The base of a solid is a right triangle whose base side has length a and whose perpendicular side has length (1/2)a. Find the volume of the solid if cross sections perpendicular to the base of the triangle are semicircles.

Answer:

Mean and Median 30 and 31 respectively.

Step-by-step explanation:

Mean refers to average of all the observations.

Mean = Sum of all the observations/ Total no. of observations

Mean = 37 + 27 + 1 + 31 + 27 + 40 + 47/ 7

= 210 / 7

= 30

Median refers to middle most value of the series.

In order to find median we need to arrange the given data in ascending order i.e. smallest to largest.

We get,

1, 27, 27, 31, 37, 40, 47

When the no. of observations is odd: (n + 1/ 2)th term

= 7 + 1/ 2

= 4th term

Therefore, Median is 31.

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The equation to represent A, the area in square feet, as a function of w, the width in feet, would be A = w x L

To represent the area (A) in square feet as a function of the width (w) in feet, you will also need to consider the length (l) of the rectangle. The formula for the area of a rectangle is:
A = l * w
However, since you want A to be a function of w, we can rewrite the equation as:
A(w) = l * w
In this equation, A(w) represents the area as a function of the width, and l is a constant value representing the length of the rectangle in feet.

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Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

[tex] \qquad\longrightarrow \sf f(x) = sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

The Derivative of f(x) with respect to x-

[tex] \qquad\longrightarrow \sf \dfrac{d}{dx} \:sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x}{2}\bigg)^2}}\;\times \dfrac{d}{dx}\:\dfrac{x}{2}\\[/tex]

[tex]\qquad\sf\because\boxed{\sf{ \: \dfrac{d}{dx} sin^{-1}x = \dfrac{1}{\sqrt{1-x^2}}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \:x^{1-1}\\[/tex]

[tex]\qquad \sf\because\boxed{\sf{ \dfrac{d}{dx }x^n = nx^{n-1}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \times 1\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \\[/tex]

[tex] \qquad\longrightarrow \sf\dfrac{1}{2}\: \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\\[/tex]

[tex] \qquad\longrightarrow \underline{\sf\: \dfrac{1}{2\:\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}}\\[/tex]

Henceforth, Option C) is the correct answer.

The probability that a randomly selected token is red and green is 27/200.

The total token = 9 red + 6 green + 5 blue

The total token = 9 + 6 + 5

The total token = 20

There are 9 red and 6 green.

So, 9 out of 20 is red and 6 out of 20 is green

Let set up an equation:

9/20 × 6/20

= 54/400

= 27/200.

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Answer:

h (-2) = -2.6 (repeating)

h(2) =2

h(5) = 4.3 (repeating)

Step-by-step explanation:

for h(-2)

= [tex]\frac{1}{3} (-2^{2} )-4\\\\\frac{1}{3} *4-4\\\\\frac{4}{3} -4=-2.6[/tex]

for h(2)

x = 2, so h(2) = 2

for h(5)

[tex]\frac{1}{3} (5^{2} )-4\\\\\frac{1}{3} *25-4\\\\\frac{25}{3} -4\\\\=4.3[/tex]

Answer:

  1. diameter

  2. semi-circle

  3. point of tangency

  4. common internal tangent

  5. major arc

  6. radius

  7. center

  8. common external tangent

  9. secant

  10. chord

  11. minor arc

Step-by-step explanation:

You want to identify the elements of the diagram by name.

Common internal tangent — HJ, the line through the point of tangency where two circles touch each other, where neither center is in the other circle.

point of tangency — G (or K or F), a single point where an external geometry touches a circle.

Center — A (or B), the point equidistant from all those on a circle.

chord — GK, a line segment whose endpoints lie on the same circle.

secant — CD, a line that has two points of intersection with a circle.

diameter — EF, a chord that passes through the center of the circle.

common external tangent — KF, a line that is tangent to two circles that are external to each other. It does not cross the line segment between the circle centers.

radius — BF (or BE), a line segment from the circle center to a point on the circle.

semi-circle — arc EGF, an arc whose measure is 180°.

Major arc — arc CDK (or CKD, or GCK, or DCG), an arc whose measure is more than 180°.

Minor arc — CK (or CD, or GD, or GK, or GE, or GF), an arc whose measure is less than 180°.

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3. To find the number of ways to choose the winners, you use combinations.

n = 100 (total number of people)

k = 10 (number of winners to be chosen)

The formula for combinations is:

C(n,k) = n! / (k! * (n-k)!)

Substituting n and k into the formula, we get:

C(100,10) = 100! / (10! * (100-10)!)

We do not need to simplify this expression.

For the club with 30 students, the number of ways to choose the officers is given by permutations because the order in which the officers are chosen matters.

n = 30 (total number of students)

k = 3 (number of officers to be chosen)

The formula for permutations is:

P(n,k) = n! / (n-k)!

Substituting n and k into the formula, we get:

P(30,3) = 30! / (30-3)!

We do not need to simplify this expression.

The value of the first and second integers are 54 and 55 respectively.

Let

First integer = x

Second integer = x + 1

Sum of the integers = 109

So,

First integer + Second integer = Sum of the integers

x + (x + 1) = 109

x + x + 1 = 109

2x + 1 = 109

Subtract 1 from both sides

2x = 109 - 1

2x = 108

divide both sides by 2

x = 108/2

x = 54

Ultimately,

First integer = x

= 54

Second integer = x + 1

= 54 + 1

= 55

Therefore, the solution in 4 steps are;

Step 1: x + (x + 1) = 109

Step 2: 2x + 1 = 109

Step 3: 2x = 108

Step 4: x = 54

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The coefficients and degree of each term are:

Second term:

degree = 4, coefficient = -8

Third term:

degree = 3, coefficient = 6

Fourth term:

degree = 0, coefficient = -1 (constant term)

Fifth term:

degree = 1, coefficient = -1

To find the leading coefficient, degree of the leading term, and degree of the polynomial, we need to identify the term with the highest degree:

The leading term has the highest degree: -8x^4

Leading coefficient = -8

Degree of the leading term = 4

Degree of the polynomial = 4

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Answer:8

Step-by-step explanation:

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

[tex] A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} [/tex]

The initial amount occurs at t = 0.

[tex] A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} [/tex]

[tex] A(0) = 934 (\dfrac{1}{2})^0 [/tex]

[tex] A(0) = 934 \times 1 [/tex]

[tex] A(0) = 934 [/tex]

After 80 years, t = 80.

[tex] A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} [/tex]

[tex] A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} [/tex]

[tex] A(80) = 934 (0.15749) [/tex]

[tex] A(80) = 147 [/tex]

The elevator and the worker both did the same amount of work, but the elevator provided more power. a.

The object is lifted to the same height the elevator and the worker both did the same amount of work against gravity is given by the formula W = mgh

m is the mass of the object, g is the acceleration due to gravity, and h is the height lifted.

The work done by both the elevator and the worker is W = (100 kg) x (9.8 m/s²) x (10 m)

= 9800 J.

Power is defined as the rate at which work is done, given by the formula P = W/t

t is the time taken to do the work.

Since the elevator reached floor 4 before the worker took less time for the elevator to do the work.

The elevator provided more power than the worker.

The formula states that when an object is raised to a specific height using a lift and a worker they both exerted an equal amount of effort against gravity.

W = mgh where m is the object's mass, g is its gravitational acceleration, and h is the height raised.

The lift's and the worker's combined work is given by W = (100 kg) x (9.8 m/s²) x (10 m)

= 9800 J.

According to the formula P = W/t power is the pace at which work is completed t is the amount of time required to complete the task.

Since the lift arrived at level 4 prior to the worker the lift's work was completed more quickly.

The lift was more powerful than the employee.

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The correct option is D, There was 1.5 inches in the rain gauge before the rain began, and the rain fell at a rate of 0.75 inch per hour.

A general linear equation is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We can use the first two points:

a = (4.5 - 3.75)/(4 - 3)

a = 0.75

Then we can write:

y = 0.75x + b

replacing the values of the first point we will get:

3.75 = 0.75*3 + b

3.75 - 0.75*3 = b = 1.5

Then the rate is 0.75 and the initial amount is 1.5

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The coordinates for the point J are (-5, 6).

The radius 12 represents the center of the circle from each band member to the edge of the circle.

The domain of the circle is -17 ≤ x ≤ 7.

The range of the circle is -6 ≤ y ≤ 18.

In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided above, we have the following equation of a circle:

x² + y² + 10x - 12y - 83 = 0

x² + 10x + y² - 12y = 83

x² + 10x + (10/2)² + y² - 12y + (-12/2)² = 83 + (10/2)² + (-12/2)²

x² + 10x + 25 + y² - 12y + 36 = 83 + 25 + 36

(x + 5)² + (y - 6)² = 144

(x + 5)² + (y - 6)² = 12²

Therefore, the center (h, k) is (-5, 6) and the radius is equal to 12 units.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-17, 7] or -17 ≤ x ≤ 7.

Range = [-6, 18] or -6 ≤ y ≤ 18.

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By using the property of incenter, measures of the sides and the angles will be,

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m ∠K = 36°

Since, By the property of incenter,

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

By the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

From ΔJMP,

tan(32°) = MP / MJ

tan(32°) = 7/MJ

MJ = 11.20

From ΔPOL,

tan(22°) = OP / OL

tan(22°) = 7/OL

OL = 17.33

From ΔKNP,

tan(36°) = NP / KN

tan(36°) = 7 / KN

KN = 9.63

Therefore, We get;

JK = JM + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

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The notation P(The lights go out|There is a thunderstorm outside) reads the probability of "The lights go out" given "There is a thunderstorm outside."If two events are independent, then the probability of one doesn't affect the other.

The two events are independent if the probability P(The lights go out) is equal to the probability that the lights go out and the probability P(There is a thunderstorm outside) is equal to the probability that there is a thunderstorm outside.

Conditional probability and independent events are related in the sense that if two events are independent, then the conditional probability of one event occurring given the other event is simply the probability of the first event happening. In other words, if events A and B are independent, then P(A|B) = P(A).

On the other hand, if two events are dependent, then the conditional probability of one event occurring given the other event is different from the probability of the first event happening. The conditional probability takes into account the additional information provided by the occurrence of the second event.

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The step with the proof that has a flaw is Step 2, AB ≅ BC, Symmetric Property.

Step 2 is the flaw in the proof. The symmetric property states that if AB = BC, then BC = AB. It does not justify that AB = BC in the first place.

Therefore, the proof needs additional steps to justify that AB and BC are congruent. One possible way to do this is to use the definition of a midpoint and the segment addition postulate as follows:

Step 1 | B is the midpoint of AC | Given

Step 2 | AB + BC = AC | Segment Addition Postulate

Step 3 | AB + AB = AC | Definition of midpoint (since B is the midpoint of AC)

Step 4 | 2AB = AC | Simplification

Step 5 | AB = AC/2 | Division Property of Equality

Step 6 | AB = BC | Substitution Property of Equality

Step 7 | _____ | Q.E.D.

Step 6 follows from the fact that B is the midpoint of AC, so AC = 2AB. Substituting AC/2 for AB in Step 2 gives AB + BC = AC/2 + BC, which simplifies to AB = BC. Therefore, Step 6 uses the transitive property of equality, which is a valid property of equality.

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The down payment would be 20% of the total cost of the dining room set, which is $6,815. So, the down payment would be $1,363.

To calculate the down payment, we'll use the following steps:
1. Determine the total cost of the dining room set, which is $6,815.
2. Find the percentage of the down payment, which is 20%.
3. Multiply the total cost by the percentage to find the down payment amount.
Using these steps, we can calculate the down payment:
Down payment = Total cost × Down payment percentage
Down payment = $6,815 × 0.20
Down payment = $1,363
So, Jess's down payment for the dining room set is $1,363.

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The order of the steps which can be used to determine an unknown value using proportion method is as follows:

Option B ---> D---> E---> A----> C.

A ratio can be defined as the expression that compares the quantity of a value that can be found in another value.

The correct step that can be used to find the a missing value when proportion method is used is as follows;

Step 1: Identify the two quantities being compared

Step 2: Write the ratio for the two known quantities

Step 3: Write a ratio that has the unknown and the know quantity.

Step 4: Equate the two ratios

Step 5: Cross multiply and solve for the unknown quantity. Describe the solution.

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Answer: Mandy sold 14,000$ in total sales

Step-by-step explanation: Divide the 5% and the 700, to get a total of 140, then multiply by 100. Hope this helps!

Answer:

936 cubic feet

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the volume of the prism next to the pyramid, we need to determine its height. Since the prism has the same base area as the pyramid, we can infer that its height is also the same as the height of the pyramid.

Given that the volume of the pyramid is 312 cubic feet, we can use the formula for the volume of a pyramid:

Volume = (1/3) * Base Area * Height

Let's assume the base area of both the pyramid and the prism is represented by "A" and the height is represented by "h".

For the pyramid:

Volume of pyramid = (1/3) * A * h_p

Given that the volume of the pyramid is 312 cubic feet:

312 = (1/3) * A * h_p

Simplifying the equation, we have:

936 = A * h_p

Now, since the prism has the same base area and height, we can use the same values for "A" and "h_p" to find the volume of the prism.

Volume of prism = A * h_p

Substituting the known values, we have:

Volume of prism = 936 cubic feet

Therefore, the volume of the prism next to the pyramid is 936 cubic feet. This is because the prism has the same base area and height as the pyramid, so their volumes will be equal.

Answer: 11100 m

Step-by-step explanation: I'm Walter H. White

The equivalent expression to 2/3 - 1/4x + 1/2x - 1/6 is given as follows:

1/2 + 1/4x.

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted, that is, we can use them to simplify an expression.

The expression for this problem is defined as follows:

2/3 - 1/4x + 1/2x - 1/6.

The like terms are simplified as follows:

Hence the simplified expression is given as follows:

1/2 + 1/4x.

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The decimal number that corresponds with the number  [ 2001 ] 11 would be A. 2663

To convert the number [2001]11 to a decimal number, we can use the formula:

Decimal number = a0 + a1 x b¹  + a2 x b ² + ... + an x b ⁿ

Given the number, [ 2001 ] 11, we would have :

a0 = 1

a1 = 0

a2 = 0

a3 = 2

b = 11

With the formula, the decimal number corresponding to the number would be:

Decimal number = 1 + 0 x 11 ¹  + 0 x 11 ² + 2 x 11 ³

Decimal number = 2663

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if its constant rate or unit rate its just multiple 6 until u get 30

(4, -2) is the solution of the given system of equations

The given system of linear equations are

2x-12y=16

4x-19y=22

The missing number in 1st step is 1/2

The missing number in 2nd step is -4

The missing number in 3rd step is 1/5

The missing number in 4th  step is 6

The solution of the equation is 4 and -2

Hence, (4, -2) is the solution of the given system of equations

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