[/tex]

where [tex]D[/tex] is the triangle bounded by [tex]C[/tex], and this integral is simply twice the area of [tex]D[/tex]. [tex]D[/tex] is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

A vector parametric equation was computed for the line segment between the points P and Q. This was used to compute the line integral of the vector field along the segment, which was found by substituting the parametrization into the field, deriving it and computing the dot product and integral. The clockwise integral around the triangle was then computed as the negative of the one we obtained earlier.

To solve this, consider the given points as vectors, i.e., ℒ = <5,0> and № = <0,2>. First, let's find a vector parametric equation ℝ(τ) for the line segment cc. To do this, we're going to create a vector equation that shows the progression from point ℒ to № with 0 ≤ τ ≤ 1.

Since t changes from 0 to 1, an equation for that movement is ℝ(τ) = (1-τ) * ℒ + τ * №. With insertions, the equation converts to ℝ(τ) = (1-τ) * <5,0> + τ<0,2> = <5-5t,2t>.

For the line integral Along C, our F(x, y) = -yi + xj, when we substitute our ℝ(τ) into this equation, our F becomes F(ℝ) = -2ti + (5-5t)j.

Derivation of ℝ(τ) will give us the rate of change of our function and help in the computation of the line integral. So, ℝ'(τ) = -5i + 2j. The integrand function for line integral then becomes F(ℝ) . ℝ'(τ) = -10t + 10t - 10t2. So our line integral ∫F .  dℝ from 0 to 1 will be ∫ (-10t + 10t - 10t2) dt.

For the clockwise integral around the triangle, since our original line integral was done in a counterclockwise direction, it will simply be the negative of the one we just computed.

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the third one bc the data range is x and the frequency is y so just match 0-10 w 5 as it’s y value and see if it matches on the graph and keep doing it for 10-20 make sure it’s y value is 10 then 20-30 it’s y value is 25 and so on

We are given the data range and frequency of the data set as follows:

       Data Range:            Frequency:

           0-10                            5

           10-20                          10

           20-30                         25

           30-40                          15

           40-50                            10

This means that the first bar is of the smallest height  and the height of first bar is: 5

The second bar is greater than the first with ha height of 10

The third bar has the highest height of 25

and then the fourth bar is smaller than the third bar with a height of 15 and the fifth bar has a height of 10.

Hence, the histogram that matches the data set is the figure attached to the answer.

Answer:

$97.20

Step-by-step explanation:

Divide the tip amount $14.58 by the percentage given 15% or .15.

$14.58 ÷ .15 =$97.20

Check your work by multiplying the answer $97.20 by the percent of tip 15%. $97.20 × .15 =$14.58 (tip amount)

Answer:

C

Step-by-step explanation:

Answer:

Select Yes or No to tell whether each method results in a random sample of the population.

1. The owner uses a database to print the names of all clients on slips of paper. The owner chooses 20 of the slips of paper without looking.- yes

3. The owner sends a survey to every client who spent more than $500 with the catering company in the past year. - no

4. The owner sends a survey to all clients whose phone number ends in 5.- yes

5. The owner sends a survey to the last 20 clients who used the catering company's services.- yes

Answer:

25%

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 21.89 × 25/100

Discount = 547.25/100

You save = $5.4725

Final Price = Original Price - Discount

Final Price = 21.89 - 5.4725

Final Price = $16.4175

Answer:

25% off

Step-by-step explanation:

Answer:

t= 3 years

Step-by-step explanation:

So far we have 2 useful relationships[tex]P_{t}= P_{o} e^{r*t}[/tex] and [tex]P_{t}=2P_{0}[/tex]

Now, clearing t

[tex]P_{t}= P_{o} e^{r*t} \\\frac{ P_{t}}{P_{o}} = e^{r*t}\\\frac{2 P_{0}}{P_{o}} = e^{r*t}\\2 = e^{r*t}[/tex]

I apply logarithm

[tex]log(2)=r*t\\ t=\frac{log(2)}{r}\\t=\frac{0.3}{0.1} \\ t=3[/tex] years

Done

Answer:

Final answer is [tex]P(B|A) = 0.25[/tex].

Step-by-step explanation:

We have been given values of

P(A) = 0.40, P(B) = 0.50, and  P(A and B) = 0.10

Now we need to find about what is the value of P(B/A).

Apply formula [tex]P (A \, and \, B)=P(A) \times P(B|A)[/tex]

Plug the given values into above formula:

[tex]P (A \, and \, B)=P(A) \times P(B|A)[/tex]

[tex]0.10 =0.40 \times P(B|A)[/tex]

[tex]\frac{0.10}{0.40} =P(B|A)[/tex]

[tex]0.25 =P(B|A)[/tex]

[tex]P(B|A) = 0.25[/tex]

Hence final answer is [tex]P(B|A) = 0.25[/tex].

Answer:

B

Step-by-step explanation:

It is less than 50% and more tha 10%

It’s B I just took the test or quiz

ANSWER

EXPLANATION

The circumference of a circle is calculated using the formula:

[tex]C=2\pi \: r[/tex]

From the question, the radius of the circle is 10 inches.

We substitute the radius into the formula to get:

[tex]C=2\pi \times 10[/tex]

Let us multiply out to get:

[tex]C=20 \pi \: in[/tex]

The question required that we leave the answer in terms of π.

The correct choice is C.

Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{22}{10}=\frac{x}{12}=\frac{33}{y}\\\\\frac{22}{10}=\frac{x}{12}\implies~x=\frac{22\times12}{10}=\frac{264}{10}=\boxed{\bf26.4}\\\\\frac{22}{10}=\frac{33}{y}\implies~y=\frac{10\times33}{22}=\frac{10\times3}{2}=5\times3=\boxed{\bf15}[/tex]

We know three things:

Angle1 = 90 degrees

Angle2 = 28 degrees

Side = 350 ft

So this means, we are dealing with an AAS triangle (angle, angle, side).

To find side x:

X / sin(90degrees) = 350ft / sin(28degrees)

X = (350ft • sin(90degrees)) / sin(28degrees)

X = 745.5...

=746ft

Makes sense? This is how you solve a AAS triangle. I’m not sure if it’s 100% but, good luck!

Answer:

  D) [tex]\left[\begin{array}{c}\frac{5}{4}\\-\frac{1}{2}\end{array}\right][/tex]

Step-by-step explanation:

For matrix [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

the inverse matrix is the transpose of the cofactor matrix, divided by the determinant: [tex]\dfrac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]

Your inverse matrix is: [tex]\dfrac{1}{2(-3)-(1)(2)}\left[\begin{array}{cc}-3&-1\\-2&2\end{array}\right][/tex]

so the solution is ...

[tex]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{cc}\frac{3}{8}&\frac{1}{8}\\\frac{1}{4}&-\frac{1}{4}\end{array}\right] \cdot\left[\begin{array}{c}2\\4\end{array}\right] =\left[\begin{array}{c}\frac{5}{4}\\-\frac{1}{2}\end{array}\right] \qquad\text{matches selection D}[/tex]

Answer: The answer is C. it would change orientation and slant down.

Step-by-step explanation:

The two lines are just mirror images of each other. In this case, the slope is just the opposite, causing it to be the way it is. The y intercept is the same which also causes the mirror imaging.

Answer:

It would change orientation and slant down.

Step-by-step explanation:

bearing in mind that the derivative of s(t) is s'(t) = velocity, thus

[tex]\bf s(t)=-2-6t\implies \left. \cfrac{ds}{dt}=-6 \right|_{t=2}\implies -6[/tex]

namely a negative rate, so the object is slowing down to a stop.

Answer:

the instantaneous velocity at t = 2 is -6

Step-by-step explanation:

The position of an object at time t is given by s(t) = -2 - 6t

To find instantaneous velocity we take derivative s'(t)

s(t)= -2-6t

s'(t)= 0 -6=-6

To find instantaneous velocity at t= 2, we plug in 2 for t

there is no 't' in s'(t)

so s'(2)= -6

the instantaneous velocity at t = 2 is -6

Answer:

D. Hot tub

Explanation:

1000 L is equal to about 246 gallons and even a deep bathtub couldn't hold that much water.

p.s. Loving your username

Answer:

the area of the hexagon is approx. 187.1 in²

Step-by-step explanation:

Picture this regular polygon as being a hexagon made up of six equilateral triangles of side 12 in.  We find the area of one such triangle and then multiply that by 6 to obtain the total area of the hexagon.

One such equilateral triangle has three sides all of length 12 in, and all the interior angles are 60°.  The height of one such triangle is

h = (12 in)sin 60°, or

                  √3

h = (12 in) -------- = 6√3 in

                     2

So, with base 12 in and height 6√3 in, the area of one such equilateral triangle is

A = (1/2)(12 in)(6√3 in) = 36√3 in²

and the total area of the hexagon is 6(36)√3 in², or approx. 187.1 in²

Answer:A. 140

Step-by-step explanation:

1/2(5)(7)(8)

Final answer:

The recursive rule for the given sequence is [tex]a_n = a_{n-1} - 13.8[/tex],

where a₁ = -7.4 and n > 1.

Explanation:

You are looking for the recursive rule for the sequence -7.4, -21.2, -35, -48.8, -62.6, and so on. To find this, we observe how the sequence progresses from one term to the next. The pattern here is that each term decreases by the same amount when compared to the previous term. By calculating the difference between successive terms, we can identify the common difference.

For instance, the second term (-21.2) minus the first term (-7.4) equals the third term (-35) minus the second term (-21.2), and this difference equals -13.8. Hence, each term is -13.8 less than the term before it.

To express this as a recursive formula, we start by stipulating the first term:

Then, we provide the recursive rule that relates each term to the one before it:

Using this recursive formula, given any term in the sequence, we can find the next term by subtracting 13.8 from the given term.

Answer:

176 cubic feet

Step-by-step explanation:

volume of each box is given by area of base * height.

Volume of Box 1 = 16 * 3 = 48

Volume of Box 2 = 16 * 3 = 48

Volume of Box 3 = 16 * 5 = 80

Total Volume = 48 + 48 + 80 = 176 ft^3

To calculate the total volume of the three boxes, we sum the individual volumes of two boxes at 48 cubic feet each and one box at 80 cubic feet, resulting in a total of 176 cubic feet.

To find the total volume of the three boxes shipped on a truck, we need to calculate the volume of each box and then sum the volumes. The volume of a rectangular prism (which is the shape of the boxes) is calculated by the formula Volume = length × width × height. In this case, the boxes have a common base of 16 square feet.

The two boxes with a height of 3 feet each have a volume of 16 square feet × 3 feet = 48 cubic feet per box. For both, this gives us a total of 48 cubic feet × 2 = 96 cubic feet.

The third box with a height of 5 feet has a volume of 16 square feet × 5 feet = 80 cubic feet.

Adding the volumes of all three boxes together, the total volume is 96 cubic feet + 80 cubic feet = 176 cubic feet. This is the total volume of the three boxes combined.

It looks like you're given

[tex]g(x)=\displaystyle\int_{6x}^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du[/tex]

Then by the additivity of definite integrals this is the same as

[tex]g(x)=\displaystyle\int_0^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du-\int_0^{6x}\frac{u^2-1}{u^2+1}\,\mathrm du[/tex]

(presumably this is what the hint suggests to use)

Then by the fundamental theorem of calculus, we have

[tex]\dfrac{\mathrm dg}{\mathrm dx}=7\dfrac{(7x)^2-1}{(7x)^2+1}-6\dfrac{(6x)^2-1}{(6x)^2+1}=\dfrac{1764x^4+169x^2-1}{1764x^4+85x^2+1}[/tex]

The Fundamental Theorem of Calculus Part 1 states the relationship between differentiation and integration. For a given function, transform the integral as hinted in the question, then use the theorem to differentiate the function by simply replacing the variable of integration with the upper limit of the integral.

The Fundamental Theorem of Calculus Part 1 is primarily used to identify the relationship between differentiation and integration, which are two basic operations in calculus. For a given function g(x) = ∫7x u² − 1 u² + 1 du from a to x, we first identify the function inside the integral, let's say f(u) = 7x u² − 1 u² + 1. Now, the mentioned integral transformation hints us that: 7x ∫f(u) du from 6x to 0 equals ∫f(u) du from 6x to 0 + ∫7x f(u) du from 0 to 6x.

Next, we simply differentiate g(x) using Part 1 of the Fundamental Theorem of Calculus, which states that if g(x) is the integral from a to x of f(t) dt, then the derivative of g(x) is f(x). So, by applying this, the derivative function g'(x) of given g(x) will be f(x), i.e., 7x x² − 1 x² + 1.

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Answer:

A. 110

Step-by-step explanation:

Angles 4 and 6 are supplementary so if we add them together they will equal 180.

(5a + 10)° + (3a + 10)° = 180°

Simplify a bit to get 8a + 20 = 180

and 8a = 160.

a = 20.  Now sub that value of a into the expression for angle 4:

5a + 10 --> 5(20) + 10 = 110°

Answer:

Option A.

Step-by-step explanation:

Given information: m║n, [tex]m\angle 4=(5a+10)^{\circ}[/tex] and  [tex]m\angle 6=(3a+10)^{\circ}[/tex].

If a transversal line intersect two parallel lines, then the interior angles on the same sides are supplementary angles. It means their sum is 180.

From the given figure it is clear that angle 4 angle 6 are interior angles on the same side. So, angle 4 and 6 are supplementary angles.

[tex]m\angle 4+m\angle 6=180^{\circ}[/tex]

[tex](5a+10)+(3a+10)=180[/tex]

On combining like terms we get

[tex](5a+3a)+(10+10)=180[/tex]

[tex]8a+20=180[/tex]

Subtract 20 from both sides.

[tex]8a+20-20=180-20[/tex]

[tex]8a=160[/tex]

Divide both sides by 8.

[tex]a=20[/tex]

The value of a is 20.

[tex]m\angle 4=(5a+10)^{\circ}\Rightarrow 5(20)+10)^{\circ}=110^{\circ}[/tex]

Therefore, the correct option is A.

Answer:

2×1082×103

Step-by-step explanation:

Just took the unit test. Image as proof

Answer:

The correct option is 3.

Step-by-step explanation:

It is given that the buckets have a height of 25 inches and a diameter of 10 inches.

The volume of a cylinder is

[tex]V=\pi r^2h[/tex]

[tex]V_1=\pi (\frac{10}{2})^2(25)[/tex]

[tex]V_1=\pi (5)^2(25)[/tex]

[tex]V_1=625\pi[/tex]

[tex]V_1=1963.49540849[/tex]

The scientific notation is

[tex]V_1=1.963\times 10^3[/tex]

[tex]V_1\approx 2\times 10^3[/tex]

The warehouse is 100 feet long, 50 feet wide, and 20 feet long.

1 feet = 12 inches

The volume of a cube is

[tex]V=length\times breadth \times height[/tex]

Using the above conversion the volume of cube in cubic inches is

[tex]V_2=(100\times 12)\times (50\times 12)\times (20\times 12)[/tex]

[tex]V_2=172800000[/tex]

The scientific notation is

[tex]V_2=1.728\times 10^8[/tex]

[tex]V_2\approx 2\times 10^8[/tex]

The number of buckets of rocks she could store in a warehouse is

[tex]n=\frac{V_2}{V_1}[/tex]

[tex]n=\frac{2\times 10^8}{2\times 10^3}[/tex]

Therefore the correct option is 3.

Final answer:

The function print_total_inches is defined to calculate the total number of inches by converting feet to inches and adding any extra inches. It multiplies the number of feet by 12 (since there are 12 inches in a foot) and adds the number of inches to get the total.

Explanation:

To define the function print_total_inches, we need to convert both feet and inches to inches only, since there are 12 inches in a foot. For the parameters num_feet and num_inches, the total number of inches is given by the formula total_inches = num_feet * 12 + num_inches. Here's an example of how the Python function might look:

   def print_total_inches(num_feet, num_inches):
       total_inches = num_feet * 12 + num_inches
       print('Total inches:', total_inches)

When you call print_total_inches(5, 8), it will output "Total inches: 68" because 5 feet is equivalent to 60 inches (5 x 12), and adding the additional 8 inches gives us a total of 68 inches.

Answer:

Values of x are 4i, -4i, 5 and -5

Step-by-step explanation:

[tex]3x^4+27x^2 + 1200[/tex] We need to find all the zeros (roots) of the above equation.

Let assume that x^4 = u^2 and x^2 = u

Putting values of x^4 and x^2 in the above equation and finding the value of u.

[tex]-3u^2 + 27u+1200=0\\Using \,\,quadratic\,\,equation\,\,to\,\,solve:\\u=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\where\,\, a= -3, b= 27 \,\,and\,\, c=1200\\u=\frac{-(27)\pm\sqrt{(27)^2-4(-3)(1200)}}{2(-3)}\\u=\frac{-27\pm\sqrt{729+14,400}}{-6}\\u=\frac{-27\pm\sqrt{729+14,400}}{-6}\\u=\frac{-27\pm\sqrt{15129}}{-6}\\u=\frac{-27\pm123}{-6}\\so, \,\, u = \frac{-27+123}{-6} \,\, and \,\, u  \frac{-27-123}{-6}\\u= -16 \,\, and \,\, u = 25[/tex]

So, values of u are -16 and 25

Putting back the value of u i.e, x^2

x^2 = -16 and x^2 =25

solving

Taking square root on both sides:

√x^2 =√-16 and √x^2 = √25

x = ± 4i (as √-1 =i) and x = ±5

So, values of x are 4i, -4i, 5 and -5.

C.) mean > median

Hope this helps chu

From the following set of data, statement C is true. Option C is correct.

The mean is the proportion of the total number of observations to the sum of the observations.

The median is a number for an organized data set (in ascending or descending order) that has the same number of observations on both sides.

11, 11, 12, 13

The mean of the data set is found as;

mean = (11+11+12+13)/4

mean=47/4

mean=11.75

The median of the data set is;

Arrange the numbers in the ascending order;

11, 11, 12, 13

median= (11+12)/2

median=11.5

mean > median

From the following set of data, statement C is true.

Hence, option C is correct.

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Answer:

C

Step-by-step explanation:

The Hypotenuse is y

The side opposite the given angle (60o) is 12.

You must use one of the trig functions to relate the angle, the side opposite and the hypotenuse.

It turns out that the function you need to use is the sine.

angle = 60o

Side opposite = 12 cm

hypotenuse = h = ???

Sin(60o) = opposite / hypotenuse  multiply both sides by the hypotenuse.

hypotenuse * sin(60o) = side opposite

Divide by sin(60o)

hypotenuse = side opposite / sin(60)

hypotenuse = 12/sin(60)

Sin(60) radical form = sqrt(3)/2

hypotenuse = 12 // sqrt(3)/2

hypotenuse = 24 // sqrt(3)   Rationalize the denominator.

hypotenuse = 24 * sqrt(3) // ( (sqrt(3)*sqrt(3) )

hypotenuse = 8 sqrt(3)

C