A marble has a radius of 9 cm. Find the volume of the marble.

Answer:

x = [tex]\frac{1}{19}[/tex]

Step-by-step explanation:

2 = 19x + 1  Subtract 1 from both sides

2 - 1 = 19x + 1 - 1

1 = 19x  Divide both sides by 19

[tex]\frac{1}{19}[/tex] = [tex]\frac{19x}{19}[/tex]

[tex]\frac{1}{19}[/tex] = x

The conversion of the unit centimeters to feet is written as 147 centimeters = 4.82283 feet.

Centimeters and feet are the units that are used for measuring the length of the any given parameter.

Conversion of the unit centimeter into feet is written as :

Value of  one centimeter =  0.0328084 feet.

To convert the given value 147 centimeters substitute in the given relation we have,

⇒ ( 147 × 1 ) centimeters = ( 147 ×  0.0328084 ) feet

⇒ 147 centimeters = ( 4.822835 ) feet

⇒  147 centimeters = ( 4.8228 ) feet ( Round upto four decimals )

Therefore, after conversion the measurements centimeters to feet we have 147 cm is equal to  ( 4.8228 ) feet ( Round upto four decimals ) .

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Answer: The new perimeter is 2334 inches.

Step-by-step explanation:

The way to find perimeter is 2L + 2W. The original length was 799 inches and 23 inches were added. 799 in. + 23 in. = 822 in. The width is 245 in. 2(822) + 2(245) = Perimeter. 1844 in. + 490 in. = 2334 in. is the Perimeter.

The height of cliff is 62.50 ft

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, the angle of elevation from point A to the top of a cliff is 38°, the point A is 80 feet from the base of the cliff,

Refer to figure attached,

The scene is making a right triangle, with an acute angle 38°, and base (distance from point to base of the cliff) 80 ft, we need to find the length of perpendicular line which is the height of the cliff,

Therefore,

We know that,

tan β = ratio of the perpendicular side to base of a triangle,

Therefore,

tan 38° = AB / 80

AB = 62.50

Hence, the height of cliff is 62.50 ft

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MaryAnn can order a total of 213 prints for cost $35, including shipping.

Each print costs $0.15, so MaryAnn can order $35/$0.15 = 233.33 prints, but since she can only order whole prints, she can order a maximum of 233 prints.

The shipping charge is a flat fee of $3.00 per order, regardless of how many prints MaryAnn orders.

Let's say MaryAnn orders x prints, then her total cost would be:

Cost = $0.15 x + $3.00

Since her total cost can't exceed her budget of $35, we can set up the following inequality:

$0.15 x + $3.00 ≤ $35.00

Subtracting $3.00 from both sides, we get:

$0.15 x ≤ $32.00

Dividing both sides by $0.15, we get:

x ≤ 213.33

Since MaryAnn can only order whole prints, she can order a maximum of 213 prints.

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The gradient of the surface can be described as a vector.

The gradient of a surface, which is a vector, represents the size and direction of the sharpest increase in value at a certain location. The magnitude of this vector, which denotes the direction of the greatest rate of rise of the surface, indicates how steep the rise is. The influence of this gradient is felt along a surface, which is the difference. It stands in for a unit that is level with the ground.

In mathematics, the vector grad f(x,y,z) = (df/dx, df/dy, df/dz) represents the gradient of a three-variable function with scalar values, f(x,y,z). Variables like optimization and electromagnetism employ the gradient of a surface, which is a crucial notion in vector calculus. In particular, the gradient of a surface is frequently used to compute the normal vector to a surface or to identify the direction of the steepest rise or drop in a landscape.

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Answer:

it will have one real solution

Step-by-step explanation:

The correct statement about position of 2 is the 2 in 142 represents 10 times the value of the 2 in 124.

We know about the place value of digits. It states that the first digit on the Right Hand Side is the units place. Moving to the left, the next digit holds the value of tens. Moving further left the value increases 10 times.

Based on this, 142 has 2 at the leftmost place. Thus, it's value is 2. But, in the number 124, the two is at second position. It makes it value 20 (as 2 × 10 = 20). Therefore, the number in 124 is ten times of the number is 142.

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Suppose that a certain population obeys the logistic equation dy/dx= ry[1-(y/k)]

a) So if y0= K/3, then

dy/dx=  ry[1-(y/k)]

The above statement is equation 1.

Equation 2 is in the form of

dy/dx + P(t)y = yⁿQ(t)

which is a Bernoulli's differential equation with n=2. So 1- 2= -1

To solve it we put

Then dz/dx= -y⁻²(dy/dx)

This above statement is equation 3.

P(t)= -r, Q(t)= -(r/K)

and integrating factor is given by

IF= e ∫(1-n)P(t)dt= e ∫(-1)(-r)dt= ert

Then the solution is given by

z(IF)= ∫(1-n)Q(t)(IF)dt+C

If given y0= K/3, then

3/K= 1/K+C

Thus the solution to this part is

y⁻1ert= ert/K+2/K= 1/K(2+ert)

To find the time at which the initial population doubled that is 2K/3

Thus

2K/3= Kert/(2+ert)

For r=0.025, then r= 55.452

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Answer:

Step-by-step explanation:

(90 +100) / 2 = 190/2 = 95

The slope of a line that is parallel to the line containing the points (3, 4) and (2, 6) is -2.

To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line containing these points. We can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Where:

m = slope

(x1, y1) = coordinates of the first point (3, 4)

(x2, y2) = coordinates of the second point (2, 6)

Substituting the given values, we get:

m = (6 - 4) / (2 - 3)

m = -2

The slope of the line containing the points (3, 4) and (2, 6) is -2.

Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2.

Therefore, the slope of the parallel line is -2.

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The weight of th baby elephant in the month of March would be 247.5 Kg.

Weight of a body is the force exerted by the earth on the body on the surface of the earth towards its center.

Given is that in January a baby elephant weighs 180kg. By March the weight of the baby elephant had increased by ⅜.

Assume the weight of the baby elephant in March would be {x} Kg. We can write -

{x} = 180 + 3/8 of 180

{x} = 180 + 3/8 x 180

{x} = 180 + 67.5

{x} = 247.5 Kg

Therefore, the weight of th baby elephant in the month of March would be 247.5 Kg.

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Answer:

About 16 years

Step-by-step explanation:

The formula for compound interest is

[tex]P(t)=P_{0}(1+r/n)^n^t[/tex], where P0 is the principal, r is the interest rate, n is the number of compounding periods, and t is the time in years.

For this problem, our n = 12 because there are 12 months in a single year and we must convert our percentage to a decimal (3.60/100 = 0.0360): [tex]7000=4000(1+0.0360/12)^1^2^t\\7000=4000(1.003)^1^2^t\\1.75=1.003^1^2^t\\log(1.75)=log(1.003)^1^2^t\\log(1.75)=12t*log(1.003)\\\frac{log(1.75)}{log(1.003)} =12t\\1/12*\frac{log(1.75)}{log(1.003)}=t\\ 15.56818868=16=t[/tex]

The number of ways the adults and the kids can be served is 831600

From the question, we have the following parameters that can be used in our computation:

Volume = 1 gallon 3 pints

By conversion

1 gallon = 8 pints

So, we have

Volume = 8 pints +  3 pints

Volume = 11 pints

Also, we have

Adult = 2 cups

Kid = 1 cup

Convert to pints

Volume = 11 pints

Adult = 4 pints

Kid = 2 pints

The number of ways is then calculated as

Ways = 11!/(4! * 2!)

Evaluate

Ways = 831600

Hence, the number of ways is 831600

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The three internal angles of the triangle are α = 21.3°, β = 139.7°, and θ = 88.9°.

We can use the Law of Cosines to solve for the angles of the triangle:

cos(α) = (b² + c² - a²) / (2bc)

cos(β) = (a² + c² - b²) / (2ac)

cos(θ) = (a² + b² - c²) / (2ab)

Substituting the values given in the problem, we get:

cos(α) = (12.2² + 50.6² - 18.5²) / (2 x 12.2 x 50.6) = 0.929

α = cos⁻¹(0.929) = 21.3°

cos(β) = (18.5² + 50.6² - 12.2²) / (2 x 18.5 x 50.6) = -0.777 (note the negative value)

β = cos⁻¹(-0.777) = 139.7°

cos(θ) = (18.5² + 12.2² - 50.6²) / (2 x 18.5 x 12.2) = 0.056

θ = cos⁻¹(0.056) = 88.9°

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The error in the solution is that, In step 2, the Distributive Property was applied incorrectly.

Equations are mathematical expressions consisting of two or more variables and constants on two sides connected by an equal to sign.

Solution of the equation is the value of the variable that the equation holds true.

Given equation is,

8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

Using the multiplication property of equality, multiplying whole equation by 2,

(2 × 8) - a = 6 (4 - 5a)

16 - a = 6 (4 - 5a)

Distributive property states that, for three numbers or expressions, a, b and c,

a (b + c) = ab + ac

Applying that,

6 (4 - 5a) = (6 × 4) - (6 × 5a) = 24 - 30a

But the student didn't multiply 6 with 5a, and thus he got 24 - 5a in step 2.

Hence the incorrect step is step 2 because of incorrect use of distributive property.

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Your question is a bit confusing. The complete question with an image is given below.

A student provided the steps for solving an equation. Which statement describes the error in the solution?

Equation : 8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

What is the equilateral triangle?

In an equilateral triangle, all sides are equal in length.

That means that all the angles of the triangle will be congruent.

Since a triangle has 3 angles that always add up to 180 degrees, each angle is 60 degrees.

Therefore, the hypotenuse of the equilateral triangle is 1.

So,

[tex]x = 1 * sin60[/tex]°

[tex]x = 1 * \sqrt{3} /2\\x = \sqrt{3} /2[/tex]

Hence, The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

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The transformed parent cube root function's equation is,

y = ∛(x-4) - 1.

The equation of the function is satisfied by all (and only those) points that lie on the graph of the function.

Hence, if a point fits on a function's graph, it must also fit the function.

The parent cube root function is transformed in the shown graph

The Parent cube root function is

y = ∛(x -h) - k

where the value of h  and k is equal to 0

h=0, k=0 in parent function

At (0,0) in the parent function, the graph changes orientation.

We can observe from the above graph that it changes direction at (4,-1) meaning it is moved 4 units to the right and 1 unit down.

So, the value of h=4  and value of k=1

The equation of the transformed function is,

y = ∛(x-4) - 1

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It is proved that x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹) = 2y²/(y² - x²).

What is an equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it contains no "equal to" symbol. It will be regarded as a phrase.

Given that

x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹) = 2y²/(y² - x²)

Now solve the left-side expression:

L.H.S =

x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹)

Now apply the formula a⁻¹ = 1/a:

= (1/x)/(1/x +1/y) + (1/x)/(1/x - 1/y)

= (1/x)/((x+y)/xy) + (1/x)/((y-x)/xy)

Now taking common  (1/x)/(1/xy):

= (1/x)/(1/xy)[1/(x+y) + 1/(y-x)]

= (xy)/(x)[(y - x + x + y)/(x+y) (y-x)]

= y[2y/(x+y) (y-x)]

Applying the algebraic identity (x - y)(x + y) = x² - y²:

= 2y²/(y² - x²)

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The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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Answer:

8x8 > 9x7 (64 > 63)

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 yard = 1/2in shadow

Then 8ft = 192 * 1/2in

Then the radio tower is 192 yards (1 yard = 3 feet)

The radio tower = 576 feet

Answer:

Step-by-step explanation:

576

Answer:

Step-by-step explanation:

256. You can make this observation because they pattern has a rule that you multiply by 2 to get the next number.

Answer:

Another observation we can make about this number pattern is that each term is obtained by doubling the previous term. This means that the pattern is an example of exponential growth, where the growth factor is 2.

We can also observe that the sequence is a power of 2, where the first term is 2^2, the second term is 2^3, the third term is 2^4, and so on. In other words, the nth term in the sequence can be represented by the formula 2^(n+1).

Additionally, we can see that the sequence is an increasing sequence, where each term is greater than the previous one. This is because we are multiplying each term by 2, which means that each subsequent term will be twice as large as the previous one.

The instantaneous rate of change calculator is the tool that displays the rate of change

The change in the rate at a certain point is referred to as the instantaneous rate of change in mathematics. It is equivalent to the rate of change in a function's derivative value at a particular location. The obtained graph is identical to the slope of the tangent line if a graph for the instantaneous rate of change at a particular point is drawn.

A free online tool known as the Instantaneous Rate of change calculator shows the rate of change, the first-order differential equation for the specified function. This tool speeds up the calculation and shows the rate of change at a particular position in a split second. With time, the tool is now widely accepted and is often used is variety of calculations.

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Answer:

m = 3

Explanation:

the slop is 3

The system of equations has no solution. Option A is the correct optio.

What is the system of equations?

Simultaneous equations, or a system of equations, Two or more equations in algebra must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.

Given system of equations is

3x - 9y =0 .....(i)

-x + 3y = -3 .....(ii)

Multiply -3 with equation (ii)

3x - 9y = 9 .....(iii)

Subtract equation (i) from (iii):

3x - 9y = 9

3x - 9y =0

________

        0 = 9

Which is a false statement.

Thus the system of equations has no solution.

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Answer:

the answer is A. 0

The indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

The integral of cos(x) is sin(x) + C, where C is the constant of integration.

The notation for the integral of cos(x) is ∫cos(x) dx, where the symbol ∫ represents the integral sign, cos(x) is the function being integrated, and dx represents the variable of integration, which in this case is x.

The antiderivative of cos(x) is sin(x), meaning that if we take the derivative of sin(x), we get cos(x). The constant of integration, C, is added because the derivative of a constant is always zero.

Therefore, the indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

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Answer:

I'd say the first and third options would be correct.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

If it is a fair spinner then

First option is true

second option is true

third option cannot be determined from info given  

4th option is true

Answer:

a8

Step-by-step explanation:

Here you go.

nth term is ar^n-1

To calculate the value of g we have to multiply the G( universal gravitational constant) and M( mass of body) divide by R square.

Earth's acceleration caused by gravity, or the magnitude of g, is 9.8 m/s2. According to this, an item falling freely on Earth would accelerate by 9.8 metres per second. The gravity of the Earth is to blame for this acceleration.

The acceleration due to gravity formula is given by

[tex]g = \frac{GM}{R^2}[/tex]

Where,

G is the universal gravitational constant, G = 6.674×10-11m3kg-1s-2.

M is the mass of the massive body measured using kg.

R is the radius of the massive body measured using m.

g is the acceleration due to gravity measured using m/s2.

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