The volume of the planet is approximately 1.02×109 km³, and the mass of the planet is about 5.683 × 1021 kg. What is the average density of the planet in grams per cubic centimeter? The average density of the planet is approximately_____ g/cm³ .​

Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

The value of sinθ is √17/7 and the value of [?] is √17

According to The Pythagorean identity,

Sin²θ + Cos²θ = 1

This is a Trigonometric equation, where 'sin' refers to 'sine' and 'cos' refers to 'cosine' which are functions revealing the shape of a right-angled triangle.

Given, cosθ=4√2/7

Cos²θ = 32/49

From equation 1 we get,

Sin²θ = 1 - Cos²θ

Sin²θ = 1 - (32/49)

Sin²θ = (49-32)/49

Sin²θ = 17/49

Sinθ = √(17/49)

Sinθ = √17 / 7

Given, sinθ = √[?] / [ ]

[?] = 17

Therefore, The value of sinθ is √17/7 and the value of [?] is √17

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The correct matches are 1) Approximately Bell-Shaped, 2) Skewed Right, 3) Uniform and 4) Skewed Left.

Uniform: In a uniform distribution, the data is evenly spread across the entire range, resulting in a rectangular-shaped histogram. All values have roughly the same frequency or probability. It suggests that there is an equal chance of observing any value within the given range.

Approximately Bell-Shaped: This description refers to a distribution that closely resembles a bell curve or a normal distribution. The data is symmetrically distributed around a central peak, with most values clustered near the mean. The histogram will have a characteristic bell shape, with the highest frequency at the center and gradually decreasing frequencies on both sides.

Skewed Left: A left-skewed distribution, also known as negatively skewed or left-tailed, is characterized by a long tail extending towards the lower values. The majority of the data is concentrated on the right side of the distribution, and the tail extends to the left. The histogram will show a longer tail on the left side and a shorter right side.

Skewed Right: A right-skewed distribution, also known as positively skewed or right-tailed, has a long tail extending towards the higher values. The majority of the data is concentrated on the left side of the distribution, and the tail extends to the right. The histogram will exhibit a longer tail on the right side and a shorter left side.

Hence the correct matches are 1) Approximately Bell-Shaped, 2) Skewed Right, 3) Uniform and 4) Skewed Left.

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For simplification the exponent rules must be known to us .

The exponent rules are mentioned below:

1)

Now,

Simplifying,

[(-0.5)² *(-0.5)²]²

Apply property 3,

[(-0.5)^4]^2

(-0.5)^8

2)

(3.3³)3

Simplify by property 3

= 3 ^12

3)

(y² × y)²÷4y²

Simplify by rule 3 and 4,

= y^6 ÷ 4 y²

= y^4/4

4)

(a^3 × a^6)^3/(a^4)^5

Simplify by rule 3 and 4,

=a^7

Hence with the use of exponent rules the expressions can be simplified.

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150 miles is the same as 150*5280 = 792000 feet, and one hour is equivalent to 60*60 = 3600 seconds. Now we divide 792000 feet by 3600 seconds to get the equivalent rate: 792000 ft/3600 sec = 220 ft/second. Now, we multiply the rate by 5 and get 1100 feet per 5 seconds. So, our answer is 1100 feet.

The probability of landing on purple to the nearest hundredth: 0.15

The total number of spins is 84, and the probability of landing on purple is 13/84 = 0.15476.

Rounding to the nearest hundredth, this is 0.15.

Elaborating:

Number of times the spinner landed on purple: 13

Total number of spins: 84

Probability of landing on purple: (13/84) = 0.15476

Probability of landing on purple to the nearest hundredth: 0.15

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The Complete Question

A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:

Spinner Results

Color Frequency

Red 18

Blue 15

Green 20

Yellow 18

Purple 13

Based on these results, express the probability that the next spin will land on purple as a decimal to the nearest hundredth.

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

Step-by-step explanation:

Sales Revenue:  $800.00

Cost of good sold:  $350,000.00

Subtract:                   $450,000.00

Sales Revenue:         $795,000.00

Cost of good sold:     $600,000.00

Subtract Sales             $195,000.00

Revenue from Cost

of goods sold.

Answer:

x = 36

y = -1

Step-by-step explanation:

The substitution method is when the value of one variable from one equation is substituted in the other equation.

y = 10/3x - 121

y = 5/4x - 46

In this case you substitute one of the equations for y.

5/4x - 46 = 10/3x - 121

Lets set the coefficient being multiplied by x to a number with a common demoninator.

15/12x - 46 = 40/12x - 121

Next isolate x and combine like terms.

15/12x - 46 = 40/12x - 121

-15/12x          -15/12x

-46 = 25/12x - 121

+121              +121

75 = 25/12x

*12/25    12/25

36 = x

------

Now lets plug x in to solve for y

(you pick either equation to do this)

y = 5/4(36) - 46

y= 45 - 46

y = -1

Answer:

The answers are all in 2d.p

1)523.81cm³

2)166.67m³

3)754.29m³

Step-by-step explanation:

1)V=1/3pir²h

V=1/3×10²×5×22/7

V=523.81cm³

2)V=4/3pir³

V=4/3×5³

V=166.67m³

3)V=1/3pir²h

V=1/3×22/7×6²×20

V=754.29m³

Answer:

First subtract (4) and (3x) from each side of the equation to isolate the x ... 5x-4=3x-8 One solution was found : x = -2 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation

Step-by-step explanation:

Answer:

x > 2

Step-by-step explanation:

To solve for x, we will first simplify the left side of the inequality by finding a common denominator for the fractions:

5/6x - 1/3 > 4/3

Multiplying both sides by 6 to eliminate the fractions, we get:

5x - 2 > 8

Adding 2 to both sides, we have:

5x > 10

Dividing both sides by 5, the final answer is:

x > 2

Hope this helps!

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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as far as I can read it, he bought £800 in shares, who knows how many, is irrelevant in this case, however we also know that he got £78 for 30 years, what was the rate?

well, we can nevermind the 30 years part and keep an eye that every year his earned interest was £78 flat, so we're looking at a simple interest rate, since it's not compounding, so let's reword all that

with an initial investment of £800 yielding £78 per year, what's the interest rate?

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \pounds 78\\ P=\textit{original amount deposited}\dotfill & \pounds 800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 78 = (800)(\frac{r}{100})(1) \implies 78=8r\implies \cfrac{78}{8}=r\implies \stackrel{ \% }{9.75}=r[/tex]

Step-by-step explanation:

Expand the given 10 n and multiply it by the given number. 2. Then the result will be in the usual form.

Answer:

f = 65

s = 144

t = 144

u = 77

Step-by-step explanation:

the sum of a triangles angles will always be 180

so we can subtract 37 and 78 from 180 to find f which is 65

in regards to s and t, the sum of those 4 angles will be 360, and we can assume the opposite sides of the angles are the same.

so the other side of the 36 angle will also be 36, so we subtract 36 and 36 from from 380 which gives us 288

then we divide it by 2 because we have 2 unknown angles that are the same size, then we get 144 for s and 144 for t

the sum of the angles of a polygon will always be 360

so we can subtract 86 and 53 and t (which we now know is 144) from 360 to find u

so u = 77

Answer:

[tex]52 + o = 180[/tex]

[tex]o = 128[/tex]

Angle o measures 128°.

The dimensions of the irregular hexagon are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm

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

Shape = irregular hexagon

Also, we have

Perimeter = 98 cm

The perimeter of a shape is the sum of its side length

An irregular hexagon has six unequal sides

using the above as a guide, we have the following:

17 + 15 + 14 + 13 + 17 + 22 = 98

This means that the side lengths are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm

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Answer:

[tex]58 + x = 180[/tex]

[tex]x = 122[/tex]

Angle x measures 122°.

The final amount is $2203. 2

From the information given, the formula for finding the amount is expressed as;

A=Pert

Such that the parameters are;

Substitute the values, we have;

A = 300 × [tex]2.71^(^2^*^1^)[/tex]

Multiply the exponents, we have;

A = 300 × [tex]2.71^2[/tex]

Find the square value and multiply, we get;

A = $2203. 2

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Answer:

320 g

Step-by-step explanation:

To find the recommended daily amount of protein, we can set up a proportion using the given information:

30% of the recommended daily amount = 96 grams

Let "x" represent the recommended daily amount of protein. We can set up the proportion as:

30/100 = 96/x

To solve for x, we can cross-multiply and solve the equation:

30x = 100 * 96

30x = 9600

Dividing both sides by 30:

x = 9600 / 30

x ≈ 320

Answer:

628.3 cubic inches

Step-by-step explanation:

Since the base diameter of the cylinder is d=20 inches, so its radius r is:

[tex]r=\frac{d}{2}=\frac{20}{2}=10[/tex]

Then, the volume V of the cylinder with radius r=10 inches and height h=2 inches is:

[tex]V=\pi r^{2} h=\pi\times 10^{2}\times 2=628.3[/tex]

Answer:

To find the volume of a cylinder, we need to use the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height. Since we are given the diameter of the base, which is 20 inches, we can find the radius by dividing it by 2. So, r = 20 / 2 = 10 inches. The height is given as 2 inches. Plugging these values into the formula, we get:

V = π(10)^2(2)

V = π(100)(2)

V = 200π

To get the volume in cubic inches, we need to multiply this by the conversion factor of 1 cubic inch per cubic inch. This does not change the value, but it gives us the correct units. So,

V = 200π cubic inches

To round this to the nearest tenths place, we need to look at the hundredths digit. If it is 5 or more, we round up; if it is less than 5, we round down. Using a calculator, we can approximate π as 3.14. So,

V ≈ 200(3.14) cubic inches

V ≈ 628 cubic inches

The hundredths digit is 0, which is less than 5. So we round down and keep the tenths digit as it is. Therefore,

V ≈ 628.0 cubic inches

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Answer:

define the height above the ground, h, as a function of time, t, using the sine function:

h(t) = A * sin(B * t + C) + D

A represents the amplitude of the function, which is half of the vertical distance covered by the rider (in this case, 30 feet).

B represents the frequency of the function, which is related to the number of complete cycles or revolutions in a given time period. In this case, the Ferris wheel completes 2 revolutions per minute, so B = 2π (since 2π radians represents one complete revolution).

C represents the phase shift of the function, which accounts for the initial position of the rider. Since the rider starts at the lowest point, there is no phase shift, so C = 0.

D represents the vertical displacement of the function, which is the average height above the ground. In this case, the center of the wheel is 30 feet above the ground, so D = 30.

Putting it all together, the trigonometric function that can be used to model the rider's height, h(t), above the ground after t seconds is:

h(t) = 30 * sin(2π * t) + 30

Therefore, the sine function can be used to model the rider's height

The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.

The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.

To provide a clearer understanding, let's break it down further:

"Subset": A subset is a collection of elements that are all contained within another set. If set A is a subset of set B, it means that every element of A is also an element of B.

"Any X ∈ C": Here, X represents a generic element of the set C. The phrase "X ∈ C" denotes that X belongs to the set C. It implies that X is one of the elements within the set C.

Combining the two parts, "it is a subset of any X ∈ C" means that "it" (referring to a specific set or collection of elements) is included in every element X of the set C. In other words, every element of C contains "it" as a subset.

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The absolute value equation for x = -4 can be written as:

|x - (-2)| = 2

We have,

For x = -8, the absolute value equation can be written as:

|x - c| = d

Substituting x = -8 into the equation, we have:

|-8 - c| = d

To satisfy the given solution set, we need to determine the values of c and d that make the equation true.

Since x = -8, the absolute value of -8 minus c should be equal to d.

For x = -8, a suitable choice of c would be -12 and d would be 4.

This gives us:

|-8 - (-12)| = 4

|4| = 4

Therefore, the absolute value equation for x = -8 can be written as:

|x - (-12)| = 4

Similarly, for x = -4, the absolute value equation can be written as:

|x - c| = d

Substituting x = -4 into the equation, we have:

|-4 - c| = d

To satisfy the given solution set, we need to determine the values of c and d that make the equation true.

Since x = -4, the absolute value of -4 minus c should be equal to d.

For x = -4, a suitable choice of c would be -2 and d would be 2. This gives us:

|-4 - (-2)| = 2

|-2| = 2

Therefore,

The absolute value equation for x = -4 can be written as:

|x - (-2)| = 2

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Answer: clean your shoes

Step-by-step explanation:

since you're walking on ice cream , your shoes will be sticky so one should clean them shoes with water.

Applying the Angle Addition Postulate, the measure of angle BDC is calculated as: 57 degrees.

The Angle Addition Postulate establishes that when two angles are adjacent, the measure of the resulting angle formed by their combination is equal to the sum of their individual measures.

Therefore, according to the Angle Addition Postulate, we would have:

(-6x + 11) + (-7x + 15) = 104

Solve for x:

-6x + 11 - 7x + 15 = 104

-13x + 26 = 104

-13x = 104 - 26

-13x = 78

x = -6

Measure of angle BDC = -7x + 15

Plug in the value of x:

Measure of angle BDC = -7(-6) + 15 = 57°

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Answer:

Step-by-step explanation:

The solution to the system of equations using Cramer's rule is x = -1 and y = 2.

To solve the system of equations using Cramer's rule, we'll need to determine the values of x and y by calculating the determinants of various matrices.

The given system of equations is:

8x + 5y = 2 (Equation 1)

2x - 4y = -10 (Equation 2)

First, let's calculate the determinant of the coefficient matrix, D:

D = |8 5|

|2 -4|

D = (8 * -4) - (5 * 2)

D = -32 - 10

D = -42

Next, we'll calculate the determinant of the matrix formed by replacing the x coefficients with the constants from the right side of the equations, Dx:

Dx = |2 5|

|-10 -4|

Dx = (2 * -4) - (5 * -10)

Dx = -8 + 50

Dx = 42

Similarly, we'll calculate the determinant of the matrix formed by replacing the y coefficients with the constants, Dy:

Dy = |8 2|

|2 -10|

Dy = (8 * -10) - (2 * 2)

Dy = -80 - 4

Dy = -84

Now, we can find the values of x and y:

x = Dx / D

x = 42 / -42

x = -1

y = Dy / D

y = -84 / -42

y = 2

Therefore, the solution to the system of equations is x = -1 and y = 2.

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