A long-distance athlete can run 1/2 kilometer in 3 minutes. How many kilometers can he run in an hour?

To assign probabilities to each color in the sample space of marbles in a box, you need to determine the total number of marbles and the number of marbles of each color. Assuming there is an equal number of each color, the probability of drawing each color is 1/5.

To assign probabilities to each color in the sample space, we need to determine the total number of marbles and the number of marbles of each color. Since there is an equal number of each color, let's assume there are n marbles of each color.

The total number of marbles is 5n. The probability of drawing a red marble is n/5n = 1/5. Similarly, the probability of drawing a green marble is n/5n = 1/5, the probability of drawing a blue marble is n/5n = 1/5, the probability of drawing a yellow marble is n/5n = 1/5, and the probability of drawing a purple marble is n/5n = 1/5.

Answer:

The scale of the drawing of girrafe is [tex]1:200[/tex].

Step-by-step explanation:

Given: scale drawing of a giraffe that is  [tex]6\rm\;{m}[/tex] tall, and the height of the giraffe in your drawing is [tex]3\rm\;{cm}[/tex].

As per question,

Dimension of giraffe is [tex]6\rm\;{m}[/tex] tall and height is [tex]3\rm\;{cm}[/tex].

For scaling the drawing, the given unit must be same.

As we know that,

[tex]1\rm\;{m}= 100\rm\;{cm}\\6\rm\;{m}=600\rm\;{cm}[/tex]

Therefore, scale of the drawing is [tex]3\rm\;{cm}:600\rm\;{cm}=1:200[/tex].

Hence, the scale of the drawing is [tex]1:200[/tex].

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Answer:

In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6...

hope it helps

if 5/8 were bought then 3/8 are still available ( 5/8 +3/8 = 1)

45000 * 3/8 = 135000/8 = 16,875 seats are still available

Answer:

i think it is -1.76

The measure of the third outgoing current will be 0.5 amperes.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.

Then the measure of the third outgoing current will be

We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.

Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆. Then we have

I₁ + I₂ + I₃ = I₄ + I₅ + I₆

0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆

1.85 = 1.35 + I₆

I₆ = 0.5

Thus, the measure of the third outgoing current will be 0.5 amperes.

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Supposed that we are given the equation:

7.20 x 10^-5 = x(0.100+x)^2 

So assuming that x is very small so that:

0.100 + x ~ 0.100

and calling it x1, so:

7.20 x 10^-5 = x1 (0.100)^2 

Then we simply solve for x1:

x1 = 7.20 x 10^-5 / (0.100)^2 

x1 = 7.20 x 10^-3

Final answer:

Successive approximations involve iterative guesses to find a solution, Newton's Method refines initial guesses using derivatives, and the Intermediate Value Theorem guarantees a solution in a given interval.

Explanation:

Successive Approximations: When solving for x using successive approximations, we make iterative guesses, refining our estimation with each step. The method involves making an initial guess, then refining it until a sufficiently accurate solution is obtained.

Newton's Method: Newton's method is a numerical technique used to find roots of a function. It involves making an initial guess and then iteratively improving upon it by using the function's derivative.

Intermediate Value Theorem: The intermediate value theorem states that a continuous function that takes on values of opposite signs at two points must have at least one root within that interval.

Answer: 0.04444

Step-by-step explanation:

The answer fam is........

Statement                          Reason

1) 4x + 5 = 17                    Given

2) 4x + 5 - 5 = 17 - 5         Subtraction property of equality

3) 4x = 12                         Simplifying

4) 4x/4 = 12/4                   Division property of equality

5) x = 3                             Simplifying

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Answer:

Here it is!

Step-by-step explanation:

Final answer:

The total amount due on the simple-interest loan is $4500.

Explanation:

To find the total amount due on a simple-interest loan, we can use the formula:

Total Amount = Principal + (Principal x Rate x Time)

Given that the Principal is $3000, the Rate is 5%, and the Time is 10 years, we can substitute these values into the formula to calculate the total amount:

Therefore, the total amount due on the loan is $4500.

Answer

Difference between m∠C and m∠A= 44.76

Step-by-step explanation:

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.

Hypotenuse AC = 13 cm

So angle B is right angle = 90 degrees

AC is the hypotenuse

BC is the adjacent side for C

cos (c)= adjacent side / hypotenuse

C= cos^-1(BC/AC)

[tex]C= cos^{-1}(\frac{5}{13})= 67.38[/tex]

angle B is a right angle= 90 degree

Angle C= 67.38 degrees

Sum of angles in a triangle is 180°

A + B +C = 180

A + 90 + 67.38 = 180

A= 180 - 90 - 67.38=22.62

Difference between m∠C and m∠A= 67.38 - 22.62=44.76

The solution is Option C.

The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )

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 printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 14a + 8   be equation (1)

Now , the equation (1) can be simplified as

Taking the common term as 2 in the equation , we get

A = 2 ( 7a + 4 )

The 2 is taken as common term , and the multiples are the values 7a and 4

So ,

The value of A = 2 ( 7a + 4 )

A = 2 ( 7a ) + 2 ( 4 )

The value of A = 14a + 8

Therefore , the value of A is 2 ( 7a + 4 )

Hence ,

The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )

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Final answer:

An a priori proposition is knowledge known through reason alone, such as mathematical truths, while an a posteriori proposition requires empirical experience, like knowledge of a physical location.

Explanation:

An a priori proposition is a type of knowledge or statement that is known to be true independently of experience. It relies on reason or logical deduction rather than empirical evidence. For example, mathematical truths, such as the statement "The square root of 9 is 3," are considered a priori because they can be known through reason alone. In contrast, an a posteriori proposition is one that requires experience or sensory input to be known. Empirical knowledge, like knowing the best route to a location, is typically a posteriori because it is based on observations from the world around us.

The foundational philosophical debate revolves around the nature of these propositions, with some philosophers questioning whether any knowledge is genuinely a priori or if all understanding comes from some form of experience. However, in many cases, a priori knowledge is associated with necessity, certainty, and independence from experience, while a posteriori knowledge is empirical and grounded in sense perception.

To find the equation of a line parallel to 3y - x = -12 that goes through the point (18, 2), first find the slope of the given line, which is 1/3. Then, use the point-slope form with the given point and the slope to write the equation of the desired line, which is y = (1/3)x - 4.

To write an equation of the line that passes through the point (18, 2) and is parallel to the line 3y - x = -12, we first need to find the slope of the given line. For a line to be parallel, it must have the same slope as the line to which it is parallel. We start by putting the equation of the given line in slope-intercept form (y = mx + b).

First, isolate y:
3y = x - 12
y = (1/3)x - 4

The slope (m) of the given line is 1/3. Our parallel line should have the same slope, so we'll use this slope and the point (18, 2) in the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Now, plug in the values:
y - 2 = (1/3)(x - 18)

This is the point-slope form of the equation for our parallel line. To put it into slope-intercept form, we distribute and simplify:

y - 2 = (1/3)x - 6
y = (1/3)x - 4

Baruka has [tex]\( \frac{32}{64} \)[/tex] gallons left. [tex]\( \frac{32}{5} \) servings of \( \frac{5}{64} \)[/tex] gallons; she has 6 servings.

To find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk Baruka has left, we need to first convert the amount of milk she has in gallons to the same unit as [tex]\( \frac{5}{64} \)[/tex] gallons.

Since [tex]\( 1 \)[/tex] gallon is equivalent to [tex]\( \frac{64}{64} \)[/tex] gallons, and she has [tex]\( \frac{1}{2} \)[/tex] gallon left, she has [tex]\( \frac{1}{2} \times \frac{64}{64} = \frac{32}{64} \)[/tex] gallons left.

Now, we can find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings are in [tex]\( \frac{32}{64} \)[/tex] gallons:

[tex]\[ \frac{\frac{32}{64}}{\frac{5}{64}} = \frac{32}{5} \][/tex]

Now, we divide [tex]\( 32 \) by \( 5 \)[/tex] to find the number of servings:

[tex]\[ \frac{32}{5} = 6.4 \][/tex]

So, Baruka has [tex]\( 6.4 \)[/tex] servings of [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk left. However, since she can't have a fraction of a serving, she has [tex]\( 6 \)[/tex] servings left.

Mrs. Ellis would need 48 tiles to cover the area of her room. The cost of a single tile is $0.84, so the total cost to tile the room not including labor would be $40.32.

To determine the cost to tile the room, we first need to figure out how many tiles Mrs.Ellis needs. We know that each tile covers an area of 2ft * 2ft, which is 4 square feet. Now, we must find out the area of the room by multiplying the length by the width (16ft * 12ft), resulting in 192 square feet. To find out how many tiles are needed, we can divide the total area of the room by the area of one tile (192ft² / 4ft² = 48). Therefore, Mrs. Ellis needs 48 tiles to cover the entire room. Since each tile costs $0.84, the total cost would be 48 * $0.84 = $40.32. Thus, the cost to tile the room excluding labor charges is $40.32.

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