A bag contains 5 red, 6 green, 7 yellow, and 8 blue jelly beans. A jelly bean is selected at random. What is the probability that it is blue?

Work Shown:

y = (4/5)x + 3

5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction

0 = 4x + 15 - 5y  ... subtract 5y from both sides

4x-5y+15 = 0 .... rearrange terms

The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.

Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.

Answer:

8 hopefully

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Answer:

A system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2

Step-by-step explanation:

The equation of the given line is 8·x - 4·y = 12

Which gives;

8·x- 12= 4·y

y = 2·x - 3

Given that the line passes through the points (0, -3) and (1, -1), we have;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we have;

[tex]Slope, \, m =\dfrac{(-1)-(-3)}{1-(0)} = 2[/tex]

y - (-3) = 2×(x - 0)

y = 2·x - 3 which is the equation of the given line

For the lines 8·x - 4·y = 12, which is the sane as y = 2·x - 3 and the line y = m·x  - 6 to have no solution, the slope of the two lines should be equal that is m = 2

Given that the line passes through the point (1.5, 0), we have;

y - 0 = 2×(x - 1.5)  

y = 2·x - 3...................(1)

For the equation, y = m·x  - 6, when m = 2, we have;

y = 2·x  - 6..................(2)

Solving equations (1) and (2) gives;

2·x - 3 = 2·x  - 6, which gives;

2·x - 2·x=  - 3 - 6

0 = 9

Therefore, a system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2.

Answer:

short answer is 2 or d

Step-by-step explanation:

Answer:

14130 yd^3

Step-by-step explanation:

The volume of a sphere is

V = 4/3 pi r^3

The diameter is 30 so the radius is d/2 = 30/2 = 15

V = 4/3 pi (15)^3

V = 4500 pi

Letting pi = 3.14

V = 14130 yd^3

Answer:

Last one

Step-by-step explanation:

The volume of the sphere is given by the relation:

V= [tex]\frac{4}{3}[/tex] *π* 15³

V= 14137.166 yd³

wich is approximatively 14130yd³

Answer:

0.007349 to 3 significant figure=0.00735

Step-by-step explanation:

Approximate 0.007349 to 3 significant figure

Significant figure start from 1 to 9 with the exclusion of 0

From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.

0.007349

The first significant number is 7 after 0

The second significant number is 3

The next

The third significant number is 4

The fourth significant number is 9

We want to approximate to three significant figure, so, all figure after 4(third significant figure) will be rounded up or down.

If the numbers are below 5(0, 1,2,3,4) they will be rounded down to 0

If the numbers are above 4(5,6,7,8,9), they will be rounded up to 1

So the number after 4 is 9, therefore it will be rounded up to make 4=5

0.007349 to 3 significant figure=0.00735

Answer:

start with -29, multiply each term by 4

start with 60, multiply each term by 0.1

start with 97 and multiply each term by 0.5

3.03 cells

Step-by-step explanation:

1. The first sequence begins with -29. -116 ÷ -29 = 4, -464 ÷ -116 = 4, etc. Each value is multiplied by 4 to get the next value.

2. The second sequence begins with 60. 6 ÷ 60 = 0.1, 0.6 ÷ 6 = 0.1, etc. Each value is multiplied by 0.1 to get the next value.

3. The colony starts with 97 cells. Splitting into two is the same as multiplying by 0.5.

4. Multiply 97 by 0.5, 5 times for 5 minutes.

97 · 0.5 · 0.5 · 0.5 · 0.5 · 0.5 = 3.03

Answer:

5 sqrt(5)

Step-by-step explanation:

sqrt(125)

sqrt( 25*5)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(25) sqrt(5)

5 sqrt(5)

Answer:

5√(5)

Step-by-step explanation:

Notice that 125 is 25×5

If you couldn't do it use the prime factorization.

Prime numbers are 2,3,5.....

125 isn't divisible by 2 and 3 so we'll go with 5.

● 125 ÷ 5 = 25

Againg 25 is divisible by 5

● 25÷5 = 5

5 is divisible by 5

● 5÷5=1

So 125= 5×5×5 = 5^2 × 5

● √(125)= √(5^2×5) = 5√(5)

Answer:

its harddd

Step-by-step explanation:

rightttttttt

Answer:

not perpendicular

Step-by-step explanation:

perpendicular line has opposite reciprocal slope

√3x-2√3 y=13

-2√3y=13-√3x

y=-13/(2√3)+√3 x/2√3

y=1/2 x-13/2√3  ( slope is 1/2)

6x-3y+11=0

-3y=-11-6x

y=-11/-3+6x/3

y=2x+11/3 slope =2

Answer:

The correct option is;

Because ∠MNL and ∠ONP are congruent angles

Step-by-step explanation:

From the diagram shown in the question, ∠MNL and ∠ONP are vertically opposite angles as they are formed by crossing of the lines LP and MO making them congruent, that is ∠MNL ≅ ∠ONP

Given that two angle of triangle LMN are congruent to two angles of triangle PON , then by the Angle Angle (AA) rule of similarity, triangle LMN and PON are similar.

The information in the diagram enough to determine that △LMN ~ △PON because∠MNL and ∠ONP are congruent angles.

These are referred to angles which have an equal measure. From the diagram ,vertically opposite angles are formed by crossing of the lines LP and MO thus,we can deduce that ∠MNL and ∠ONP are congruent angles.

This means that there is enough information to determine that △LMN ~ △PON using a rotation about point N and a dilation.

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Answer:

1. 900

2. 350

Step-by-step explanation:

the formula,

A= P(1+rt)

A= final amount

P= starting amount

r= intrest rate

t= time

1. A=750(1+.05*4)

A=750(1.2)

A=900

2. A=1500(1+.1*2)

A=1500(1.1)

A=1650

But theyre

asking for how much intrest will they get back, so you subtract the new amount by the starting amount to find how much intrest was earned

1650-1500=350

Answer:

4x^2 + 8x + 4

4(x^2 + 2x + 1) - remove GCF of 4

4(x + 1)(x + 1) - factor

4(x + 1)^2 - collect like terms

Step-by-step explanation:

Then also expand it out by distributing:

21x^3 + 35x²

Form 1:

21x^3 + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

Update:

You could also multiply two binomials and make a quadratic.

Example:

(7x + 2)(3x + 5)

7x(3x + 5) + 2(3x + 5)

= 21x² + 35x + 6x + 10

= 21x² + 41x + 10

The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

The polynomial will be solved as below:-

21x³ + 35x²

Form 1:

21x³ + 35x² - unfactored

Form 2:

7x²(3x + 5) - factored with GCF of 7x² brought to the front

You could also multiply two binomials and make a quadratic.

E = (7x + 2)(3x + 5)

E = 7x(3x + 5) + 2(3x + 5)

E = 21x² + 35x + 6x + 10

E = 21x² + 41x + 10

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Answer:

-2

Step-by-step explanation:

The slope formula is

m = ( y-2-y1)/(x2-x1)

Using two points on the line  (0,4) and  (2,0)

m = ( 0-4)/(2-0)

   = -4/2

  =-2

Answer:

-2

Step-by-step explanation:

Slope is change in y over change in x

the change in y is -2 and the change in x is 1 so you do -2/1 and that as a whole number is -2.

Answer:

3 seconds

Step-by-step explanation:

Given the function :

h(t) = 16t2 - 144.

h = height = 144 and t = time after t seconds the ball penny was dropped.

When the penny lands, h = 0

Therefore, our function becomes ;

16t2 - 144 = 0

The we can solve for t

16t^2 - 144 = 0

16t^2 = 144

Divide both sides by 16

(16t^2 / 16) = 144 / 16

t^2 = 9

Take the square root of both sides

t = 3

Therefore, the time between when the rock was dropped and when it landed is 3seconds

Answer:

t = 3 seconds

Step-by-step explanation:

Answer:

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

Step-by-step explanation:

x ^ 1.4

Rewriting the decimal as an improper fraction

x ^ 14/10

x ^ 7/5

The top is the power and the bottom is the root

[tex]\sqrt[5]{x^7}[/tex]

or (x ^ 1/5) ^7

or ([tex]\sqrt[5]{x}[/tex])^7

Answer:

The answer is C.

Step-by-step explanation:

In order to find the solution of the linear equation, you have to find the coordinates where they intersect.

So according to the graph, both lines intersect at the coordinates of ( 0 , 1 ).

(Correct me if I am wrong)

Answer:

8

Step-by-step explanation:

Let's denote the number of members ordered chicken a, the number of members ordered beef b.

We have:

a + b = 12 (total number of members is 12)

10a + 14b = 136 (the chicken costs 10$, the beef costs 14$)

a + b = 12 => a = 12 - b

Substitute a into second equation, we have:

10(12 - b) + 14b = 136

=> 120 - 10b + 14b = 136

=> 4b = 16

=> b = 4

=> a = 12 - b = 12 - 4 = 8

=> Number of members ordered chicken: a = 8

Answer:

([tex]\frac{3}{5}[/tex] b, 0 )

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

Here m = - [tex]\frac{5}{3}[/tex] and b = b , thus

y= - [tex]\frac{5}{3}[/tex] x + b ← equation of line

The line crosses the x- axis when y = 0, substitute y = 0 into equation and solve for x, that is

- [tex]\frac{5}{3}[/tex] x + b = 0 ( multiply through by 3 to clear the fraction )

- 5x + 3b = 0 ( subtract 3b from both sides )

- 5x = - 3b ( divide both sides by - 5 )

x = [tex]\frac{3}{5}[/tex] b , thus

x- intercept = ( [tex]\frac{3}{5}[/tex] b, 0 )

Answer:

( b, 0 )

Step-by-step explanation:

Answer:

1.1460277. Put in your decimal place given to you.

This is the percentage rate.

Step-by-step explanation:

f(x)=0=60100

55=120150

60100=a*b^0

120150/60100=60100/60100*b^5

b^5^(1/5)=5square root(120150/60100)=1.14860277

answer

-6r+-11=-37

-6r=-37+11

-6r=-48

r=8

Answer:

$32

Step-by-step explanation:

the skirt is on sale. 40 times 0.20 (because of 20 divided by 100) is 8. That means that the skirt is $32 since $40-$8=$32.

Answer:

$32

Step-by-step explanation:

discount is $8

Answer: [tex]f^{-1}(1)+f(-14)=20[/tex]

[tex]f^{-1}(-2)=10[/tex]  

Step-by-step explanation:

The given table :

x: -14,-7,-12,9,10,-2

f(x):11,-12,5,1,-2,13

Since f is invertible ( given) , then [tex]f^{-1}(x)[/tex]  exists.

Now , from table [tex]f^{-1}(1)=9[/tex]  [ x= 9 corresponding to f(x) =1]

[tex]f(-14)=11[/tex]                            [ f(x) = 11 corresponding to x=-14]

then, [tex]f^{-1}(1)+f(-14)=9+11=20[/tex]

So, [tex]f^{-1}(1)+f(-14)=20[/tex]

Also, x= 10 corresponding to f(x) =-2, then

[tex]f^{-1}(-2)=10[/tex]  

Answer:

1. r = 2.82 cm

h = 5.6 cm

The maximum volume possible to the nearest 10 mL = 140 mL

2. Size side of square base of box is 5.64 cm

Height of box = 5.6 cm

The surface area of the box is 189.96 cm²

The volume of the box is 178.13 cm³

3.  The procedure for solving the problem was through noting that the shape of the cross-section of the pyramid is an isosceles triangle ans also that smallest possible box for the pretty perfume is one which fits the angle of inclination of the lid. This was found out by initially using the combined height of the perfume and the lid (placed to fit the spherical outline of the bottle) to calculate the dimensions of the pyramid, from which it was observed that the angle of inclination of the lid is larger than that of the calculated dimension, such that the lid outline would be visible and could eventually tear the perfume box  

With the inclination angle, β, which is the base angle of the isosceles triangle, the angle at the top of the pyramid cross-section is calculated and the following relations are used to calculate the triangular cross-section of the pyramid

h = a·cos(α/2)

b = 2·a·cos(β)

[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]

[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]

With the calculated dimensions, a, b, and h the area, A, of the square pyramid is calculated as 2×b×a + b² and the volume, V, as 1/3×b²×h

The attached diagram shows the the cross-section of the perfume in the pyramid box.

Step-by-step explanation:

1. The surface area of the cylinder = 2πr² + 2πrh = 150 cm².........(1)

The volume of the cylinder, V = πr²h = 100 mL = 100 cm³..............(2)

From equation (2), h = 100/(π·r²)

Substituting the value if h in equation (1), we have;

2πr² + 2πr100/(π·r²) = 150

2πr² + 200/r = 150

(2πr³ + 200)/r = 150

2πr³ + 200 = 150×r

2πr³ -150·r+ 200 = 0

150 = 2πr² + 2πrh

h = (150 - 2πr²)/(2πr)

h = (75- πr²)/(πr)

Substituting the value of h in the equation for the volume, we have;

V = πr²h =  πr²(75- πr²)/(πr)

V = 75·r - π·r³

At maximum volume, dV/dr = 0, we have

d(75·r - π·r³)/dr = 75 - 3·π·r²= 0

3·π·r²= 75

π·r² = 25

r = 5√π/π

h = (75- πr²)/(πr) = (75- π(5√π/π)²)/(π(5√π/π)) = (75 -25)/(5·√π)

h = 50/(5·√π)= 10·√π/π

The maximum volume = πr²h = π×25/π×10·√π/π =  250·√π/π = 141.05 cm³

The maximum volume possible = 141.05 cm³ = 141.05 mL

The maximum volume possible to the nearest 10 mL = 140 mL

The dimensions of the bottle are;

r = 2.82 cm

h = 5.6 cm

The surface area of the bottle = 2π(2.82)² + 2π×2.82 ×5.6 = 149.2 cm

2

Given that the cylindrical bottle has r = 2.82 cm and h = 5.6 cm, we have;

Size side of square base of box = 2 × 2.82 = 5.64 cm

Height of box = 5.6 cm

The surface area of the box = 2 × Area of base + 4 × Area of side

The surface area of the box = 2 *5.64^2 + 4 * 5.6 * 5.64 = 189.96 cm²

The volume of the box = Area of base × Height = 5.64^2*5.6 = 178.13 cm³

3. Diameter of spherical bottle = 7 cm = 2×r

Volume of the sphere  bottle = 4/3πr³ = 4/3*3.5^3*π = 343/6·π = 179.6 cm³

The surface area of the sphere  bottle = 4πr² = 4*(7/2)^2*π = 49·π = 156.94 cm²

3 i. The volume of a cone = 1/3πr²h = 1/3*(5/2)^2*4.5 = 9.385·π = 29.45 cm³

The  surface area of a cone = πrS

S = √(4.5^2 + (5/2)^2) = 5.15

The  surface area of a cone = π*2.5*5.15 = 40.43 cm²

3 ii. The depth of fitness of the lid on the bottle = 7/2 - √(7/2)^2 - 2.5^2) = 1.05

The total height of the spherical bottle with the conical lid = 7 + 4.5 - 1.05 = 10.45 cm

3 iii. Given that the box is shaped like a pyramid we have;

Width of the box at middle of the height of the spherical bottle = 7 cm

Height of the box = 10.45 cm

[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]

[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]

With the aid of a graphing calculator, the width of the square pyramid is found to be 12.12 cm

The volume = 1/3*12.12^2*10.45 = 511.68 cm²

The surface area = 2*12.12*√(12.12/2)^2 + 10.45^2) +12.12²= 439.7 cm²

The angle of inclination of the lid = tan⁻¹ (4.5/2.5) = 60.95°

The angle of inclination of the calculated box is tan⁻¹ (10.45/6.06) = 59.88

Since the lid is steeper, we make use of the angle of the lid

The base angles are thus = 60.95°

The angle at the top is thus 180 - 60.95*2 = 58.11°

Therefore, by the formula, we find that

a = 12.25 cm

b = 11.897 cm

h = a·cos(α/2)

h = 10.707 cm

The volume = 1/3*11.897^2*10.707 = 505.15 cm³

The surface area = 2*11.897*√(11.897/2)^2 + 10.707^2) +11.897²= 432.98 cm²

The angle at the top of the box = 2

Given that:

Then the maximum volume possible to the nearest 10 mL =

Given that:

Hence, the surface area of the box is

The volume of the box is :

This refers to the measure of the total area of an object.

The procedural method used to solve the problem was to identify the shape of the pyramid, then finding out the smallest possible box for the pretty perfume and then using the calculated dimensions, found the answers.

Read more about surface area here:
https://brainly.com/question/76387

Answer:

The speed is 74.0 miles per hour and the angle is 65.1° north-east

Step-by-step explanation:

We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.

Since the wind is moving south east, it is at 45 south of east or a bearing of 135.

Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles

Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles

The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles

The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles

The total vertical displacement of the plane is 176.64 miles - 42.43 miles =   134.21 miles

The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles

The direction of this displacement is thus

Ф = tan⁻¹(total vertical displacement/total horizontal displacement)

= tan⁻¹(134.21/62.43)

= tan⁻¹(2.1498)

= 65.05°

= 65.1° to the nearest tenth degree.

The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.

So the speed is 74.0 miles per hour and the angle is 65.1° north-east

Answer:

x = 4

Step-by-step explanation:

The midsegment ( median is equal to half the sum of the parallel bases, that is

[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values

[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2

7x - 2 = 26 ( add 2 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

Answer:

27°

Step-by-step explanation:

arc RT = 66

1/2(120 - 66) = 27

Answer:

∠ U = 27°

Step-by-step explanation:

The inscribed angle S is half the measure of its intercepted arc, thus

arc RT = 2 × ∠ U = 2 × 33³ = 66°

The secant- tangent angle U is half the measure of the difference of the measures of the intercepted arcs, that is

∠ U = 0.5( RS - RT) = 0.5(120 - 66)° = 0.5 ×54° = 27°

Answer:

C

Step-by-step explanation:

In a function, each domain has one range. But a range can have many domains.

Think about it like this:

Patty is eating dinner

Patty is swimming

Both can't happen at the same time.

But:

Patty is eating dinner

Leo is eating dinner

C has two domains of -3, each having different ranges.

Hope that helps, tell me if you need further info. =)

Answer:

C. C{(6,-9),(-3,6),(-3,-7),(-9, -2)}

Step-by-step explanation:

If you see the same x-coordinate used more than once, it is not a function.

Here, you only see this in choice C, where x = -3 for two points. That makes this relation not a function.

Answer:

990 ways to choose 6 starters out of 14 with exactly two of the three triplets.

Step-by-step explanation:

Ways to choose 2 of the triplets

= C(3,2) = 3! / (2!1!) = 3

Ways to choose the remaining 4 starters out of 11 players left

= C(11,4) = 11! / (4!7!) = 330

Total number of ways to choose 6 starters

= 3*330 = 990

Answer:

Explanation:

We know that , if any vertical line cuts the given graph of relation at exactly one point, then the relation can be called as function.

From Given graph , we find that the vertical line through any point on x-axis greater than zero (ex : X = 5) cuts the graph at more than one point.

Hence, Given relation is not a function.

Hope this helps...

Good luck on your assignment...

Answer:

x^2y^2(x+y)(x^2-xy+y^2)

Step-by-step explanation:

x^5y^2+x^2y^5

Factor out the greatest common factor

x^2y^2( x^3+y^3)

Apply the Sum of Cubes Formula x^3+y^3 =(x+y)(x^2-xy+y^2)

x^2y^2(x+y)(x^2-xy+y^2)

Answer:

The answer is

Step-by-step explanation:

[tex] {x}^{5} {y}^{2} + {x}^{2} {y}^{5} [/tex]

To factorize the expression first factor

x²y² out

We have

x²y²( x³ + y³)

Using the expression

Factorize the terms in the bracket

So we have

x³ + y³ = ( x + y)(x² - xy + y²)

Combine the expressions

We have the final answer as

Hope this helps you