IF A SOUP RECIPE YIELDS 20 GALLONS, HOW MANY 5-FLUID OUNCE PORTIONS WILL THE RECIPE YIELD?

Answer: 63

Step-by-step explanation:

The given arithmetic sequence is defined by the formula:

ak = 3 + 4(k - 1)

To find the 16th term, we can substitute k = 16 into this formula and simplify:

a16 = 3 + 4(16 - 1)

a16 = 3 + 4(15)

a16 = 3 + 60

a16 = 63

Therefore, the 16th term of the arithmetic sequence is 63.

The simplification of the given expression

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

is y = 7

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

find the square root of 25

[tex]y =( \sqrt{47 + \sqrt{9 - 5} } [/tex]

simplify root 9 - 5

[tex]y = ( \sqrt{47 + \sqrt{4} } [/tex]

find the square root of 4

[tex]y = ( \sqrt{47 + 2)} [/tex]

Add root 47 and 2

[tex]y = ( \sqrt{49} )[/tex]

Find the square root of 49

y = 7

Therefore, the solution to the given expression is y = 7

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Rolling a six-sided die 80 times and recording the number of l's rolled and it is a Binomial Distribution.

The binomial distribution is a probability distribution used in statistics that summarizes the probability that a value will take on one of two independent values ​​given a set of parameters or assumptions. The binomial distribution is calculated by multiplying the probability of success by the power of the number of successes and by multiplying the probability of failure by the power of the difference between the number of successes and the number of trials. The product is then multiplied by the combination of trials and successes.

For example, suppose a casino develops a new game where participants bet on the number of heads or tails in a specified number of coin tosses. Suppose a contestant wants to bet $10 that 20 coin tosses will result in exactly 6 heads. The participants wanted to calculate the probability of this happening, so they used calculations from the binomial distribution.

The probability is calculated as :

(20! / (6! × (20 - 6)!)) × (0.50)⁶ × (1 - 0.50)⁽²⁰⁻⁶⁾. Therefore, the probability of getting exactly 6 heads out of 20 coin tosses is 0.037, or 3.7%.

In this case, the expected value is 10 heads, so the contestant made a bad bet.

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Your question is incomplete. The complete question is: Which of the graphs below illustrates water boiling in Denver, Colorado? (Altitude 1,600 meters.)

Answer:

Explanation:

The normal boiling point of water is 100°C. That is the temperature at which water boils when the atmospheric pressure is 1 atm, i.e. at sea level.

The liquids boil when its vapor pressure equals the atmospheric pressure; so the higher the atmospheric pressure the higher the boiling point, and the lower the atmospheric pressure the lower the boiling point.

Since, it is stated that the altitude of Denver, Colorado is 1,600 m, the atmospheric pressure (the pressure exerted by the column of air above the place) is lower than 1 atm (atmospheric pressure at sea level).

Hence, water boiling point in Denver is lower than 100°C.

The graphs shown represent the temperature (T °C) as water is heated. Since when liquids boil their temperature remains constant during all the phase change, the flat portion of the graph represents the time during which the substance is boiling.

In the graph A, the flat portion is below 100°C; in the graph B, the flat portion is at 100 °C; in the graph C the flat part is above 100ªC, and, in graph D, there is not flat part. Then, the only graph that can illustrate water boiling in Denver, Colorado is the graph A.

Find the percent of each number :-

1.) 64% of 75 tiles :

[tex] \implies \sf \: \dfrac{64}{100} \times 75 \\ \\\implies \sf \:0.64 \times 75 \\ \\ \implies \sf \: 48 \\ [/tex]

Hence, 64% of 75 tiles is 48 tiles.

2.) 20% of 70 plants.

[tex] \implies \sf \: \dfrac{20}{100} \times 70 \\ \\\implies \sf \:0.2 \times 70 \\ \\ \implies \sf \: 14 \\ [/tex]

Hence, 20% of 70 plants is 14 plants.

3.) 32% of 25 pages .

[tex] \implies \sf \: \dfrac{32}{100} \times 25 \\ \\\implies \sf \: 0.32 \times 25 \\ \\ \implies \sf \: 8 \\ [/tex]

Hence, 32% of 25 pages is 8 pages.

4.) 85% of 40 e -mails.

[tex] \implies \sf \: \dfrac{85}{100} \times 40 \\ \\\implies \sf \:0.85 \times 40 \\ \\ \implies \sf \: 34 \\ [/tex]

Hence, 85% of 40 e -mails is 34 e-mails.

5.) 72% of 350 friends.

[tex] \implies \sf \: \dfrac{72}{100} \times 350 \\ \\\implies \sf \:0.72 \times 350 \\ \\ \implies \sf \: 252 \\ [/tex]

Hence, 72% of 350 friends is 252 friends.

6.) 5% of 220 files.

[tex] \implies \sf \: \dfrac{5}{100} \times 220 \\ \\\implies \sf \:0.05 \times 220 \\ \\ \implies \sf \: 11 \\ [/tex]

Hence, 5% of 220 files is 11 files.

Answer:

A right angled triangle is similar to triangle ABC

Step-by-step explanation:

If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°

And if a triangle has one angle of 90° then it is a right angled triangle

Hope you understand :)

The equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.

A line that meets a curve at a point and has the same slope as the curve there is said to be the tangent line to that curve. A line that is perpendicular to the tangent line at a given position is the normal line to a curve at that location. In other words, the normal line's slope equals the tangent line's slope's negative reciprocal. The normal line is helpful for determining the direction of greatest change of the curve at a place whereas the tangent line gives information about the instantaneous rate of change of the curve at that point.

The given function is f(x) = 1/x.

The slope of the function is the derivative of the function thus,

f(x) = 1/x

f'(x) = -1/x²

f'(7) = -1/49

The equation of the line is given as:

y - y1 = m(x - x1)

where, m is the slope of the equation.

The equation of the tangent line is:

y - f(7) = f'(7)(x - 7)

y - 1/7 = -1/49(x - 7)

y = (-1/49)x + 8/49

b. The equation of the normal line to the graph is given as:

The slope of the normal line is negative and opposite of the tangent line.

That is,

m = 49.

y - f(7) = 49(x - 7)

y - 1/7 = 49(x - 7)

y = 49x - 342

Hence, the equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.

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The pieces of information would prove that the polygon trig is a parallelogram is GI || TR (option b).

Now, suppose you have a quadrilateral named TRIG. The question asks which of the given information would prove that TRIG is a parallelogram. Let's examine each option to determine which one satisfies the conditions of a parallelogram.

a) GT || IR: This option tells us that GT is parallel to IR. However, we cannot conclude that TRIG is a parallelogram from this information alone.

b) GI || TR: This option states that GI is parallel to TR. Again, we cannot immediately conclude that TRIG is a parallelogram from this information.

c) GO ≅ OR, TO ≅ OI: This option tells us that GO is congruent to OR and TO is congruent to OI. However, this information alone does not prove that TRIG is a parallelogram.

d) GR ≅ TI: This option states that GR is congruent to TI. Similarly, we cannot conclude that TRIG is a parallelogram from this information.

e) GO ⊥ OI: This option tells us that GO is perpendicular to OI. Unfortunately, this information alone does not prove that TRIG is a parallelogram either.

f) GT ≅ TR: This option states that GT is congruent to TR. However, this information alone does not prove that TRIG is a parallelogram.

The answer is option (b) GI || TR. If GI is parallel to TR, then by definition, TRIG has opposite sides parallel, which means it is a parallelogram.

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Complete Question:

Polygon TRIG is a quadrilateral.

Which of the following pieces of information would prove that TRIG is a parallelogram?

a) GT || IR

b) GI || TR

c) GO ≅ OR, TO ≅ OI

d) GR ≅ TI

e) GO ⊥ OI

f) GT ≅ TR

The exact value of sin∅ if cos∅ =3/8 and in the fourth quadrant is 292⁰

We should recall that the the angles of the 4th quadrant range from 270° to 360°.  that is to say that in the fourth quadrant, 270≤x≤360

The given angle is cos∅ =3/8

cos∅ = 0.375

Find the angle we take the cos inverse

That ∅ = Cos⁻¹0.375

∅ = 68⁰

In the fourth quadrant, cos is positive that 360-68 = 292⁰

Then the exact value of sin is 292⁰

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When three dices are rolled.

Total number of outcomes =  = 216

Sum of 13 can be achieved in the following ways:

From the digits 6,4,3

So, there are 3! ways =  = 6

From the digits 6,2,5

So, there are 3! ways =  = 6

From the digits 5,4,4

So, there are  ways = 3

From the digits 6,6,1

So, there are  ways = 3

From the digits 3,5,5

So, there are  ways = 3

So, total numbers whose sum is 13=

So, Probability = .

Therefore, the probability of getting sum as 21 on rolling three dice =   .

The shape of the resultant matrix of the multiplication of a "2 by 4" matrix and a "4 by 3" matrix will be a "2 by 3" matrix, the correct option is (d).

We know that the general rule for matrix multiplication, which is If matrix A is "m by n" matrix (it has m rows and n columns) and the matrix B is "n by k" matrix (it has n rows and k columns),

Then the product AB is an "m by k" matrix, which means, that the resulting matrix will have "m" rows and "k" columns.

In this case, the "2 by 4" matrix means that matrix has 2-rows and 4-columns, and

The "4 by 3" matrix means the matrix has 4-rows and 3-columns.

Since the number of columns in the first matrix (4) matches the number of rows in the second matrix (4), we can perform the multiplication.

The resulting matrix will have 2 rows and 3 columns,

Therefore, the shape of the resultant matrix is (d) 2 by 3.

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The given question is incomplete, the complete question is

Please identify from the following choices which has the shape of the resultant matrix of multiplication of a "2 by 4" and "4 by 3" matrices.

(a) 3 by 2

(b) 2 by 4

(c) 4 by 4

(d) 2 by 3

Step-by-step explanation:

To find the range, we need to subtract the smallest value from the largest value in the dataset:

Range = Largest value - Smallest value

Range = 92 - 3

Range = 89

To find the variance and standard deviation, we need to calculate the mean first:

Mean = (Sum of all values) / (Number of values)

Mean = (92+19+41+24+75+53+70+3+67+64+9) / 11

Mean = 45.09 (rounded to two decimal places)

Next, we need to calculate the variance:

Variance = (Sum of squared differences from the mean) / (Number of values - 1)

Variance = [(92-45.09)^2 + (19-45.09)^2 + (41-45.09)^2 + (24-45.09)^2 + (75-45.09)^2 + (53-45.09)^2 + (70-45.09)^2 + (3-45.09)^2 + (67-45.09)^2 + (64-45.09)^2 + (9-45.09)^2] / (11-1)

Variance = 1071.45 (rounded to two decimal places)

Finally, we can calculate the standard deviation by taking the square root of the variance:

Standard deviation = Square root of variance

Standard deviation = Square root of 1071.45

Standard deviation = 32.74 (rounded to two decimal places)

The range tells us the difference between the highest and lowest values in the dataset, which in this case is 89. The variance and standard deviation tell us how spread out the data is from the mean. The higher the variance and standard deviation, the more spread out the data is. In this case, the variance and standard deviation are both relatively high, indicating that the data is fairly spread out.

Lattice permutation is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1.

In mathematics, a lattice permutation group is a type of permutation group, also known as a Coxeter group, which acts on a set of vectors in a lattice.

A lattice permutation group is a special type of finite group that can be used to generate symmetries in a lattice structure. They are related to Coxeter groups, which are groups that act on a set of points in a Euclidean space, and are generated by reflections.

Lattice permutation groups are generated by permutations of the lattice points, and can be used to study the symmetry of a lattice. These groups are important in the study of crystallography, and can be used to classify the symmetry of a lattice.

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The complete question is:

______ is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1.

Answer:

D, 12 cm.

Step-by-step explanation:

First, draw out the circle with a hexagon in it. I did this by dividing the circle into thirds and then halving each of those because it was easier to visualize. I ended up with something like the image below. Now, we know that the sum of all of the angles that come together at the center of the circle is going to be 360. We can divide 360 by 6 to get 60. The top angle of the triangle, the angle closest to the center, is 60 degrees. We also know that the length of all of these legs that are going out will be the same, because the radius of the circle is constant. This makes each triangle an isosceles triangle. Given the isosceles base angle theorem, both base angles of the triangle must be the same. The sum of all angles in a triangle is 180 degrees. So the equation for x, one of the angles, would be  60 (angle closest to center) + 2x = 180. Let's subtract 60 from both sides to get 2x = 120. Divide both sides by two to get x = 60. Okay, so now we know that all angles in the triangle are 60 degrees. By the equilateral triangle theorem, we know these triangles must be equilateral because all of their angles are 60 degrees. Equilateral triangles also have the same side lengths. Because 12 is one side length, then all side lengths = 12. Therefore, the length of one side of the hexagon is 12.

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Answer: 2 meters

Step-by-step explanation:

The length of one train car is 80 millimeters. Therefore, the length of the entire train is:

25 cars × 80 mm per car = 2000 mm

To convert millimeters to meters, we need to divide by 1000:

2000 mm ÷ 1000 = 2 meters

Therefore, Venell's model train is 2 meters long.

The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.

An employee who earned $20,000 will contribute $260 to the welfare fund.

To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.

The first $1000 will have a contribution rate of 4%.

Contribution for the first $1000 = 4% of $1000 = $40.

The next $1000 will have a contribution rate of 3%.

Contribution for the next $1000 = 3% of $1000 = $30.

The next $1000 will have a contribution rate of 2%.

Contribution for the next $1000 = 2% of $1000 = $20.

The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.

Contribution for the remaining amount = 1% of $17,000 = $170.

Now, let's sum up the contributions for each tier:

$40 + $30 + $20 + $170 = $260.

Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.

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35 is a reasonable prediction of the number of times he will select 2 yellow socks?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.

In the given question,

The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:

P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25

So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.

To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:

E(X) = n * p

where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.

In this case, n = 175 and p = 1/25. So,

E(X) = 175 * (1/25) = 7

Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.

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The decimal number 555 is written as 4210 in base-5.

Answer:  [tex]555_{10} =4210_{5}[/tex]

Step-by-step explanation:

Decimal to base five conversion

here

                                    D   Q            Remainders

                                    5  |555               0

                                     5  |111                   1

                                      5  |22                  2

                                       5  |4                     4

                                             0  

Answer:

Step-by-step explanation:1.4 -1, 1 2, -1

The probability that the sum of the numbers on the dice will be a square number is 1/6.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

We can first make a list of every conceivable result when rolling two dice in order to determine the likelihood that the sum of the numbers on the two dice will be a square number:

[tex](1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6[/tex])

[tex](2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]

[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)[/tex]

[tex](4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]

[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)[/tex]

[tex](6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)[/tex]

The sums can then be listed, and the square numbers can be identified:

2, 3, 4, 5, 6, 7

3, 4, 5, 6, 7, 8

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9, 10

6, 7, 8, 9, 10, 11

7, 8, 9, 10, 11, 12

The likelihood that the sum of the numbers on the dice will be a square number is 6 out of a total of 36 potential outcomes.

P(square sum) = 6/36 = 1/6.

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Answer:

To convert 49% to a fraction, we can simply write it as 49/100. This is because a percentage is a way of expressing a number as a fraction of 100. So 49% means 49 out of 100, which can be written as the fraction 49/100.

Answer:

49/100

Step-by-step explanation:

Percent means out of 100.

49%

49/100

The fraction of the students in the class are women is  one-third (1/3)

If there are 16 men in the class of 24 students, we can find the number of women by subtracting the number of men from the total number of students:

Number of women = Total number of students - Number of men

Number of women = 24 - 16

Number of women = 8

Therefore, there are 8 women in the class.

To find the fraction of students in the class who are women, we divide the number of women by the total number of students:

Fraction of students who are women = Number of women / Total number of students

Fraction of students who are women = 8 / 24

Fraction of students who are women = 1/3

So, one-third (1/3) of the students in the class are women.

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All rules towards each statement shown in table below.

The relationships between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It entails the study of trigonometric functions like sine, cosine, and tangent, which connect a triangle's angles and side lengths.

Rules towards each statement:

                                                                  Statements

Rule1.     Cos x/ Sin x  (Sec 2x - 1)             Pythagorean identity

Rule2.    Cos x/Sin x  (Tan 2x)                  Algebra

Rule3.    Cos x/Sin x (Sin 2x/Cos 2x)       Reciprocal

Rule4.    Sin x/Cos x                                 Odd/ Even

Rule5.    Tan x                                           Quotient

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As per trigonometric functions, rules towards each statement are:

Rules towards each statement:

                                                                 Statements

Rule1.     Cos x/ Sin x (Sec 2x - 1)             Pythagorean identity

Rule2.    Cos x/Sin x (Tan 2x)                  Algebra

Rule3.    Cos x/Sin x (Sin 2x/Cos 2x)       Reciprocal

Rule4.    Sin x/Cos x                                 Odd/ Even

Rule5.    Tan x                                           Quotient

Trigonometry is a branch of mathematics that focuses on the relationships between triangles' sides and angles. It requires studying the trigonometric functions that link the angles and side lengths of a triangle, such as sine, cosine, and tangent.

Rules towards each statement:

                                                                 Statements

Rule1.     Cos x/ Sin x (Sec 2x - 1)             Pythagorean identity

Rule2.    Cos x/Sin x (Tan 2x)                  Algebra

Rule3.    Cos x/Sin x (Sin 2x/Cos 2x)       Reciprocal

Rule4.    Sin x/Cos x                                 Odd/ Even

Rule5.    Tan x                                           Quotient

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The probability of each of the events of {at most three lines are in use}, {fewer than three lines are in use}, {at least three lines are in use, {between two and five lines, inclusive, are in use}, {between two and four lines, inclusive, are not in use} and {at least four lines are not in use} are 0.70, 0.45, 0.55, 0.80, 0.35 and 0.40 respectively.

The problem involves finding probabilities of different events for a mail-order company with six telephone lines. The probability mass function (pmf) is given, and we use it to calculate the probabilities of different events such as "at most three lines are in use" or "between two and five lines, inclusive, are in use".

To calculate these probabilities, we use basic probability formulas such as the addition rule, subtraction rule, and the complement rule.

P(X ≤ 3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70

P(X < 3) = 0.10 + 0.15 + 0.20 = 0.45

P(X ≥ 3) = 1 - P(X < 3) = 1 - (0.10 + 0.15 + 0.20) = 0.55

P(2 ≤ X ≤ 5) = P(X ≤ 5) - P(X < 2) = (0.10 + 0.15 + 0.20 + 0.25 + 0.20) - 0.10 = 0.80

P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.20 = 0.65, so P(2 ≤ X ≤ 4)ᶜ = 1 - 0.65 = 0.35

P(X ≥ 4) = 0.20 + 0.05 + 0.05 = 0.30, so P(X ≤ 3) = 1 - P(X ≥ 4) = 0.70 - 0.30 = 0.40

These formulas are applied based on the given events to determine the probabilities.

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Step-by-step explanation:

7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd

Answer:

A. To find the derivative of h(x), we can use the chain rule:

h(x) = a(-2x + 1)^5 - b

h'(x) = a * 5(-2x + 1)^4 * (-2) = -10a(-2x + 1)^4

To find the second derivative, we can again use the chain rule:

h''(x) = -10a * 4(-2x + 1)^3 * (-2) = 80a(-2x + 1)^3

B. To show that h is monotonic, we need to show that h'(x) is either always positive or always negative. Since h'(x) is a multiple of (-2x + 1)^4, which is always non-negative, h'(x) is always either positive or negative depending on the sign of a. If a > 0, then h'(x) is always negative, which means that h(x) is decreasing. If a < 0, then h'(x) is always positive, which means that h(x) is increasing.

C. To find the critical points, we need to find where h'(x) = 0:

h'(x) = -10a(-2x + 1)^4 = 0

-2x + 1 = 0

x = 1/2

Thus, the critical point is at x = 1/2. This value is independent of a and b, as neither a nor b appear in the calculation of the critical point.

The required average density of the giant envelope is equal to 3.30 x 10^9  kg/m^3.

Average density of the giant's envelope, required the mass and volume of the envelope.

Let us assume that the giant is a sphere with a radius of 0.6 AU,

the volume of the envelope is ,

V = (4/3)πr³

  = (4/3)π(0.6 AU)³

  = (4/3)(3.14)(0.6 × 149.6 ×10⁶ )³

To convert this volume to units of cubic meters,

Multiply by the conversion factor by,

1 AU = 149.6 x 10⁶m

⇒1 AU³ = (149.6 x 10⁶ km)³

⇒1 AU³ = 3.35 x 10³³ m³

Now ,calculate the density of the giant's envelope using the formula,

density = mass / volume

Giant's envelope has a mass of 0.5 solar masses,

which is equivalent to,

M = 0.5 x 1.99 x 10³⁰ kg

   = 9.95 x 10²⁹ kg

Average density of the giant's envelope is equals to,

⇒ density = 9.95 x 10²⁹ kg / (4/3)(3.14)(0.6 × 149.6 ×10⁶ )³

                = 3.30 x 10^9 kg/m^3

Therefore, the average density of the giant's envelope is approximately 3.30 x 10^9  kg/m^3.

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Answer:

k = -5

Step-by-step explanation:

According to the Remainder Theorem, when we divide a polynomial f(x) by (x − c), the remainder is f(c).

Therefore, if we divide polynomial f(x) = x³ + kx + 9 by (x - 2) and the remainder is 7 then:

To find the value of k, simply substitute x = 2 into the function, equate it to 7 and solve for k.

[tex]\begin{aligned}f(2)=(2)^3 + k(2) + 9 &= 7\\8+2k+9&=7\\2k+17&=7\\2k&=-10\\k&=-5\end{aligned}[/tex]

Therefore, the value of k is -5.

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