Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range

Answer:

x = 8

y = -3

Step-by-step explanation:

Multiply the first equation with (-2)

(-2) * (x - 4y) = 20

-2x + 8y = -40 now find the sum of it with second equation

2x + 5y - 2x + 8y = 1 - 40 add like terms (2x will eliminate -2x)

13y = -39 divide both sides by 13

y = -3

Now we can use this to find the value of x

x - 4y = 20 rewrite the equation using the value we found for y

x - 4(-3) = 20 multiply (-4) and (*3) (product will be positive because we are multiplying two negatives)

x + 12 = 20 subtract 12 from both sides

x = 8

Answer: d. 40 pounds

Step-by-step explanation: let e equal the number of pounds weigh on Earth and m equal the number of pounds weighs on Mars.

so

72m=180e

1m= 72m/72

e= 180/72 = 2.5

1m=2.5e

16m=1 x16

e= 16 x 2.5

e= 40

so therefore, 16m=40e

I hope this helps

The second-order equation as its equivalent system of first-order equations is

[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]

An equivalent system that has the identical answer is known as an equivalent structure. Given a gadget of two equations, we can produce an equal system by way of replacing one equation by means of the sum of the 2 equations, or by way of changing an equation by means of a couple of of itself.

Systems of linear equations are equivalent if and handiest in the event that they have an equal set of solutions. In other phrases, two systems are equal if and only if each answer of one in all of them is likewise a solution of the opposite.

In the structures sciences, a machine equivalent system is the conduct of a parameter or thing of a machine in a way just like a parameter or component of a distinctive system. Similarity means that mathematically the parameters and additives will be indistinguishable from each different.

Taking v = u, we have:

u" + 4u' + 6u = 4sin(3t)

--> v' + 4v + 6u = 4sin(3t)

So the system of equations is:

u' = 0u + 1v

v' = -6u - 4v + 4sin(3t)

So we can write it as:

u(1) = 7.5

v(1) = u'(1) = 9

So the initial condition matrix is:

[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]

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The sum of the given series is 49 and it converges to infinity.

According to the statement

we have given that a series which is 7, -8, 64/7, 512/49

And we have to find that the series is converges or diverges.

So, For this purpose,

The nth term in the series is 6 multiplied by the (n-1)th power of -8/7:

So,

[tex]a_{1} = 7(\frac{-8}{7} )^{1-1}[/tex]

[tex]a_{2} = -8(\frac{-8}{7} )^{2-1}[/tex]

[tex]a_{3} = \frac{64}{7} (\frac{-8}{7} )^{3-1}[/tex]

And so on then

Sum of the series become to the nth partial sum

[tex]S_{N} = 7(1 +\frac{-8}{7} + ......+ (\frac{-8^(n-2)}{7^(n-2)}) + (\frac{-8^(n-1)}{7^(n-1)}))[/tex]

Multiplying both sides by -8/7 gives

[tex]\frac{-8}{7} S_{N} = 7(\frac{-8}{7} +\frac{-8^{2} }{7^{2}} + ......+ (\frac{-8^(n-1)}{7^(n-1)}) + (\frac{-8^n}{7^n}))[/tex]

and subtracting this from [tex]S_{N}[/tex] gives

[tex]\frac{-1}{7} S_{N} = 7(1-\frac{-8^n}{7^n} )[/tex]

[tex]S_{N} = 49 (-1 + (8/7)^n)[/tex]

Now the sum of the series is 49 and the it converges to infinity.

So, The sum of the given series is 49 and it converges to infinity.

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the expression is simplified to give - 39

Given the expression;

= 24- 4 to the power of 2 x 3+15

= 24 - (4^2 × 3 ) + 15

First, expand the bracket

= 24 - ( 16 × 3) + 15

Find the product of the bracket

= 24 - 48 + 15

From our knowledge of BODMAS, we add before we subtract

Now, let's add first

= 24 - 63

The, subtract

= - 39

The expression is simplified to - 39

Thus, the expression is simplified to give - 39

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Answer:

Use this equation to find out!

Step-by-step explanation:

Since you didn't specify the n-gon, you have to use this equation to find out!

Number of Diagonals = n(n-3)/2

Hope this helps! :)

The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.

According to the statement

we have given that the property of the hypotenuse of the triangle and we have to complete it.

So, For this purpose, we know that the

A hypotenuse is the longest side of a right-angled triangle, and The length of the hypotenuse can be found using the Pythagorean theorem.

Now we discuss about the properties of the hypotenuse;

And from these properties we have to complete the given property.

So, The Hypotenuse is the Longest side of right triangle; side Opposite from the right angle.

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Answer:

(a + b)(a + b - 2)

Step-by-step explanation:

(a + b)² - 2(a + b) ← factor out (a + b) from each term

= (a + b)(a + b - 2)

The probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.

Given A)Number of green marbles=5,number of red marbles=3, number of blue marbles=4,

B) Number of peaches=7,number of apples=3,

C) Number of red token=10, number of blue token=6,green tokens=4,

D)Number of golf balls=13, number of tennis balls=2.

We are required to find the following probabilities:

A) Probability of getting red marble=Number of red marbles/ Total marbles.

=3/12

=1/4

=0.25

B) Probability of getting peaches=Number of peaches/Total fruits.

=7/10

=0.7

C) Probability of getting green tokens=Number of green tokens/Total tokens

=4/20

=1/5

=0.2

D)Probability of getting golf balls= Number of golf balls/ Total balls.

=13/15

=0.867

The sequence will be from C-A-B-D.

Hence the probability of getting red balls is 0.25, probability of getting peaches from fruits is 0.7, probability of getting green tokens is 0.2, probability of getting golf balls is 0.867.

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Solving a linear equation, we will see that after 9 days he cuts the last section.

We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.

So, the length as a function on the number of days, is:

L(x) = 20m - 2m*x

Here we just need to solve:

L(x) = 2m

Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).

Solving that, we get:

20m - 2m*x = 2m

20m - 2m = 2m*x

18m/2m = x = 9

After 9 days he cuts the last section.

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Using a proportional relationship, it is found that the unit rate of change is of 9.

The relation d = 9t is graphed at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, we have d as a function of t, hence the relationship is:

d = kt.

When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:

k = d/t = 1.8/0.2 = 9

The relation d = 9t is graphed at the end of the answer.

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Answer:

10/13

Step-by-step explanation:

There are 52 cards in a standard deck. There are 4 queens (queen of spades, clubs, hearts, diamonds) and 36 (2 - 10 of four suites) number cards. Therefore the probability of drawing a queen or a number card is (4 + 36)/52 = 40/52 = 10/13.

Answer: 8:3

Step-by-step explanation:

360:135

We can simplify both, dividing both of them by a common divisor (45)

360/45= 8

135/45= 3

The ratio in lowest terms is 8:3

the ratio of girls to boys in the school, expressed in the lowest terms, is 8:3.

To find the ratio of girls to boys in the school, we divide the number of girls by the number of boys.

Ratio of girls to boys = Number of girls / Number of boys

Ratio of girls to boys = 360 / 135

To express the ratio in the lowest terms, we can simplify the fraction by finding the greatest common divisor (GCD) of 360 and 135 and then dividing both the numerator and denominator by the GCD.

The GCD of 360 and 135 is 45.

Ratio of girls to boys = (360 / 45) / (135 / 45)

Ratio of girls to boys = 8 / 3

So, the ratio of girls to boys in the school, expressed in the lowest terms, is 8:3. This means that there are 8 girls for every 3 boys in the school.

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Answer:

The total selling price for the parcel is 1,524,600 dollars.

Step-by-step explanation:

We are given that 10 acre parcel was sold for $3.50.

First we need to figure out how many square foot is in 10 acres.

when we convert 10 acres we get 435600 square feet.

Since we know that parcel was sold for $3.50 per square foot we simply multiply 435600 by 3.5 = 1,524,600

The computation shows that the total distance will be 260.52km.

From the information given, it was stated that the race has 78 laps through the town of Monte Carlo and that each lap of the race has a distance of 3.34 km.

Therefore, the total distance will be:

= 78 × 3.34

= 260.52 km

Therefore, the distance is 260.52km.

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Answer:

$0.17425/Km

Step-by-step explanation:

8.5L/100Km*$2.05/L

= $0.17425/Km

Answer:

5

Step-by-step explanation:

y^1 = 5^1 (y = 5)

Anything raised to the power of 1 is just itself.

So, 5^1 = 5

The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.

To find the total surface area of the 27 blocks:

A cube's surface area

Given that the box's side length is 15 inches:

Surface Area of 3-inch side length blocks:

Surface Area of 4-inch side length blocks:

Surface Area of 5-inch side length blocks:

Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.

To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:

So,

The side length of the blocks is 5 inches.

The total surface area of the 27 blocks is 4050 square inches.

This is 3 times the surface area of the box.

Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.

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The height of the tree and the building are 7.6 m and 28.6 m respectively.

An equation is an expression that shows the relationship between two or more variables and numbers.

Two triangles are similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Triangle BGD, CHD and AFD are similar triangles.

CH = 1.6, DH = 8, GH = 30,  GF = 105

FH = GF + GH = 105 + 30 = 135

FD = FH + DH = 135 + 8 = 143; GD = 30 + 8 = 38

Hence, using similar triangles:

BG/CH = GD / DH

BG / 1.6 = 38/8

BG = 7.6 m

Also:

building/CH = DF / DH

building / 1.6 = 143/8

building = 28.6 m

The height of the tree and the building are 7.6 m and 28.6 m respectively.

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Answer: Vertical: angles ABF and DBE. Adjacent: angles ABC and CBD

Step-by-step explanation:

vertical angles are angles that share a common point. they are right across from each other, and in this case, share point B. adjacent angles are angles that are directly next to each other, and share a line or segment. in this case, the two angles share the segment BC. hope this helps.

The value of x from the given diagram is -10

Two triangles are known to be similar if the ratio of their similar sides is equal. The diagram shown is similar to the required diagram.

Given the following parameters

<ABC = 2x

<BAC = 3x + 10

Equate the expression since both angles are equal. Substitute;

2x = 3x + 10

Subtract 3x from both sides

2x-3x = 3x-3x+10

-x = 10

x = -10

Hence the value of x from the given diagram is -10

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The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

For given question,

We have been given a function g(x) = 4x / (x² + 2x - 3)

We need to find a power series for the function, centered at c, for c = 0.

First we factorize the denominator of function g(x), we have:

[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]

We can write g(x) as,

[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]

We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1

and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex]  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex]     if |x| < 1 and  if [tex]|\frac{x}{6}| < 1[/tex]

[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1

Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]

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Answer:

x - 4 = 2y

Step-by-step explanation:

"four less than a number x" therefore; x - 4

"is twice another number y" therefore; 2y

Answer:

9

Step-by-step explanation:

when you divide 576 by 9 you get 64 which is a perfect cube

cbrt(64) = 4

so your answer is 9

The length of the bedroom exists at x = 9 and y = 6.

From the given information, we get

Then  [tex]$\frac{(1/4)}{(9/4)} = \frac{1}{x}[/tex]

Solve this for x.

simplifying the value of x we get

Equate (1/9) to 1/x.

x = 9 (feet).

Convert 1.5 inches to feet using a proportion:

[tex]$\frac{(1/4)}{(1.5)} = \frac{1}{y}[/tex]

Solve this for y.

simplifying the value of y we get

(1/4)y = 3/2

Multiply both sides of the equation by 4.

y = 6

Therefore, the length of the bedroom exists at x = 9 and y = 6.

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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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Answer:

Step-by-step explanation:

For missing hypotenuse: [tex]\sqrt({a^{2} + b^{2})[/tex]

Plug in the side lengths that are known to find the hypotenuse.

1. No, the angle is less than 18 degrees (closer to 15), so it is not safe

2. The length rounded to the nearest tenth is approximately 15.5 feet.

Using proportions, it is found that:

A. The vegetables weigh 66 pounds.

B. 0.5 pints are dispensed after 25 seconds.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

4 and 1/8 pounds is equivalent to 4.125 pounds. Since each pound has 16 ounces, the weight of the vegetable is of:

W = 16 x 4.125 = 66 pounds.

Every second, 0.16 gallons are dispensed. Hence the amount dispensed in 25 seconds is:

A = 25 x 0.16 = 4 gallons.

Each gallon has 8 pints, hence the number of pints dispensed is:

4/8 = 0.5 pints.

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