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The ratio of the diameter of the Earth's Moon to a beach ball is 11,452.

The ratio of the diameter of the Earth's Moon to a beach ball can be calculated using the following formula: Ratio = (Diameter of Moon / Diameter of Beach Ball). Using this formula, we can calculate the ratio to be 11,452. To calculate this, we first need to convert the diameter of the Earth's Moon to meters. Since it is given in the question that the diameter of the Earth's Moon is 3,472,964 meters, we can plug this value into the formula. The diameter of the beach ball is given as 0.3048 meters. Plugging this into the formula, we get 3,472,964 / 0.3048 = 11,452. Therefore, the ratio of the diameter of the Earth's Moon to a beach ball is 11,452.

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The value of Cos 60 degrees is \(\frac{1}{2}\).

Right-angled triangle measurements are studied using trigonometry, which deals with the triangle's length, height, and angles.

Some degree values of sine functions and cosine functions are taken from the trigonometry table to find the value of cos 60 degrees.

We know that

⇒90° – 30° = 60° ———– (1)

From the trigonometry formula,

⇒sin (90° – a) = cos a

We can find the value of cos 60

We can write it as

⇒Sin (90° – 60°) = cos 60°

⇒Sin 30° = cos 60° ——(2)

We know that the value of sin 30 degrees is ½

Now substitute the value in (2)

⇒\(\frac{1}{2}\) = cos 60°

Therefore, the value of Cos 60 degrees is \(\frac{1}{2}\).

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Answer:

B. False

Pont (2, -3) lies on the fourth quadrant.

Step-by-step explanation:

You're welcome.

a) the coffee is cooling at a rate of 2.8°C per minute when its temperature is 90°C.

b) the estimated change in temperature over the next 6 seconds is approximately -0.28°C.

c) you should wait approximately 22.158 minutes before drinking the coffee if the optimal temperature is 65°C.

(a) To determine how fast the coffee is cooling when its temperature is T = 90°C, we need to find the rate of change of temperature with respect to time. This can be done using the formula for exponential decay:

dT/dt = -k(T - T_room)

where dT/dt represents the rate of change of temperature, k is the cooling constant, T is the temperature of the coffee, and T_room is the room temperature.

Given that T = 90°C and T_room = 20°C, and k = 0.04, we can substitute these values into the formula:

dT/dt = -0.04(90 - 20)

      = -0.04(70)

      = -2.8°C/minute

Therefore, the coffee is cooling at a rate of 2.8°C per minute when its temperature is 90°C.

(b) To estimate the change in temperature over the next 6 seconds when T = 90°C using linear approximation, we can use the formula:

ΔT ≈ dT/dt * Δt

where ΔT represents the change in temperature, dT/dt is the rate of change of temperature, and Δt is the time interval.

Given that dT/dt = -2.8°C/minute and Δt = 6 seconds, we need to convert Δt to minutes:

Δt = 6 seconds * (1 minute / 60 seconds)

   = 0.1 minutes

Substituting the values into the formula:

ΔT ≈ -2.8°C/minute * 0.1 minutes

    = -0.28°C

Therefore, the estimated change in temperature over the next 6 seconds is approximately -0.28°C.

(c) The function that models the temperature after t minutes is given by the exponential decay formula:

T(t) = T_initial * \(e^{(-kt)\)

where T_initial is the initial temperature, k is the cooling constant, and t is the time in minutes.

Given that T_initial = 90°C and k = 0.04, we can substitute these values into the formula:

T(t) = 90 * \(e^{(-0.04t)\)

To find how long you should wait before drinking it if the optimal temperature is 65°C, we need to solve the equation T(t) = 65:

65 = 90 * \(e^{(-0.04t)\)

Divide both sides by 90:

0.7222... = \(e^{(-0.04t)\)

To isolate t, take the natural logarithm (ln) of both sides:

ln(0.7222...) = -0.04t

Now, divide by -0.04:

t ≈ ln(0.7222...) / -0.04

Using a calculator to evaluate ln(0.7222...) / -0.04, we find:

t ≈ 22.158 minutes

Therefore, you should wait approximately 22.158 minutes before drinking the coffee if the optimal temperature is 65°C.

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Given the z-table and the standard normal distribution shown in the graph, In statistics, the z-score is a standard score that shows how many standard deviations a data point is from the mean.

A z-score of 0 means that the data point is equal to the mean, a z-score of 1 means that it is one standard deviation above the mean, and a z-score of -1 means that it is one standard deviation below the mean.The z-score that represents a value that is likely to occur is usually between -2 and 2. In other words, the probability of a z-score falling between -2 and 2 is approximately 95%.

Similarly, a z-score of 3.24 has a probability of 0.9993, which means that it is very unlikely to occur, and a z-score of -3.50 has a probability of 0.0002, which means that it is extremely unlikely to occur. Therefore, the z-score that represents a value that is likely to occur is 1.49.

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The statements written as number sentences is

x - y = 25

5p = q/2

14 - 2y = 6

15 × 4 = x + y - 4

From the question, we are to write the given statements as number sentences

Let one of the numbers be x and the other be y

Then,

The statement written as a mathematical expression is

x - y = 25

Product of 5 and p is

5 × p = 5p

and

Quotient of q and 2 is

q/2

∴ The statement written as a number sentence is

5p = q/2

The statement written as a mathematical expression is

14 - 2y = 6

Product of 15 and 4 is

15 × 4

and

Four less than the sum of x and y is

x + y - 4

Thus,

The statement written as a number sentence is

15 × 4 = x + y - 4

Hence, the statements written as number sentences is

x - y = 25

5p = q/2

14 - 2y = 6

15 × 4 = x + y - 4

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Answer:

x=0

Step-by-step explanation:

12=24x+12

Swap sides so that all variables are on the left side.

24x+12=12

Subtract 12 from both sides.

24x=12-12

Subtract 12 from 12 to get 0.

24x=0

The product of two numbers is equal to 0 if one of them is 0. Since 24 is not equal to 0, x must equal 0.

x=0

have a nice day!

Answer:

\( \longrightarrow \tt {4}^{2} + 2 + 3 \times 4 + 4\)

\( \longrightarrow \boxed{\tt{\: 34}} \: \)

---------- HappY LearninG <3 ------

Answer:

the answer is 34

Step-by-step explanation:

see the image

Answer:

Population: all men in the country

Sample: the 1,002 men selected

Step-by-step explanation:

The population describes the people/group of people involved.

The sample describes a portion taken out of the population.

Thus, in this case study, the population is all men in the country

The sample is the 1,002 men selected.

Answer:

parallel means that the line has the same slope as

\(y = \frac{1}{2} x + 9\)

Slope point formula :

y - y1 = m (x - x1)

m represents the slope.

x and y represents the point in the form (x, y).

Since the slopes are the same we can substitute the slope into the formula:

\(y - y1 = \frac{1}{2} (x - x1)\)

then we can substitute our point (2, - 5)

\(y - ( - 5) = \frac{1}{2} (x - 2)\)

Final answer:

Change the - 5 to positive.

\(y + 5 = \frac{1}{2} (x - 2)\)

Leave y by it's own and subtract 5 to get rid of it. Do this both sides to make it equal.

\(y + 5 - 5 = \frac{1}{2} (x - 2) - 5\)

Get rid of the brackets by multiplying:

\(y =( \frac{1}{2} \times x) - ( \frac{1}{2} \times 2) - 5\)

simplify:

\(y = \frac{1}{2} x - 1 - 5\)

Answer:

\(y = \frac{1}{2} x - 6\)

We need to find the inverse of the function gof (x). First we need to find the composite function gof (x) which is given by:

\(g(f(x)) = g(3x - 6)\)

= \((1/3)(3x - 6) + 1\)

= x - 1 + 1

= x

Thus,

gof (x) = x.

Now we need to find the inverse of the function gof (x) to obtain

\((gof)^-1 (x).\)

We have gof (x) = x

which implies\((gof)^-1 (x)\)

= gof (x)^-1

= x^-1

= 1/x,

x ≠ 0

Therefore,

\((gof)^-1 (x) = 1/x\)

which is option (3) (x+1) since 1/x can be written as 1/(x+1-1), where (x+1-1) is the denominator of 1/x.

Hence, the correct option is (3).

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To find (g(f))^-1 (x), substitute the expression for f(x) into g(x) and simplify. The composition of g(f) is x and its inverse is also x. Therefore, (g(f))^-1 (x) equals x.

To find (g(f))^-1 (x), we need to first find the composition of g(f) and then find its inverse. Start by substituting the expression for f(x) into g(x): g(f(x)) = g(3x-6) = \frac{1}{3}(3x-6) + 1 = x - 1 + 1 = x. So, g(f(x)) = x. Now, to find the inverse of g(f), we switch the x and y variables and solve for y: y = x. Therefore, (g(f))^-1 (x) = x.

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The area of ΔAFD is 42 squared unit.

The area of a triangle is the amount of space that the triangle would occupy on a 2 dimensional plane.

Area of a triangle = 1/2 x base x height

To solve the given problem, let the height be resented by x and the base be represented by y. So that applying the trigonometric function to determine the values, we have;

i. Sin θ = opposite/ hypotenuse

Sin 30 = x/ 14

x = 14 x Sin 30

     = 7

The height is 7 units.

ii. Cos θ = adjacent/ hypotenuse

   Cos 30 = y/ 14

  y = 14 x Cos 30

       = 12

The base is 12 units.

Therefore, the area of triangle AFD can be determined by;

Area of ΔAFD = 1/2 x 12 x 7

                       = 42

The area of ΔAFD is 42 squared unit.

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Answer: u = 3

Step-by-step explanation:

Divide each side by -7 to get u = 3.

Answer:

3

Step-by-step explanation:

-7u = -21

To solve the problem we need to isolate u. Since -7 is being multiplied by u, we could divide to get rid of it.

-7u

\( \frac{ - 7u}{ - 7} = - 21 \div - 7\)

u= -21/-7

u = 3

The ratio of force F12 to force F78 is 1:1.


A ratio is a quantitative relationship between two numbers that describe how many times one value can contain another. The ratio represents the number that needs to be multiplied by the denominator in order to yield the numerator.

So, here, the ratio of force is 1 because the blocks are identical and the table is frictionless. Therefore, the force that block 1 exerts on block 2 will be the same as the force that block 7 exerts on block 8. The ratio of two identical forces will always be 1.

To calculate the ratio, simply divide F12 by F78:

F12/F78 = 1/1 = 1

Therefore, the correct answer is 1.

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Answer:

Between the triangles, two pairs of corresponding sides are proportional, and that a pair of corresponding angles are congruent. The angles that are congruent are the included angles of their respective sides. By the SAS Similarity Postulate, this is enough to prove that.

Answer:

y = 3/2x-14

Step-by-step explanation:

      The given line is y=-2/3x. So, the slope of the given line is -2/3.

Now, we have to find the perpendicular line to y= -2/3x passing through the point (4,-8).

       The product of two perpendicular lines is -1.

m1.m2 = -1.

-2/3.m2= -1

m2 = 3/2

        Now, we need to find the equation of the line passing through the point (4,-8) with slope 3/2.

The equation of slope-point form is (y-y1) = m(x-x1)

        y-(-8) = 3/2 (x-4)

        y+8 = 3/2x -6

Now, we have to add 6 on both sides.

        y + 8 + 6 = 3/2x - 6 + 6.

        y + 14 = 3/2x

        y = 3/2x - 14.

Answer:

y=4x+-3 is your equation

Answer:

y' = 2x + 1

y'' = 2

Step-by-step explanation:

y = x² + x + 8

y' = 2x + 1

y'' = 2

Answer:

Step-by-step explanation:

add 2 to both sides to get

\((x-3)^2=-3\)

if u do square root to get rid of exponent, answer is

\(x=\sqrt{3}i+3,\:x=-\sqrt{3}i+3\)

one of the calculators i used to confirm said answer was  x=i√3+3,−i√3+3  but idunno

Answer:

each doll cost $35

Answer:

The dolls cost $35 dollars each

Step-by-step explanation:

Because $70 ÷ 2 dolls = $35 dollars each

(sorry if wrong!)

Let's say we had point A at (0,0). It is exactly 1 unit away from the vertical line x = 1. We move 1 unit to the right to land on this mirror line, and then move another unit to arrive at A ' (2,0)

So A(0,0) moves to A ' (2,0) after mirroring over the line x = 1.

Then note the distance from A ' (2,0) to the second mirror line x = 5 is 3 units. We'll move 3 units to the right to land on this second mirror line, and then another 3 units to the right to arrive at A '' (8,0)

-------------

Overall, we start at A(0,0) and ended at A '' (8,0)

This describes a horizontal translation of 8 units to the right.

Answer:

let's say we had point A at (0,0). It is exactly 1 unit away from the vertical line x = 1. We move 1 unit to the right to land on this mirror line, and then move another unit to arrive at A ' (2,0)

So A(0,0) moves to A ' (2,0) after mirroring over the line x = 1.

Then note the distance from A ' (2,0) to the second mirror line x = 5 is 3 units. We'll move 3 units to the right to land on this second mirror line, and then another 3 units to the right to arrive at A '' (8,0)

Step-by-step explanation:

On solving the provided question, we can say that equality of given trapezium we find, y=13/10 and x=21

A convex quadrilateral with exactly one pair of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices.

Since ABCD~PQRS

then, on comparing

5y-3/4 = 7/8

y=13/10

On comparing angle,

3x+24=87°

3x=63°

x=21

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Answer:

There is no solution

Step-by-step explanation:

There are no values of (a) that make the equation true.

Answer:

a = 11/13

Step-by-step explanation:

Multiply both sides by 1 - a

12(1 - a) = 1 + a

= 12 - 12a = 1 + a

Subtract 12 from both sides

= -12a = -11 + a

Subtract a from both side

-13a = -11

Divide by -13 each side

-13a/13 = -11/-13

= a = 11/13

Answer:10

Step-by-step explanation:

8/80=1/10*100=10

Answer: “5” is an exponent

Step-by-step explanation:

The given vertices when plotted gives a parallelogram.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

To solve this problem, we simply need to plot the vertices and check if the opposite sides are equal to each other.

Kindly find the attached image of the parallelogram below.

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Here, we want to find the value of x in the diagram, given the value of the slope

From the question, we have two points, separated by a horizontal distance

Mathematiclly the slope of a line is;

Now, what this mean is that, the x value from the tip of the triangle to the dotted line represented by 12 is 48

This is not the value of x, we want to calculate

Now, the x-distance from the tip of the rectangle to the dotted line marked as 5 is (48-x)

Thus, we have it that;

Answer:

Step-by-step explanation: It is isosceles because the two tick marks on two of the sides show that they are the same length. A single tick is missing from the bottom so it is a different length. The two triangle are vertical, making them congruent so two of the sides on the big triangle are also the same.