If the volume of a sphere is 4500cm squared what is the radius of the sphere

Answer:

Step-by-step explanation:

The first one gives us everything we need except the radius, which is easy enough to solve for if you're careful with your algebra. The area of a sector of a circle is given as:

\(A_s=\frac{\theta}{360}*\pi r^2\) where θ is the measure of the central angle of the circle. For us, that fills in as follows:

\(48\pi=\frac{270}{360}*\pi r^2\) and manipulate it as follows:

\(r^2=\frac{(360)(48\pi)}{270\pi}\) the π's cancel out, leaving us with simple multiplication and division to get

r = 8. Now for the next one, which is a bit more involved.

In order to find the area of the shaded part, we need to find the area of the right triangle there and subtract it from the area of the sector of the circle. First the area of the sector, which is given as:

\(A_s=\frac{\theta}{360}*\pi r^2\) where θ again is the measure of the central angle of the circle, 90°:

\(A_s=\frac{90}{360}(3.1415)(10)^2\) which simplifies a bit to

\(A_s=\frac{1}{4}(3.1415)(100)\), giving us an area of

\(A_s=78.5375m^2\). Now onto the area of the triangle.

Since this triangle is inscribed in the circle and the circle's radius is 10, tha also gives us both the height and the base measures of the triangle. The area then is:

\(A_t=\frac{1}{2}(10)(10)\) which is

\(A_t=50m^2\)

Subtract that from the area of the sector to get that the shaded area is 28.5 square meters, choice A.

The value of the variable h in the given fraction problem (h/6) - 1 = -3 is; h = -12

We are given the fraction problem as (h/6) - 1 = -3

Now, from this given fraction problem, the first step will be to rearrange the equation by adding 1 to both sides to get;

(h/6) - 1 + 1 = -3 + 1

(h/6) = -2

Now, the next step will be to multiply both sides by 6 to get;

(h/6) * 6 = -2 * 6

h = -12

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Complete question is;

Solve for h if (h/6) - 1 = -3

37.5 mile per hour

112.5 miles

rate = 60km per hour

1 mile = 1.6 kilometer

Let's convert:

The car's rate in miles per hour is 37.5 mile per hour

In 1 hour, the car travels 37.5 mile

In 3 hours, the car will travel = 3 × 37.5miles

= 112.5 miles

In 3 hours, the car will travel 112.5 miles

Answer:

I have written the answers on the attached image

hope i helped!

The complete multiplication grid is shown in the figure. The missing numbers are -6, -40, and -24.

A table displaying the outcomes of multiplying two integers. One number runs down a row, while the other runs down a column, with the results shown where the two intersect.

We know that a multiplication grid means we have to multiply the number to complete the grid.

As we can see in the figure, \(6\times 8=48\)

Then, \(6 \times (-4) =-24\)

So, the missing number of the third row is -24.

Now, what we can multiply in -4 to get 20 that is -5.

This means that if we multiply -5 and -4 we will get 20.

So, the missing number of the first row is -5.

Then, \(-5\times 8=-40\)

So, the missing number of the second row is -40.

So, the complete multiplication grid is shown in the figure.

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The required scale factor that Amir will use to go from Polygon F to G is 1/9.

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
Area of polygon F = 36 square units
Area of polygon G = 4 square units

Now,
The scale factor to go from polygon F to polygon G is given as,
SF = Area of polygon G / Area of polygon F
SF= 4/36
SF = 1/9

Thus, the required scale factor that Amir will use to go from F to G is 1/9.

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The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.

Let the relation R R R be asymmetric. A loop in the directed graph corresponds to an ordered pair of the form ( a , a ) (a , a) (a , a). By the definition of asymmetric, the relation R R R cannot contains any ordered pairs of the form ( a , a ) (a , a) (a , a) and thus the directed graph cannot contain any loops.

They are typically represented by labeled points or small circles. We connect vertex a to vertex b with an arrow, called an edge, going from vertex a to vertex b if and only if arb. This type of graph of a relation r is called a directed graph or digraph .

It is a set where either there are many components or only the beginning or ending are provided. By n(A), we refer to the total number of components, and if n(A) is a characteristic number, then the set is constrained.

Let A be finite non-empty set.

Then the exist relation R on A which is both equivalence and order relation.

Suppose A = {\(a_{1} , a_{2} , a_{3} , ...... a_{n} ,\)}

And, R = { \((a_{1} ,a_{1}) , (a_{2} ,a_{2} ) ,(a_{3} ,a_{3} )........(a_{n} ,a_{n} )\) }    

R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric.

Then R is equivalence relation and an order relation.

Therefore,

The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.

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A campsite is in the shape of a rectangle. The green region represents campsites with shade. The yellow region represents campsites without shade. The probability that your campsite has shade 1/2.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

A campsite is in the shape of a rectangle.

The green region represents campsites with shade.

The yellow region represents campsites without shade.

There are only two possibilities either shaded or not shaded So, the total number of outcomes would be 2.

The probability that your campsite has shade = 1/2

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Answer:  This is not a right triangle.

the squares of the two shorter sides must add to the equal the square of the longest side.

a² + b² = c²

Step-by-step explanation:

5² + 5² ?=? 12²

25 + 25 ≠ 144

50 ≠ 144   So this is not a right triangle.

The subject is taught in a non-theoretical manner in Al Bluman's Elementary Statistics. Today's world speaks statistics, and Bluman's market-leading Step-by-Step Approach makes it simple to learn and comprehend.

Bluman gives your students all the assistance they need to understand the foundations of statistics and draw that link by assisting them in transitioning from the computational to the conceptual.

Elementary Statistical Methods are the collection, analysis, presentation, and interpretation of data, and probability. The analysis includes descriptive statistics, correlation and regression, confidence intervals, and hypothesis testing.

Thus, The subject is taught in a non-theoretical manner in Al Bluman's Elementary Statistics. Today's world speaks statistics, and Bluman's market-leading Step-by-Step Approach makes it simple to learn and comprehend.

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In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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The correct compound inequality to the amount of money Wren can spend with a monthly budget for housing between 25% and 35% will be:

224.0< h< 313.60

Given that:

wren own an average weekly net pay $ 896.00

and, Wren can spend with a monthly budget for housing between 25% and 35%.

Now, Spend money for housing by 25% = 25% of $896.00

= 25÷100 × 896

= 0.25 ×896

= $ 224.00

Again, spend money for housing by

35%=  35% of 896                                                            

=35÷100 × 896

= 0.35 × 896

= $ 313.60

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answer 5/6 decimal form is 0.83

Answer:

5/6

Step-by-step explanation:

100 ÷ 4 = 25

144 ÷ 4 = 36

Under root of 25 = 5

Under root of 36 = 6

Final Answer = 5/6

Hope this helps!

Sorry for the mistake before I did not see the under root!

a) The minimum number of dogs that could have a mass of more than 26 kg is of: 5.

b) The maximum number of dogs that could have a mass of more than 26 kg is of: 16.

The frequency table shows the number of times that each value, or values in each range, appears in the data-set.

11 weights are between 20 and 30, hence:

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Answer:

An example of a balance that has a greater integer value than a balance of -$12, but represents a debt of less than $5 is any integer belongs to [-6,-11]

Step-by-step explanation:

Let x be the balance that has a greater integer value than a balance of -$12, but represents a debt of less than $5.

We are given that a balance that has a greater integer value than a balance of -$12

So, x>-12

We are given that balance represents a debt of less than $5.

Debt = -5

So, x< -5

So, -5>x>-12

So, x∈[-6,-11]

Hence an example of a balance that has a greater integer value than a balance of -$12, but represents a debt of less than $5 is any integer belongs to [-6,-11]

Answer:

10x^2 - 13x - 3

Step-by-step explanation:

(5x + 1)(2x - 3) = 10x^2 - 15x + 2x - 3 = 10x^2 - 13x - 3

Answer:

  (d)  219.80 ft

Step-by-step explanation:

The side opposite the angle is given, and we want to find the side adjacent. The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(20°) = (80 ft)/(distance to sculpture)

This rearranges to ...

  distance to sculpture = (80 ft)/tan(20°) ≈ 219.80 ft

Answer:

2,4,5

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

The volume of the given cube is determined as (q cm)³.

The volume of a cube is calculated from the cube its edge length.

Mathematically, the formula for the volume of a cube is calculated by applying the following formula.

V = L x L x L = L³

where;

The volume of the given cube is calculated as follows;

V = q cm  x q cm x q cm

V = (q cm)³

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The geometric series to give a series for 1 1+x Then differentiate your series to give a formula for + ((1+x)-4)= ... (1 +x)2 1 dx is (1+x)^(-4) = -4/(1+x) + 4/(1+x)^3.

To obtain a series representation for 1/(1+x), we can use the geometric series formula:

1/(1+x) = 1 - x + x^2 - x^3 + ...

This series converges when |x| < 1, so we can use it to find a series for 1/(1+x)^2 by differentiating the terms of the series:

d/dx (1/(1+x)) = d/dx (1 - x + x^2 - x^3 + ...) = -1 + 2x - 3x^2 + ...

Multiplying both sides by 1/(1+x)^2, we get:

d/dx (1/(1+x)^2) = -1/(1+x)^2 + 2/(1+x)^3 - 3/(1+x)^4 + ...

To obtain a formula for (1+x)^(-4), we can use the power rule for differentiation:

d/dx (1+x)^(-4) = -4(1+x)^(-5)

Multiplying both sides by (1+x)^4, we get:

d/dx [(1+x)^(-4) * (1+x)^4] = d/dx (1+x)^0 = 0

Using the product rule and the chain rule, we can expand the left-hand side of the equation:

-4(1+x)^(-5) * (1+x)^4 + (1+x)^(-4) * 4(1+x)^3 = 0

Simplifying the expression, we get:

-4/(1+x) + 4/(1+x)^3 = (1+x)^(-4)

Therefore, (1+x)^(-4) = -4/(1+x) + 4/(1+x)^3.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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If the mean is 60, standard deviation is 10 and there are 50 students in the class, then the probability that it will be a failing paper is 0.1587.

Let us assume that any paper with a score below 50 is considered a failing paper.

We know that the mean of exam scores (μ) = 60 and

the standard deviation (σ) = 10,

This means that the distribution of exam scores follows a normal distribution with mean μ = 60 and standard deviation σ = 10,

To find the probability that a randomly selected paper is a failing paper, we need to find area under the normal curve to left of score of 50.

By using standard normal distribution, where we standardize exam scores by subtracting mean and dividing by standard deviation,

⇒ Z = (X - μ)/σ

Where X = exam score, μ = mean, and σ = standard deviation.

Substituting the values,

we get,

⇒ Z = (50 - 60)/10 = -1,

By using standard normal distribution table, the probability is approximately 0.1587.

Therefore, the required probability is 0.1587.

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The dot product also referred to as the scalar product, of the two vectors can be used to determine the value of two perpendicular vectors.

In the case of two perpendicular vectors, u = (u1, u2, u3) and v = (v1, v2, v3), their dot product is zero:

u v = u 1 v 1 + u 2 v 2 + u 3 v 3 = 0

This means that you can use this equation to find the values of the other vector if you know the values of one vector.

You can set up the dot product equation, for instance, if you have one vector u = (1, 2, 3) and you want to find a vector v that is perpendicular to u.

u · v = 1v1 + 2v2 + 3v3 = 0

You can then choose any two values for v1 and v2, and solve for v3 using this equation. For example, if you choose v1 = 1 and v2 = -1, you can solve for v3 as follows:

1v1 + 2v2 + 3v3 = 0

1 - 2 + 3v3 = 0

v3 = 1/3

So a vector v that is perpendicular to u = (1, 2, 3) is v = (1, -1, 1/3).

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The measure of arc CD is 4x + 15, and that the measure of angle DEA is 120 degrees, we can use the fact that the sum of the measures of the arcs in a circle is equal to 360 degrees to solve for x.

Now we can write the equation:

(6x + 5) + (4x + 15) + 240 = 360

10x + 260 = 360

Subtracting 260 from both sides:

10x = 100

Dividing both sides by 10:

x = 10

The value of x is 10, the measure of arc CD is 55 degrees, and the measure of angle DEA is 120 degrees.

Given that the measure of arc AB is 6x + 5 and the measure of arc CD is 4x + 15, and that the measure of angle DEA is 120 degrees, we can use the fact that the sum of the measures of the arcs in a circle is equal to 360 degrees to solve for x.

Let's call the center of the circle E. Since DEA is a central angle, the measure of arc DE is equal to twice the measure of angle DEA, so arc DE has a measure of 2 * 120 = 240 degrees.

Now we can write the equation:

(6x + 5) + (4x + 15) + 240 = 360

Simplifying the left side:

10x + 260 = 360

Subtracting 260 from both sides:

10x = 100

Dividing both sides by 10:

x = 10

So the value of x is 10.

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Answer:

Explanation is in photo

Step-by-step explanation:

The price of the chair before the reduction is 24.96.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Sale Price for Cahir = 20.80

Reduction = 20%

So, the price before reduction is

= 20.80 + 20.80 x 20/100

= 20.80 + 4.16

= 24.96

Hence, the price of the chair before the reduction is 24.96

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Answer:7 familes

21 divided by 3=7

Step-by-step explanation:

Answer:

7 families

Step-by-step explanation:

xnnhcnhffnhdbhdgndnydyndn

Answer:

x=2.75

Step-by-step explanation:

4x - 9=2

4 * 2.75=11

11 - 9=2