homeroom 101 and homeroom 102 share a hallway bulletin board. if homeroom 101 uses 3/5 of their half to display artwork, what fraction of the bulletin board is used to display homeroom 101 artwork

Answer:

  54°

Step-by-step explanation:

The ratio values can be used to find the angles, then the desired difference can be found. Alternatively, the desired difference can be figured in terms of the ratio units given.

The number of ratio units representing the largest angle is 5. The number of ratio units representing the smallest angle is 2. The difference of these is 5 -2 = 3.

The total number of ratio units is 3 +2 +5 = 10. This is the number of ratio units representing the straight angle, 180°.

The difference is 3 of those 10 ratio units:

  3/10 × 180° = 54° . . . . . . largest - smallest difference

There are 10 ratio units in total (3+2+5=10), so each represents 180°/10 = 18°. Multiplying the given ratios by 18° gives the angle values:

  3×18° : 2×18° : 5×18° = 54° : 36° : 90°

The difference between the largest and smallest is ...

  90° -36° = 54° . . . . . . largest - smallest difference

The distance between the points (-8, -3) and (-2, -5) is √40 units

Using distance formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Therefore, using (-8, -3) and (-2, -5).

x₁ = -8

x₂ = -2

y₁ = -3

y₂ = -5

d =  √(-2 + 8)² + (-5 + 3)²

d = √(6)² + (-2)²

d = √36 + 4

d = √40

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The required order of the number from least to greatest square root is

1/√3 < √1 < √2 < √2.5

Which number is greatest in value:

In the above numbers 1, 1/3 and 2.5 do not have square roots.

So, we will write 1, 1/3 and 2.5 inside the square root as shown below.

√1 = 1

√(1/3) = 1/√3 = 0.577350269

√2.5 = 1.58113883

√2 = 1.414

Arranging these numbers according to their value, we get the order as-

0.577350269 < 1 < 1.414  < 1.581138831

Hence, the required order of the number from least to greatest square root is 1/√3 < √1 < √2 < √2.5.

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Answer:

8/3 or 2(2/3) Textbooks to storybooks

Step-by-step explanation:

Textbooks:  (8 books)*(12 rupees/book) = 96 rupees

Storybooks:  (4 books)*(9 rupees/book) = 36 rupees

Total is 132 rupees

Ratio:  Textbook/Storybook = 96/36

96/36 = 8/3 or 2(2/3) Textbooks to storybooks

The probability that all of the cards drawn are red is 0.0253.

A standard deck of playing cards has 52 cards.

Of the 52 cards, 26 of the cards are red cards.

When we draw the first card, the probability of getting red is 26/52.

When we draw the second card, the probability of getting red is 25/51.

When we draw the third card, the probability of getting red is 24/50.

When we draw the fourth card, the probability of getting red is 23/49.

When we draw the fifth card, the probability of getting red is 22/48.

Therefore, the probability of drawing 5 red cards without replacement is

= [tex]\frac{26}{52}* \frac{25}{51}* \frac{24}{50} *\frac{23}{49}* \frac{22}{48}[/tex]

= 26*25*24*23*22/52*51*50*49*48

= 0.0253

Therefore, we have found that the probability that all cards drawn are red is 0.0253.

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Answer:

27.7 m²

Step-by-step explanation:

     In regular polygon, all the sides and angles are equal. The polygon in the picture is a equilateral triangle.

 a = 8 m

 √3 = 1.732

   [tex]\sf \boxed{\bf Area \ of \ equilateral \ triangle= \dfrac{\sqrt{3}a^2}{4}}[/tex]

                                                       [tex]\sf =\dfrac{1.732 * 8 * 8 }{4}\\\\ = 1.732*2*8\\\\= 27.71\\\\= 27.7 \ m^2[/tex]

Answer:

1. Becky's rate of sales is 9 cups per hour

2. Mayisha's rate of sales is 10 cups per hour

3. Becky is selling 1 fewer cups per hour than Mayisha

4. Becky started with 2 fewer cups than Mayisha

Step-by-step explanation:

1. 30-12=18 18/2=9

2. 31-21=10 21-11=10

3. 10-9=1

4. 30+9=39 31+10=41 41-39=2

Answer:

Becky's rate of sales is [tex]\boxed{\sf 9}[/tex] cups per hour.

Mayisha's rate of sales is [tex]\boxed{\sf 10}[/tex] cups per hour.

Becky is selling [tex]\boxed{\sf 1\: fewer}[/tex] cup(s) per hour than Mayisha.

Becky started with [tex]\boxed{\sf 2}[/tex] fewer cups than Mayisha.

Step-by-step explanation:

Mayisha

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 31 & 21 & 11\\\cline{1-4} \end{array}[/tex]

Becky

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 30 & & 12\\\cline{1-4} \end{array}[/tex]

Selling at a steady rate.

To calculate the rate of sales, use the rate of change formula:

[tex]\sf Rate\:of\:change = \dfrac{change\:in\:y}{change\:in\:x}[/tex]

Therefore:

[tex]\textsf{Becky's rate of sales}=\dfrac{12-30}{3-1}=-9[/tex]

Therefore, as the number of cups reduces by 9 each hour, Becky's rate of sales is 9 cups per hour.

[tex]\textsf{Mayisha's rate of sales}=\dfrac{11-31}{3-1}=-10[/tex]

Therefore, as the number of cups reduces by 10 each hour, Mayisha's rate of sales is 10 cups per hour.

As 9 is one less than 10, Becky is selling 1 fewer cup(s) per hour than Mayisha.

As Becky had 30 cups left after 1 hour, and her rate of sales is 9 cups, then she started with 30 + 9 = 39 cups.

As Mayisha had 31 cups left after 1 hour, and her rate of sales is 10 cups, then she started with 31 + 10 = 41 cups.

As 39 is 2 less than 41, Becky started with 2 fewer cups than Mayisha.

Answer: 8r + 9.8s + 8.1

Step-by-step explanation:

   Given:

-(-8r-9.8s)+8.1

   Distribute:

   ↳ A - times a - becomes a +, a -times a + stays a -

8r + 9.8s + 8.1

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[tex]\textbf{Heya !}[/tex]

the denominators are equal, so subtracting these two fractions is a piece of cake:-

[tex]\sf{\cfrac{21}{15}-\cfrac{9}{15}}[/tex]

[tex]\sf{\cfrac{21-9}{15}}[/tex]

[tex]\sf{\cfrac{12}{15}}[/tex]

`hope it's helpful to u ~

The shortest possible time to perform the tasks is 30 minutes, these activities would be performed in this time by the couple made up of you and your aunt 1.

To calculate the shortest time to complete the wedding tasks, we must carefully observe the information in the table and identify the time that each person takes to complete the tasks. Subsequently, we must identify the people who take the shortest time, in this case it is you and your aunt 1 as shown below:

You

aunt 1

Additionally, we must subtract the two values, to know how long it will take in total for both people to perform the three required activities.

According to the above, the most efficient couple is your aunt 1 and you because you will take 30 minutes to complete the activities.

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Answer:

95 - 20[tex]\sqrt{15}[/tex]

Step-by-step explanation:

(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²

= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )

each term in the second factor is multiplied by each term in the first factor, that is

5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis

= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms

= 95 - 20[tex]\sqrt{15}[/tex]

Answer:

95 - 20√15

Step-by-step explanation:

I assume the expression is (5√3 − 2√5)^2 (?).

(5√3 − 2√5)*(5√3 − 2√5)

25√3^2 - 20√15 + 4√5^2

25*3 - 20√15 +4*5

75 - 20√15 +20

95 - 20√15

Answer:

3:4

Step-by-step explanation:

It's males to females. so we make 42:56 simplify that we get 3:4

Alex bought 24.75 gallons of paint to use for the house painting.

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

Let x represent the amount of paint bought by Alex, hence:

(1/3)x + 3/2 + 2(3/2) + 12 = x

X = 24.75 GALLONS

Alex bought 24.75 gallons of paint to use for the house painting.

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Answer: The domain is all real numbers, and the range is all real numbers greater than or equal to –4.

Step-by-step explanation:

The domain is the set of inputs, and the range is the set of outputs.

Answer: Option A

Step-by-step explanation

The domain is the set of allowed x inputs of a function.

We can replace x with any number we want to get some output for y = f(x)

This tells us the domain is the set of all real numbers.

-----------

The range is the set of numbers y such that

In other words, we can have y = -4 or y > -4

This is because y = -4 is the lowest output possible, as indicated by the vertex point.

The recursive definition of the geometric sequence is given as follows:

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The recursive definition of the geometric sequence is given as follows:

For this sequence, the first term and common ratio are given as follows:

[tex]a_1 = \frac{1}{9}, q = 3[/tex].

Then the recursive definition is:

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The symbolic representation for the given statement " If two angles are not congruent, then they have the same measure" is ~q → p. So, option A is correct.

It is given that,

p - "Two angles have the same measure"

q - "The angles are congruent"

Statement: " If two angles are not congruent, then they have the same measure"

So, symbolically it is written as,

The hypothesis "two angles are not congruent" is represented by ~q and the conclusion "they have the same measure" is represented by p.

That is,

The representation is "If ~q then p i.e., ~q → p. So, option A is correct".

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Answer:

[tex](f-g)(x)=x^2-6x+5[/tex]  dom: (-∞,∞)

[tex](\frac{f}{g})(x)=x-7+\frac{7}{x+2}[/tex] dom: (–∞,–2)u(–2,∞)

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)=(x^2-5x+7)-(x+2)[/tex] *distribute the negative sign into (x+2)!

[tex]x^2-5x+7-x-2\\x^2-6x+5[/tex]

a parabola (anything that begins with [tex]x^2[/tex]) will have a domain of (-∞,∞) or all real numbers!!

[tex](\frac{f}{g} )(x)= \frac{x^2-5x+7}{x+2}[/tex]      use synthetic division to divide (the attached picture)

domain: Because the graph is not continuous, you have to write the domains on both sides of the asymptote which is (-∞,-2)u(-2,∞)

synthetic division:

1. take the divisor (x+2) and solve for x.    x= –2 this goes in the top left corner

2. write the numbers AND their signs on the top row. if there is no number and just the variable (like [tex]x^2[/tex] ) just write 1.

3. the first number gets pulled down

4. multiply -2 by 1 and subtract it from –5. (-5-2= -7)

multiply -2 by -7 and add that to the next number in the top row which is -7. (-7 + 14=7)

5. the first number in the bottom row of numbers is the first number in the answer but with one less exponent than the dividend. **write 1 as x**

6. the last number in the bottom row, if it is not 0, is a remainder. write it as that number over the divisor. in this case the remainder is 7. so write it as [tex]\frac{7}{x+2}[/tex]

Using it's concepts, the domain and the range of the graph are given as follows:

In this graph, have that the function is defined for all values of x except x = -1, and assumes all real values, hence the domain and the range of the graph are given as follows:

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The number of employees is 91.

According to the statement

Given that the standard deviation = 24.5

The width in the question = 13

We solve for the margin of error E.

E = width / 2

E= 13/2 = 6.5

At 90%

Alpha = 1-0.90

= 0.1

Alpha/2 = 0.1/2 = 0.05

Z 0.05 = 1.576

Now find the Sample size n

= ((1.576x24.5)/2)²

= 90.8

= 91

So, The number of employees is 91.

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Some of the metrics that I would look at to determine whether or not a new feature will be successful are as follows:

It should be noted that metrics are the measures of quantitative assessment used for comparing, and tracking performance or production.

Metrics are heavily relied on in the financial analysis of companies to make decisions.

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The sum of the angles, a, b and c is; 360° because, the sum measures 3 of all the equal angles in the regular hexagon.

It follows from the task content that the angle measures given in the task are a, b and c which are in a cyclic polygon (hexagon) in which case, the sum of all 6 angles in the hexagon is; 720.

Consequently, the sum of angle measures; a,b and c is; 720/2 = 360°.

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Answer:

a. The free throw percentage obtained by the Lions is of 81.25%.

b. The free throw percentage for the Eagles was of 37.04%.

c. The field goal percentage for the Lions was of 56.01%.

d. The field goal percentage for the Eagles was of 34.43%.

e. The Lions scored 96 points.

f. The Eagles scored 64 points.

Solution:

a. The lions attempted 16 free throws and made 13, which means lions scored 13 out of 16,

The free throw percentage obtained by the Lions = [tex]\frac{13}{16}[/tex] × 100 = 81.25%

The free throw percentage obtained by the Lions is 81.25%

b. The eagles attempted 27 free throws and made 7 which means 7 out of 27, so:

The free throw percentage obtained by the eagles = [tex]\frac{7}{27}[/tex] × 100 = 25.92 %

The free throw percentage obtained by the eagles is 25.92 %

c. The lions attempted 51 two-point shots and made 22, and attempted 16 three-point shots and made 10.

Total attempted = 51 + 16 = 67

Total shots made = 22 + 10 = 32

The field goal percentage (two-point and three-point shots combined) for the Lions = [tex]\frac{32}{67}[/tex] × 100 = 47.76 %

The field goal percentage for the Lions was of 47.76 %.

d. The eagles attempted 41 two-point shots and made 19, and attempted 16 three-point shots and made 7.

Total attempted = 41 + 19 = 60

Total shots made = 19 + 7 = 26

The field goal percentage (two-point and three-point shots combined) for the eagles= [tex]\frac{32}{67}[/tex] × 100 = 43.33 %

The field goal percentage for the eagles was of 43.33 %.

e. Total goals secured by lions 13 free throws, 22 two's and 10 three's. So

Total points = 10 × 1 + 22 × 2 + 10 × 3 = 84

The Lions scored 84 points.

f. Total goals secured by eagles 7 free throws, 19 two's and 7 three's. So

Total points = 7 × 1 + 19× 2 + 7 × 3 = 66

The eagles scored 66 points.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

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The Surface Area of the sphere is 1017.16 unit^2.

what is the surface area of the sphere?

The surface area of the sphere is 4*pi*r^2.

where, r is the radius

Calculation :

given  radius is 9 units

putting value in the formula of the sphere

S(area)=4*pi*r^2

            =4*3.14*9^2

            =4*3.14*81

            =1017.16 UNIT^2

The Surface Area of the sphere is 1017.16 unit^2.

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The Surface Area of the sphere is 1017.16 unit^2.

The surface area of the sphere is 4*pi*r^2.

where, r is the radius

Calculation :

given  radius is 9 units

putting value in the formula of the sphere

S(area)=4*pi*r^2

           =4*3.14*9^2

           =1017.16 UNIT^2

The Surface Area of the sphere is 1017.16 unit^2.

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Using proportions, it is found that out of the next 1500 pizzas, she should expect 420 pan style pizzas.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The proportion of pan style pizzas is given as follows:

294/(284 + 313 + 159 + 294) = 0.28.

Hence, out of 1500 pizzas, this amount is equivalent to:

0.28 x 1500 = 420

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Answer:

d; y - 1 = 4/5(x + 2)

Step-by-step explanation:

the equation for a point-slope form line is y - y1 = m(x - x1)

plug in the points and you will get your answer

y - 1 = 4/5(x + 2)

that is your answer

The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.

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

Let a represent the speed of the airplane and b represent the speed of the wind, hence:

(a + b)6 = 2400  

a + b = 400     (1)

Also:

(a - b)7.5 = 2400

a - b = 320   (2)

From eqn 1 and 2:

a = 360 km/h, b = 40 km/h

The speed of the airplane is 360 km/h while the speed of the wind is 40 km/h.

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Using it's concept, any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].

The domain of a function is the set that contains all possible input values for the function.

Function [tex]y = 2\sqrt{x}[/tex] is defined for [tex]x \geq 0[/tex], hence any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].

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Beau can wrap 32 inches of ribbon outside the mirror.

Area of Beau Thai's mirror is 60 sq. inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Given information:

Length of mirror = 6 inches

Width of mirror = 10 inches

To Find:

The amount of ribbon Beau could wrap around the outside of the mirror.

Perimeter of the mirror = 2(6+10)

                                       = 2(16)

                                       = 32 inches

The area of Beau Thai's mirror.

Area of the mirror = 6*10

                              = 60 sq. inches

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Answer:

First, transform the given equation into the slope-intercept form, y = mx + b.

2x - 3y < 12

3y > 2x - 12

y > [tex]\frac{2}{3}[/tex]x - 4

Since the equation is y > [tex]\frac{2}{3}[/tex]x - 4, first draw the graph of y = [tex]\frac{2}{3}[/tex]x - 4 with a dotted line (because it is >, not ≥) and shade the area above the dotted line.

The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].

Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].

We are required to find the solution of the differential equation when y(0)=1.

dy/dx=[tex]2xy/(x^{2} -1)[/tex]

Taking y to left side and dx to right side.

1/y dy=2x/[tex](x^{2} -1)[/tex] dx

Integrating both sides.

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

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

Solving right side.

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

let [tex]x^{2} -1[/tex]=z

differentiating both sides with respect to x.

2x=dz/dx

2x dx=dz

Put 2x dx=dz in 1.

[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]

log y=log z+log c

Put z=[tex]x^{2} -1[/tex]

log y=log([tex]x^{2} -1[/tex])+log c

log y=log [{[tex]x^{2} -1[/tex])c]

y=([tex]x^{2} -1[/tex])c------------2

Put x=0 and y=1

1=(0-1)c

1=-c

c=-1

Put c=-1 in 2 to get the solution.

y=-1([tex]x^{2} -1[/tex])

y=[tex]-x^{2} +1[/tex]

Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is

y=[tex]-x^{2} +1[/tex].

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