A star system with more than 2 but less than a million stars. which type of star system is pictured?

For function g(x, y) = 9x² + 6y²,

the absolute minimum is 15 and the absolute maximum is 303

For given question,

We have been given a function g(x, y) = 9x² + 6y² subject to the constraint −1≤x≤1 and −1≤y≤7

We need to find the absolute maximum and minimum values of the function.

First we find the partial derivative of function g(x, y) with respect to x.

⇒ [tex]g_x=18x[/tex]

Now, we find the partial derivative of function g(x, y) with respect to x.

⇒ [tex]g_y=12y[/tex]

To find the critical point:

consider [tex]g_x=0[/tex]        and      [tex]g_y=0[/tex]

⇒         18x = 0         and      12y = 0

⇒          x = 0           and       y = 0

This means, the critical point of function is (0, 0)

We have been given constraints −1 ≤ x ≤ 1 and −1 ≤ y ≤7

Consider g(-1, -1)

⇒ g(-1, -1) = 9(-1)² + 6(-1)²

⇒ g(-1, -1) =  9 + 6

⇒ g(-1, -1) = 15

And g(1, 7)

⇒ g(1, 7) =  9(1)² + 6(7)²

⇒ g(1, 7) = 9 + 294

⇒ g(1, 7) = 303

Therefore, for function g(x, y) = 9x² + 6y²,

the absolute minimum is 15 and the absolute maximum is 303

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Volume=80cubic feet

Length×Width×Height =80cubic feet

Base area×Height =80cubic feet

25square feet×Height =80cubic feet

Height =80÷25

=3.2feet

The height of the rectangular prism is 3.2 feet.

To determine the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet,

The volume of a rectangular prism, that is V = lwh, where l is the length, w is the width, and h is the height of the prism.

Given:

Volume (V) = 80 cubic feet

Base area (A) = 25 square feet

We know that the base area is equal to the product of the length and width:

A = lw.

Calculate the length (l) and width (w) from the given base area:

We know that A = lw, and A = 25 square feet.

If we assume the length to be greater than the width, we can express the base area as lw = 25.

We need to find two factors of 25 that have a difference as small as possible. The factors of 25 are 1, 5, and 25.

We can choose l = 5 feet and w = 5 feet.

V = lwh.

80 = 5 * 5 * h

Divide both sides of the equation by 25:

80/25 = h.

h = 16/5 = 3.2 feet.

Therefore, the height of the rectangular prism is 3.2 feet.

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The improper fraction is 25 / 6 hours

The mixed fraction is  [tex]4\frac{1}{6}[/tex] hours.

The time is written as a decimal. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.

A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is greater than the denominator.

In order to convert 4.6 hours to a mixed fraction, the proper fraction has to be determined. To determine this value, multiply 0.6 by the minutes in an hour

0.6 x 60 minutes = 10 minutes

The decimal becomes : [tex]4\frac{10}{60}[/tex] hours

[tex]4\frac{1}{6}[/tex] hours

To convert the mixed fraction to an improper fraction, multiply the denominator by the whole number and add the numerator, then divide by the denominator

The improper fraction is : 25 / 6 hours

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7.1 cm  long is the arc intersected by a central angle .

What is length of an arc?

Given,

Central angle = π / 2

radius = 4.5 cm

we apply formula of length of arc.

length of the arc = angle ×  radius

                              = (π/2) × (4.5 cm)

Now put value of π = 3.14

length of the arc = (3.14 / 2) × (4.5) cm

                            = 7.065 cm ≈ 7.1 cm

Therefore, 7.1 cm  long is the arc intersected by a central angle .

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The power series  is

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence

The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.

Its radius of convergence is 0.5

Let,

f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....

The power series expansion (geometric series),

valid for I2xI < 1 , IxI < 0.5

so, radius of convergence = 0.5

The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5

Now, g(x) = ln(1-2x)

= -2 [tex]\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx[/tex]

=-2 [tex]\int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx[/tex]

g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....

is the power series expansion for g(x).

radius of convergence =0.5

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The question given is incomplete. Completed question is given below the answer.

The set,  {(x, y)|9<x2+y2<25} is open and connected.

The following set, {(x, y)|9<x2+y2<25} is:

A. is open (all points of the set are interior)

B. is connected (since it can not be divided into parts)

C. it is not simply connected (it has holes)

D. False, according to the previous answers

Open Set:

In mathematical terms, a set is said to be open if all its points are interior.

That is to say, no point that belongs to the border of the set or is isolated belongs to the set.

Determine the qualities of the given set. (Select all that apply.)

{(x, y)|9<x2+y2<25}

A. open

B. connected

C. simply connected

D. none of the above

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The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.

The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.

The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.

Consequently, solving the system of equations by means of substitution, we have;

y = (30.50-4x)/5

Hence, we have;

11x + 14((30.50-4x)/5) = 84.50

x = 4.5 pounds of meat and

y = 2.5 pounds of cheese.

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Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].

Flux is the presence of a pressure field in a detailed physical medium or the glide of electricity through a surface. In electronics, the term applies to any electrostatic field and any magnetic subject. Flux is depicted as "traces" in a plane that contains or intersects electric powered fee poles or magnetic poles.

The definition of flux is a flow of liquid from the body, or a regular movement or exchange. An instance of flux is diarrhea. An example of flux is an ever-converting list of the responsibilities of a particular process. regular or frequent alternate; fluctuation.

Flux is a go-platform computer program that adjusts a show's color temperature in keeping with vicinity and time of day, offering practical respite for the eyes. the program is designed to reduce eye stress at some stage in night-time use, supporting reducing the disruption of sleep patterns.

Our field is IR^3 be,

F= (bz-cy,cx-az,ay-bx)

Now divergence theorem says that Flux can be calculated by

[tex]\int\limits^ {} \, F.n = \int\limits^ {} \,( c.F) dv[/tex]

Now let's calculate the divergence of a vector field

F = (ia/ax + ja/ay + k*a/az)*((bz-cy)i+((x-dz))+(ay-bx)*k)

a/ax(bz-cy)+a/ay(cx-az)+a/az(ay-bx)

= 0+0+0

=0

Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].

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Step-by-step explanation:

she increased the amount from 48g to 54g. that is 54-48 = 6g.

so, the question really is, how many % of 48 is 6 ?

100% = 48g

1% = 100%/100 = 48/100 = 0.48g

how many % are 6g ?

as many as how often 1% (0.48g) fits into 6g :

6 / 0.48 = 12.5%

Answer:

Y = 2+- square root of 6

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Lets solve ~

Let's calculate its discriminant ~

[tex]\qquad \sf  \dashrightarrow \: {y}^{2} -4y - 2=0[/tex]

[tex]\qquad \sf  \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = (-4) {}^{2} - (4 \times 1\times - 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 16 - ( - 8)[/tex]

[tex]\qquad \sf  \dashrightarrow \: d = 24[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt {d }= 2 \sqrt{6} [/tex]

So, by quadratic formula :

[tex]\qquad \sf  \dashrightarrow \: y= \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \dfrac{ - {(-4)}^{} \pm 2\sqrt{6} }{2 ×1} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:y=\pm \cfrac{2(2\pm\sqrt{6} }{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \:y= { 2+\sqrt{6}}{} \: \: and \: \: t = {2-\sqrt{6}}{} [/tex]

The mark on the tape measure that is closest to 3.16228 is 3.1875

The measurement is given as:

Length = 3.16228

The tape measure is marked in sixteenths of an inch i.e 1/16 or 0.0625

So, we have the following range:

0.0625, 0.125, 0.1875, 0.25,.....

Rewrite the range as follows:

3.0625, 3.125, 3.1875, 3.25,.....

The length 3.1622 is between 3.125 and 3.1875.

The difference between the measurement and the range is

3.16228 - 3.125 = 0.03728

3.1875 - 3.16228 = 0.02522

0.02522 is smaller than 0.03728

Hence, the mark on the tape measure that is closest to 3.16228 is 3.1875

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Complete question

The length of tile B 3.16228 is about inches. Which mark on the tape measure is closest to 3.16228 inches? Remember, the tape measure is marked in sixteenths of an inch.

If (x+5) is a factor of f(x) then the condition that will be true is f(-5)=0.

Given that (x+5) is a factor the polynomial f(x) and we are required to be the condition that will be true.

Polynomial is combination of algebraic terms may be in addition, subtraction, multiplication and division. If the highest power of variable in polynomial is one then it is said to be monomial ,If the highest power of variable in polynomial is two then it is said to be binomial,If the highest power of variable in polynomial is three then it is said to be trinomial and many more polynomials.

Factors are the numbers which when multiplied gives the number whose factors they are.

It is given that (x+5) is a factor of f(x).

Put (x+5)=0

x=-5

means when we are putting x=-5 then we will get 0.

Hence if (x+5) is a factor of f(x) then the condition that will be true is f(-5)=0.

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The expression has 2 factors, and the second factor has 2 terms.

We can write an expression of N factors as:

[tex]y = A_1*A_2*...*A_n[/tex]

Here, the expression is:

4*(8x + 5)

This expression has 2 factors, which are:

4 and (8x + 5)

Now, if we look at the only factor 8x + 5, we have two terms (the terms are the parts that are added), the terms are:

8x and 5.

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Answer: Statistical

Step-by-step explanation:

I think its statistical because its quantitative data, meaning you can count it.

When a detailed scoring guide or rubric is used to score open-ended questions, the result is scored.

The scoring guide assign points to special degrees of student performance. Instructors use them when a scholar's response can earn a number of the full possible factors, commonly for built-reaction items and performance responsibilities.

Rubrics and scoring guides were implemented into cutting-edge classrooms to offer college students higher know-how of what's being assessed, what standards grades are primarily based upon, and what clean and compelling product standards are addressed.

Even as scoring guides illustrate how college students can earn a certain amount of points for precise questions and responses, rubrics assign ratings primarily based on how well a pupil's reaction meets a degree of overall performance.

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Using the volume for rectangular prisms, the volume of the chimney is: 216 in.³.

The volume of a rectangular prism = (length)(width)(height).

The Chimney in Emily's house is a composite solid consisting of two rectangular prism. To find the volume, we have to decompose the figure into two rectangular prisms. Then solve for the volume of each before finding the total volume.

Volume of the bigger rectangular prism = (length)(width)(height) = (4)(4)(12)

Volume of the bigger rectangular prism = 192 in.³

Volume of the smaller rectangular prism = (length)(width)(height) = (4)(2)(3)

Volume of the smaller rectangular prism = 24 in.³

The volume of the chimney = volume of the two rectangular prism

The volume of the chimney = 192 + 24

The volume of the chimney = 216 in.³

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The variable that you would have to plot on the y axis (height) is the dependent variable while the variable that is on the x axis (arm span) is the independent or the explanatory variable.

The slope was gotten through the use of the points  (37,39) and (19,25)

This gave the slope of 7/9. This tells us that  height of the person got to be raised by 7/9 inches when arm span increases by 1 inch.

From the given model, a person that has the arm span of 66 would have the height of

12 + 7/9 * 66

= 63.3 inches

A person who is  74 inches height the arm span of = 62*9/7

= 79. 71 inches.

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The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.

According to the statement

we have given that the Uan zhang bought a 10-year bond that pays 8. 25 percent interest per 6 months.

And we have to find that the yield to maturity on this bond.

So, For this purpose,

The amount given is $911. 10.

Years to maturity = n = 10

Coupon rate = C = 8.25%

Semiannual coupon = $1,000 × (0.0825/2) = $41.25

Yield to maturity = i

Present value of bond = PB = $911.10

Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.

Try YTM = 9.4%:

= $522.90 + 391.54 ≅ $914.43

The YTM is approximately 9.66 percent. Using a financial calculator provided an exact YTM of 9.656 percent (2 × 4.828%).

So, The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.

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The length of the rectangle is 77cm.

According to the statement

we have given that the area of a painting is 4081 c m squared. and width of the painting is 53 cm.

And we have to find the Length of the painting.

So, For this purpose

Area of rectangle is the region occupied by a rectangle within its sides. It depends on its sides.

So, the formula to find the area of rectangle is

Area = Length*Breadth

4081 = L*53

L = 4081/53

L = 77 cm.

So, The length of the rectangle is 77cm.

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The volume of a solid is  [tex]\frac{26}{3} \pi[/tex].

Given

The given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis

Curve is y = x + 1

Line is y = 0

We have to find out the volume v of the solid obtained by rotating the region bounded by these curves.

If the region bounded above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is revolved about the x-axis, the volume V of the generated solid is given by [tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]. We can also obtain solids by revolving curves about the y-axis.

Volume of a solid:

According to washer method:

[tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]

Using washer method, where a=0 and b=2, we get

V = [tex]\pi \int\limits^2_0 {(x+1)^{2} } \, dx[/tex]

= [tex]\pi[ \frac{(x+1)^{3} }{3} ]0 \ to \ 2[/tex]

= [tex]\pi [\frac{(3+1)^{3} }{3} -\frac{(0+1)^{3} }{3}][/tex]

= [tex]\pi [\frac{27}{3} -\frac{1}{3} ][/tex]

= [tex]\pi [\frac{26}{3}][/tex]

= [tex]\frac{26}{3} \pi[/tex]

Therefore the volume of a solid is  [tex]\frac{26}{3} \pi[/tex].

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Answer:

7.

Step-by-step explanation:

Calculate the means for each group:

mean of 0-4 is 2

mean of 5-9 is 7

mean of 10-14 is 12

Mean = (Sum of frequencies * mean) / sum of frequencies

= required mean = [ (2(2) + 1(7) + 2(12)] / (2+1+2)

=  35/ 5

= 7.

Answer:

Mean:36

Median:27

Mode:27

Range:50

Step-by-step explanation:

Mean: 19+26+27+27+30+53+69/7=36

Median: The middle number in the sequence when arranged in ascending order which is 27

Mode: The number that appeared more than others which is 27

Range: This is the difference between the largest number and the lowest number in the sequence which is 50.

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from 2007 to 2012 is only 5 years, so we can see this as a compound interest with a rate of 1.2% per annum for 5 years, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113505\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=113505\left(1+\frac{0.012}{1}\right)^{1\cdot 5}\implies A=113505(1.012)^5\implies A\approx 120481[/tex]

The required length of the hypotenuse of the triangle is √19.

To find the required length of the hypotenuse of the triangle:

Legs in the right triangle refer to the perpendicular and base.

Hypotenuse:

[tex]= \sqrt{perpendicular^{2}+base^{2} } \\= \sqrt{3^{2}+\sqrt{10^{2} } } \\=\sqrt{19}[/tex]

Therefore, the required length of the hypotenuse of the triangle is √19.

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Answer:

3,500 people

Step-by-step explanation:

10% of 35,000 is the same as .10 × 35,000, or 3,500.

Kathy has 22 more Euros than British pounds.

Linear equation is an algebraic equation that is a representation of the straight line. Linear equations are composed of variables and constants. These equations are of first-order, that is, the highest power of any of the involved variables i.e. 1. It can also be considered as a polynomial of degree 1. Linear equations containing only one variable are called homogeneous equations. The corresponding variable is called the homogeneous variables.

For instance,

300 / 2 = 150 dollars.

150 /1.64 = 91.46 British pounds

150 /1.32 =113.64 Euros

113.64 - 91.46 =22.18 ≅ 22

Thus Kathy has 22 more Euros than British pounds.

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Question 17: B. A’ (1,2), B’ (3,2), C’ (3,5)

Translating 4 to the right means that you should add 4 to the x value of your coordinate point.

Question 18: C. (3,-5)

This is because reflecting over the x-axis would mean to move down the same amount of units above the x-axis the original point is (the original point is five units above the x-axis so you just move down five units). Look at the attached picture for more help.

Question 19: A. C’ (0,-2)

We can see that the triangle has been translated 1 unit to the right and 2 units up. This would mean you add 1 to the x-value of the coordinate and add 2 to the y-value of the coordinate. I can’t see point C clearly, but I’m guessing that it’s at (-1,-4). This would give point C’ as (0,-2)

Hope this helps! Let me know if you need more help! Have a fantastic day!

The mean, median, and mode of the 5 number 5, 7, 8, a, b. are equal so

the possibilities of a+b is 20.

The" mean" is the" average" you are used to, where you add up all the figures and also divide by the number of figures.

The" median" is the" middle" value in the list of figures. To know the median, your figures have to be listed in numerical order from lowest to largest, so you may have to rewrite your list before you can find the median.

The" mode" is the value that occurs utmost often. However, also there's no mode for the list, If no number in the list is repeated.

Given numbers are: 5, 7, 8, a, b

Total number =5

Then,

The mean = (5+7+8+a+b) / 5

Mean=(20+a+b) / 5          ------------------ (1)

Median=middle value in the list of figures

Median=8                  ------------------(2)

According to the question ,mean and median  are equal

Compare equation (1) and (2),

we get

= (20+a+b) / 5=8  20+a+b

=40a+b=20

there is no repetition of any number, so no mode is there

hence, all the possibilities of a+b is 20.

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The correct option is option (d) 8 hours.

Amelia need to work for 8 hours to buy new sweater $40.

When two expressions are connected with the equals sign (=) in a math equation, it expresses the equality of the two expressions. A number that may be entered for the variable to produce a true number statement is the solution to an equation.

Let the hours Amelia need to work=h

Amalia paid=$20

Payment of each hour=$2.50

So, we can make an equation with given problem

40=20+2.50h

40-20=2.5h

20=2.5h

[tex]h=\frac{20}{2.5}[/tex]

h= 8

So, Amelia need to work for 8 hours to get $40.

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The probability of winning exactly 21 times is:-0.32

Given,

The probability of winning on an arcade game, p = 0.659

Number of times you play arcade game, n = 30

By assuming this as a normal distribution, we get

Mean=μ=30×0.659 =19.77

Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]

= [tex]\sqrt{30(0.659)(1-0.659)}[/tex]

≈ 2.60

Let X be a binomial variable

Then, the z score for x = 21 will be:

z = (x - μ) / σ = [tex]\frac{21-19.77}{2.60}[/tex]

≈ 0.47

Now, the probability of winning exactly 21 times

P (x ≥ z) = P (21 ≥ 0.47) = 0.32

Hence the probability of winning exactly 21 times is 0.32

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