Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the
nearest hundredth.

Only graph B represents a proportional relationship.

What is a graph ?

A graph is a visual representation of data that shows the relationship between two or more variables. It is a way of presenting information in a clear and concise manner that makes it easy to interpret and understand.

Graphs can be used to show trends over time, compare different groups or categories, or illustrate the relationship between two or more variables.

Graph A shows a non-proportional relationship because as x increases, the corresponding y values do not increase or decrease at a constant rate.

Graph B shows a proportional relationship because as x increases, the corresponding y values increase at a constant rate.

Therefore, The slope of graph B is constant and represents the constant of proportionality between x and y.

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Answer: (b)

Step-by-step explanation:

Given

R is inversely proportional to A i.e

\(R\propto \dfrac{1}{A}\\\\R=\dfrac{C}{A}\quad [\text{C=Constant}]\)

when \(R=4,\ A=100\)

Insert the values to get C

\(\Rightarrow 4=\dfrac{C}{100}\\\\\Rightarrow C=400\)

When A=250

\(\Rightarrow R=\dfrac{400}{250}\\\\\Rightarrow R=1.6\)

option (b) is correct

the approximate area enclosed by the curves y = x² + 5 and y = 6 - 5x is approximately 24.192 square units.

To determine the area enclosed by the curves y = x² + 5 and y = 6 - 5x, we need to find the points of intersection between the two curves and then calculate the definite integral of the difference between the curves over that interval.

Setting the two equations equal to each other, we have:

x² + 5 = 6 - 5x

Rearranging the equation, we get:

x² + 5x + 1 = 0

Using the quadratic formula, we can solve for x:

x = (-5 ± √(5² - 4(1)(1))) / (2(1))

x = (-5 ± √(25 - 4)) / 2

x = (-5 ± √21) / 2

The points of intersection are approximately x ≈ -4.79 and x ≈ 0.79.

To find the area enclosed by the curves, we need to integrate the difference between the curves over the interval between these two x-values.

Let's integrate the difference between the curves:

Area = ∫[x₁, x₂] [(6 - 5x) - (x² + 5)] dx

Where x₁ = -4.79 and x₂ = 0.79.

Area = ∫[-4.79, 0.79] (6 - 5x - x² - 5) dx

Area = ∫[-4.79, 0.79] (-x² - 5x + 1) dx

Integrating, we get:

Area = [- (x³ / 3) - (5x² / 2) + x] | from x = -4.79 to x = 0.79

Evaluating the definite integral, we have:

Area = [(- (0.79³ / 3) - (5(0.79)² / 2) + 0.79) - (-((-4.79)³ / 3) - (5(-4.79)² / 2) + (-4.79))]

Calculating the values, we find:

Area ≈ 24.192

Therefore, the approximate area enclosed by the curves y = x² + 5 and y = 6 - 5x is approximately 24.192 square units.

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Answer:

x=50

Step-by-step explanation:

1. multiply the numbers

48x25=24x

1200=24x

2. Divide both sides by the same factor

1200/24 = 24/24x

simplify the expression

x=50

Answer:

Step-by-step explanation:

Vertex form of the equation of a quadratic function with vertex (h,k):

f(x) = a(x - h)² + k

To find a we need to put the point and the vertex into this equation:

3 = a(-6 + 2)² - 13

10 = a(-4)²

16a = 10

a = ⁵/₈

Therefore, vertex form of the quadratic function:

f(x) = ⁵/₈(x+2)² - 13

We need to know about composite functions to solve the problem. The value of hk^-1(x) is x-7/3.

Composite functions are functions where the output of one function is used as an input of the other function. In the given question we know the values of h(x) and k(x). We need to find the value of the inverse of the composite function of h and k. In the given function, the output of k(x) will become the input of h(x). Once we have found the composite function, we need to find the inverse of the function.

h(x)=1+3x

k(x)=x+2

hk(x)=1+3(x+2)=1+3x+6=3x+7

y=3x+7

x=y-7/3

hk^-1(x)=x-7/3

Therefore the value of hk^-1(x) is given by x-7/3.

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No . of girls in Ms. Jeffry's environmental club = 6

No . of boys in Ms. Jeffry's environmental club = 12

To find the maximum number of groups she can make , we have to find the highest common factor ( HCF ) of the number of boys and girls in her club .

Factors of 6 = 1 , 2 , 3 and 6

Factors of 12 = 2 , 3 , 4 , 6 and 12

Hence the highest common factor of 6 and 12 are 6 .

Therefore , the maximum number of groups Ms . Jeffry can make where the number of girls and boys are same are 6 .

Answer:

$555.56

Step-by-step explanation:

Since they got a $1000 rebate, that brings the price from $30,000 to $29,000. They also paid $9,000 down, so that leaves $20,000 to pay monthly.

Since it is over 36 months, divide the remaining price by 36.

20,000 ÷ 36 = 555.555555555555

yes, the probabilities associated with each X are all positive and they all add up to 1.

What is probability?

The probability of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anywhere between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes.

For the given probability distribution, we have

A) The sum for all probabilities in the second column is 1. So, this is a probability distribution.

b) yes, the probabilities associated with each X are all positive and they all add up to 1 in the given table.

Hence, the probabilities associated with each X are all positive and they all add up to 1

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Answer:  

Slope-int form: y = mx + b

x/10 + y/1000 = 1

y/1000 = -x/10 + 1

y = 1000(-x/10 + 1)

y = -100x + 1000

Step-by-step explanation:

The constraint for node 8 is not provided in the given information. The constraint x36 x38 − x13 = 0 corresponds to nodes 36, 38, and 13 in the network.

The constraint x36 x38 − x13 = 0 involves three variables: x36, x38, and x13.

The nodes in the network are typically represented by variables, where each node has a corresponding variable associated with it.

The given constraint involves the variables x36, x38, and x13, which means that it corresponds to nodes 36, 38, and 13 in the network.

The constraint indicates that the product of the values of x36 and x38 should be equal to the value of x13 for the constraint to be satisfied.

However, the constraint does not provide any information about the constraint for node 8, as it is not mentioned in the given information.

Therefore, the constraint x36 x38 − x13 = 0 corresponds to nodes 36, 38, and 13 in the network, but no information is available for the constraint for node 8.

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To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

To reach your fundraising goal of $75, you can sell pencils for $0.50 and bracelets for $1.00.

1. Calculate the total amount of money needed to reach the goal:
  Goal amount = $75

2. Determine the number of pencils and bracelets you need to sell to reach the goal:
  Let's assume you sell x number of pencils and y number of bracelets.

  The amount raised from selling pencils = x * $0.50
  The amount raised from selling bracelets = y * $1.00

  The total amount raised from both items should be equal to the goal amount:
  x * $0.50 + y * $1.00 = $75

3. Simplify the equation:
  0.50x + 1.00y = 75

4. Solve for one variable in terms of the other:
  Let's solve for x in terms of y:
  0.50x = 75 - 1.00y
  x = (75 - 1.00y) / 0.50

5. Substitute the value of x into the equation:
  (75 - 1.00y) / 0.50 * 0.50 + y * $1.00 = $75
  75 - 2y + y = 75
  -y = 0
  y = 0

6. Find the value of x:
  x = (75 - 1.00 * 0) / 0.50
  x = 75 / 0.50
  x = 150

To reach your fundraising goal of $75, you will need to sell 150 pencils for $0.50 each and 0 bracelets for $1.00 each.

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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The Dimension Index is 0.322.

The Dimension Index is calculated using the formula:

\[ \text{Dimension Index} = \frac{\text{Actual Value} - \text{Minimum Value}}{\text{Maximum Value} - \text{Minimum Value}} \]

Given that the Actual Value is 8.5, the Minimum Value is 4.0, and the Maximum Value is 19.3, we can plug these values into the formula:

\[ \text{Dimension Index} = \frac{8.5 - 4.0}{19.3 - 4.0} = \frac{4.5}{15.3} \approx 0.294 \]

So, the Dimension Index is approximately 0.294.

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The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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\( \bf\bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)\)

\( \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}\)

\( \bf \longrightarrow \bigg( - 3 \frac{1}{4} d + \frac{3}{5} \bigg) - \bigg(2 \frac{7}{8} d + \frac{7}{10} \bigg)\)

\( \bf \longrightarrow \bigg( - \frac{4 \times 3 + 1}{4} d + \frac{3}{5} \bigg ) - \bigg(\frac{8 \times 2 + 7}{8} d + \frac{7}{10} \bigg)\)

\( \bf \longrightarrow\bigg( \frac{ - 13}{4}d + \frac{3}{5} \bigg) - \bigg( \frac{23}{8}d + \frac{7}{10} \bigg)\)

\( \bf \longrightarrow \frac{ - 13}{4}d + \frac{3}{5} + \frac{ - 23}{8} d + \frac{ - 7}{10} \)

\( \bf \longrightarrow \bigg( \frac{ - 13}{4}d + \frac{ - 23}{8}d \bigg) + \bigg( \frac{3}{5} + \frac{ - 7}{10} \bigg)\)

\( \bf \longrightarrow \bigg( \frac{(2 \times - 13) + (1 \times - 23) }{8}d \bigg) + \bigg( \frac{(2 \times 3) + (1 \times - 7)}{10} \bigg)\)

\( \bf \longrightarrow \bigg( \frac{ (- 26) + ( - 23)}{8}d \bigg) + \bigg( \frac{(6) + ( - 7)}{10} \bigg) \)

\( \bf \longrightarrow\bigg( \frac{ - 26 - 23}{8} d\bigg) + \bigg( \frac{6 - 7}{10} \bigg)\)

\( \bf \longrightarrow\frac{ - 49}{8}d + \frac{ - 1}{10} \)

\( \bf \longrightarrow \boxed{ - \frac{49}{8}d - \frac{1}{10} } \: {\underline{\underline{ans}}}\)

\( \bf\bigg( - 2 \frac{1}{2} n + \frac{1}{4} \bigg) + \bigg(3 \frac{3}{4} n - \frac{5}{8} \bigg)\)

\( \bf \longrightarrow \boxed{\frac{5}{4}n - \frac{3}{8} } \: {\underline{\underline{ans}}}\)

\( \bf\frac{1}{5}(3x + 10) - \frac{11}{15}x\)

\( \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}\)

\( \bf\longrightarrow\frac{1}{5}(3x + 10) - \frac{11}{15}x\)

\( \bf\longrightarrow\frac{1}{5}(3x) + \frac{1}{5}(10) + \frac{-11}{15}x\)

\( \bf\longrightarrow\frac{3}{5}x + 2 + \frac{-11}{15}x\)

\( \bf\longrightarrow\bigg(\frac{3}{5}x + \frac{-11}{15}x\bigg) + 2\)

\( \bf \longrightarrow \boxed{\frac{-2}{15}x + 2} \: {\underline{\underline{ans}}}\)

Answer:

g(-2) = 3

x = -2.535 and -0.131

Step-by-step explanation:

Answer: 2.5 cups of grand zucchini.

Step-by-step explanation: When you add 2.5 to 2.5, that creates 5, just like 2 loaves of zucchini bread is mad with 5 cups of grand zucchini.

Mountain Mack can carve 60 fishing lures and 50 duck decoys in a week.

Let's denote the number of fishing lures carved by Mountain Mack as "L" and the number of duck decoys carved as "D". Based on the given information, we can set up a system of equations: When Mountain Mack spends all his time carving fishing lures, he can  carve 60 lures in a week:

L = 60

When Mountain Mack spends all his time carving duck decoys, he can carve 50 decoys in a week:

D = 50

For every 10 duck decoys carved, Mountain Mack must give up 12 fishing lures:

12 * (D / 10) = L

Now, let's solve the system of equations to find the values of L and D.

From equation (3), we can simplify it as:

12 * (D / 10) = L

12D/10 = L

6D/5 = L

Substituting L = 60 into the equation above:

6D/5 = 60

Solving for D:

6D = 5 * 60

D = 300/6

D = 50

So, we find that D = 50, which matches the information given.

Now, substituting D = 50 into equation (2):

L = 6D/5 = 6 * 50/5 = 60

Therefore, L = 60, which also matches the information given. Hence, the values of L and D satisfy all the given conditions.

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Total number of yo -yo expected to not work this year would be 30.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers.

Here in this question we are given that,

Last year,

Total number of yo-yos made = 300,000

Number of yo-yos didn,t worked last year = 20.

so ratio , 300000/20=15000

so for every 15000 yo-yos one didn,t work.

In current year,

Total number of yo-yos made = 450,000.

so let number of yo-yo didn,t work be n.

so ratio would be .

=450000/n

By using ratio and proportion,

15000=450000/n

n=30

so Total number of yo -yo expected to not work this year would be 30.

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The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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Answer:  i have a answer but it is not up there srry

Step-by-step explanation:  

Answer:

y = x - 8

Step-by-step explanation:

In order to solve this, we need to use point-slope form.:

y - y1 = m(x - x1)

Substitute the numbers into the equation:

y - (-8) = 1(x - 0)

y + 8 = x

y = x - 8

Answer:

The equation is 19+3.5h=10+4.75h. The answer is 7.2 hours.

Step-by-step explanation:

The equation for this problem would be 19+3.5h=10+4.75h. All you have to do is find h. So subtract 3.5h from both sides and 10 from both sides. You will get the equation 1.25h=9. Divide 1.25 from both sides and you will end up with h=7.2 hours.

Answer:

9

Step-by-step explanation:

9 (t3+0.5)

his running time is 9

Answer:

1.5 Hrs

Step-by-step explanation:

SWIM:  Time: T    Rate: 2.5mph   Distance: 2.5T

RUN:    Time: T+0.5  Rate: 9mph   Distance: 9T+4.5

BIKE:    Time: 2T+1  Rate: 16mph   Distance: 32T+16

2.5T+9T+4.5+32T+16 =  64

43.5T+20.5=64

43.5T=43.5

T=1

RUN: T+0.5= 1+0.5=1.5      

The length of g 1029.8 in the given  ΔFGH.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

The Law of Sines (or Sine Rule) is very useful for solving triangles:

\(\frac{a}{sinA} = \frac{b}{sinB} + \frac{c}{sinC}\)

840 / sin(38) = g /sin(49)

g = (840 / sin(38) ) *sin(49)

g= (840/0.615) *0.754 = 1029.8

Hence, the length of g 1029.8 in the given  ΔFGH.

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Answer:

255

Step-by-step explanation:

10n^2+5

where n=5

10×5²+5

10×25+5

250+5

255

The 5th term of Sequence is 255.

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).

Given:

10n² +5

Now for 5th term put n= 5 we get

10n² +5

= 10(5)² +5

= 10 x 25 + 5

= 250+ 5

= 255

hence, the 5th term is 255.

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Answer:

11.6 mi

Step-by-step explanation:

A^2+B^2=C^2

A^2+4.2^2=12.3

A^2=133.65

A=11.5607093

A=11.6

The sample space of rolling a fair, 11-sided number cube is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.

To determine the sample space of a fair 11-sided number cube rolled during a board game, we need to list all possible outcomes or numbers that can appear on the cube. Since the number cube has 11 sides, the possible outcomes range from 1 to 11. Thus, the sample space can be represented as {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.

Each number in the sample space represents a distinct outcome when rolling the number cube. For example, rolling a 1, 2, 3, or any other number in the sample space is a possible outcome of the roll.

It's important to note that the assumption here is that the number cube is fair, meaning that each side has an equal probability of landing face up.

In summary, the sample space of rolling a fair, 11-sided number cube during a board game is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.

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