Ratios equivalent to 4:14

Answer:

we conclude that the rule will be:

[tex]a_n=\frac{31}{12}+\frac{1}{6}n[/tex]

Step-by-step explanation:

Given

[tex]a_6=3\frac{7}{12}=\frac{43}{12}[/tex]

[tex]a_1=2\frac{3}{4}=\frac{11}{4}[/tex]

We know the arithmetic sequence with the common difference is defined as

[tex]a_n=a_1+\left(n-1\right)d[/tex]

where a₁ is the first term and d is a common difference.

so

a₆ = a₁ + (6-1) d

substituting a₆ = 43/12 and a₁ = 11/4 to determine d

[tex]\frac{43}{12}=\:\frac{11}{4}\:+\:5d[/tex]

switch sides

[tex]\frac{11}{4}+5d=\frac{43}{12}[/tex]

subtract 11/4 from both sides

[tex]\frac{11}{4}+5d-\frac{11}{4}=\frac{43}{12}-\frac{11}{4}[/tex]

[tex]5d=\frac{5}{6}[/tex]

Divide both sides by 5

[tex]\frac{5d}{5}=\frac{\frac{5}{6}}{5}[/tex]

[tex]d=\frac{1}{6}[/tex]

as

a₁ = 11/4

[tex]d=\frac{1}{6}[/tex]

Therefore, the nth term of the Arithmetic sequence will be:

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substituting d = 1/6 and a₁ = 11/4

[tex]a_n=\frac{11}{4}+\left(n-1\right)\frac{1}{6}[/tex]

    [tex]=\frac{11}{4}+\frac{1}{6}n-\frac{1}{6}[/tex]

    [tex]=\frac{31}{12}+\frac{1}{6}n[/tex]

Therefore, we conclude that the rule will be:

[tex]a_n=\frac{31}{12}+\frac{1}{6}n[/tex]

Answer:

Step-by-step explanation:

9

3

4

Answer:

1. 9

2. 3

3. 4

Step-by-step explanation:

I have taken the test and got 100% on it so I hope this helped you!

Answer:

Diane is faster since her speed is higher.

Step-by-step explanation:

We can find each speed in yards per second.

Tom:

25 yards / 4 seconds = 6.25 yards/second

Diane:

20 yards / 3 seconds = 6.67 yards/second

Diane's speed is higher, 6.67 yd/s vs 6.25 yd/s, so Diane is faster.

Answer: Diane is faster since her speed is higher.

Answer:

55?

Step-by-step explanation:

........................

Answer:

AB=55

Step-by-step explanation:

9x+1=7x+13

2x=12

x=6

9x+1=9(6)+1

55

Answer:

Concept: Linear Systems

Answer:

it is a simultaneous equation.

the -9d can be cancelled to find the answer

The requried solution of the given system of equations is c = 8 and d = -7.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
Given a system of equations,
6c-9d=111  - - - - - (1)
5c-9d=103 - - - - -(2)

Solving the above two equations,
by subtracting 2 from 1|
c = 111 - 103
c = 8

Now,
6(8) - 9d = 111
d = - [111 - 48] / 9
d = -63 / 9
d = -7

Thus, the requried solution of the given system of equations is c = 8 and d = -7.

Learn more about simultaneous equations here:

https://brainly.com/question/16763389

#SPJ2

Answer:

84

Step-by-step explanation:

Set up a proportion. The ratio number of gray mice corresponds (is across from) the total number of gray mice (24)

5/2 = x/24                            Cross multliply

2*x = 5*24                            Multiply 5 by 24

2x = 120                               Divide by 2

x = 120/2

x = 60 Which represents the number of white mice.

So the white mice + gray mice = 60 + 24 = 84

i can give a better answer if you give the recipe but for 24 pancakes its double and for 6 pancakes is half

Answer:

[tex]d=\dfrac{t^2}{a}[/tex]

Step-by-step explanation:

The time  in seconds, required for an object accelerating at a constant rate of a meters/second to travel a distance of d meters is given by this  equation.

t = va

We need to find the expression for d in terms of t and a.

As velocity = distance/time

[tex]t=\dfrac{d}{t}a\\\\t^2=da\\\\d=\dfrac{t^2}{a}[/tex]

So, the distance d is [tex]\dfrac{t^2}{a}[/tex].

Step-by-step explanation:

I have no idea what you are asking to do lol

Answer:

i guess its b and d

Step-by-step explanation:

-2+2=0

Answer:

option B is correct

B and D

because B is -2 and D is 2

to make 0

we can combined that 2numbers then we got -2+2=0

Step-by-step explanation:

hope my answer is helpful to you

This question is incomplete, the remaining part of the question is upload as an image alongside this answer.

Answer:

Width = 2x = 2( r/√2 ) =  √2 r units

Height = 2y = 2( r/√2 ) =  √2 r units

Step-by-step explanation:

From the Figure on the image; lets consider the circle of radius r, centered at the origin.  

let ABCD be the largest rectangle that can be inscribed inside the circle.  

Let the half width of the rectangle be x, then in right triangle ONB using Pythagorean theorem,  

half height of rectangle y = √(r² - x²)

Thus the width of the inscribed rectangle = 2x and height of the inscribed rectangle = 2√(r² - x²)

thus the area of the inscribed rectangle = length × width

⇒ A(x) = 2x(2√(r² - x²))

⇒ A(x) = 4x√(r² - x²)  

now in order to maximize the area, we find critical points.

so we find the derivative and set that zero, that is Ai(x) = 0.

so using product rule, we get

A'(x) = 4x × ( -2x / 2√(r² - x²) ) + ( 4 × √(r² - x²)  )

A'(x) = ( -4x² / √(r² - x²) ) + ( 4√(r² - x²)  )

Now for critical points, set A'(x) = 0

so

( -4x² / √(r² - x²) ) + ( 4√(r² - x²)  ) = 0

( 4x² / √(r² - x²) ) =  ( 4√(r² - x²)  )

x² = r² - x²

2x² = r²

x² = r²/2

x = ±√(r²/2)

Now since x represent the with, it cannot be negative, Thus

x = r/√2

hence

y = √(r² - x²) = √(r² -  r²/2) = √(r²/2) =  r/√2

Therefore, the dimensions of the rectangle of largest area will be;

Width = 2x = 2( r/√2 ) =  √2 r units

Height = 2y = 2( r/√2 ) =  √2 r units

Answer:

d = 50t

Step-by-step explanation:

In the table, the values across from each other are equivalent.

[tex]\begin{tabular}{|c|c|}\cline{1-2} Time in hours (t) & Distance in miles (d) \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 50 \\\cline{1-2} 2 & 100 \\\cline{1-2} 3 & 150 \\\cline{1-2}\end{tabular}[/tex]

By looking at the second row of the provided table, we can see that d is equal 50 times the value of t. We can write this as an equation:

d = 50t

The correct answer choice is d = 50t, or the 4th option.

Let me know if you have any questions!

Answer: 47 inches

Step-by-step explanation:

Let x = length of the shortest piece

188 inches = 3x + x

188 inches = 4x

47 inches = x

Answer:

The shorter piece is 47 unches long

Step-by-step explanation:

l + s = 188

l = 3s

3s + 3 = 188

4s = 188

4s/4 = 188/4

s = 47

l = 3s

l = 3(47)

l = 141

Answer:

Step-by-step explanation:

add then subtact D from 3

Answer:

Answer: B. 5

Step-by-step explanation:

Combination

It's a selection of items from a collection, such that the order of selection does not matter.

It can be calculated by using factorials with the formula:

[tex]\displaystyle _mC_n=\frac{m!}{(m-n)!\ n!}[/tex]

Let's calculate:

[tex]\displaystyle _5C_1=\frac{5!}{(5-1)!\ 1!}[/tex]

[tex]\displaystyle _5C_1=\frac{5!}{(4)!\ 1!}[/tex]

Since 5!=5*4! and 1!=1:

[tex]\displaystyle _5C_1=\frac{5*4!}{(4)!\ 1!}[/tex]

Simplifying:

[tex]\displaystyle _5C_1=\frac{5}{1}=5[/tex]

Answer: B. 5

Step-by-step explanation:

5/8 binod

be happy binod here's ur answer binod

Answer:

5/8

Step-by-step explanation:

Answer:

4/7

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Given

Total outcome = 2blue ties+1red tie+2blue coats+2orange coats

Total outcome = 7

If he wears a blue tie, then the expected outcome will be 2.

Probability that he wears blue tie = 2/7

If he wears a blue coat, then the expected outcome will be 2.

Probability that he wears blue coat = 2/7.

The probability that he wears either a blue tie or a blue coat will be 2/7+2/7 = 4/7

Answer:

4,900

Step-by-step explanation:

Because i just know

Answer: 25%

Explanation:

1. Turn it into a fraction 150/200

2. Divide numerator (150) by denominator (200) to get 0.75

3. Subtract 0.75 from 1 to get 0.25

4. Turn 0.25 into a percentage by simply taking away the “0.” and adding a “%” at the end (25%)

Answer:

-2.375

Step-by-step explanation:

43/8=5.375

5+5.375=10.375

8-10.375=-2.375

Answer:

(0,6) ==> y-axis

(5,-2) ==> Quadrant IV

(-1,10) ==> Quadrant II

(5,0) ==> x-axis

(8.7,2.3) ==> Quadrant I

[tex]( - \frac{1}{4} \: \: \: - 6 \frac{1}{2} ) \: = = > quadrant \: iii[/tex]

Answer:

1/2

Step-by-step explanation:

Answer:

8:12:3

Step-by-step explanation:

Flats:Terraced is 2:3

Detached:Terraced is 1:4

First make the Terraced the same.

Flats:Terraced is 8:12

Detached:Terraced is 3:12

Terraced:Detached is 12:3

Now that we know, we can combine it.

Flats:Terraced:Detached is 8:12:3

Hope this helps :D

Answer:

what do you need help with the answer is going to be anything under -6 for example -7, -8, -9, -6.5 something along those lines

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

if you add negitive 8 to 8 then the sum will be 0

Answer:

-8

Step-by-step explanation:

when you add a negative number your basically subtracting its absolute value.

Answer: D. (4, 1)

Step-by-step explanation:

When we have a reflection over a line, the perpendicular distance to that line is invariant.

Then, if we have the point

(-7, 4) and we have a reflection over the line x = -3

The distance between the x component and the line is:

I -7 - (-3)I = 4

Then the reflected point will also be at a distance of 4 units to the line x = 3, and this is at the point x = 1.

Then the new point is (1, 4)

Now we do a reflection over the line x = y.

This type of reflection just changes the x-component by the y-component, and the y-component by the x-component.

Then the new point will be (4, 1)

Then the correct option is D.

Answer:

2

Step-by-step explanation:

20/10=2

The answer is:

30 seconds!

Answer:

Average Mean = 1.8

Step-by-step explanation:

Missing:

X:0 1 2 3 4 5 6

P(x): 0.20 0.30 0.20 0.15 0.10 0.05

Computation:

Average Mean [Probability distribution]

∑[P(x) × X]

= 0 x 0.20 + 1 x 0.30 + 2 x 0.20 + 3 x 0.15 + 4 x 0.10 + 5 x 0.05

= 1.8

Average Mean = 1.8

Answer:

According to the Heron's formula, Area (A) of the triangle having sides a,b,c units is

A=

s(s−a)(s−b)(s−c)

where

s=

2

a+b+c

For the given triangle,

a=18 cm

b=24 cm

c=30 cm

s=

2

18+24+30

=36

A=

36(36−18)(36−24)(36−30)

A=

36×18×12×6

A=

216×216

=216 cm

2

Smallest side =18 cm

Area of the triangle =

2

1

×base×altitude=216

2

1

×18× altitude=216

Altitude =

9

216

=24 cm

Step-by-step explanation:

hope this will help

[tex]\boxed{\boxed{\pink{\bf \leadsto The \ length \ of \ shortest \ altitude \ is \ 2.4\sqrt{6} \ units . }}}[/tex]

Here given measure of sides are 18 , 24 and 30 units. Firstly let's find the area of ∆ using Heron's Formula.

[tex]\boxed{\red{\bf Area_{\triangle} =\sqrt{s(s-a)(s-b)(s-c)}}}[/tex]

Where s is semi Perimeter . And here s will be ( 18 + 24 + 30 ) / 2 = 36 units .

[tex]\bf \implies Area = \sqrt{s(s-a)(s-b)(s-c)} [/tex]

[tex]\bf \implies Area = \sqrt{ 36 ( 36 - 18)(36-24)(36-30)}[/tex]

[tex]\bf \implies Area = \sqrt{ 36 \times 18 \times 12} [/tex]

[tex]\bf \implies Area = \sqrt{ 6^2 \times 6\times 6 \times 2 \times 3} [/tex]

[tex]\bf \implies Area = 6^2\sqrt{6} unit^2 [/tex]

[tex]\bf \boxed{ \implies Area_{triangle} = 36\sqrt{6} units^2} [/tex]

Also we know that ,

[tex]\boxed{\red{\bf Area_{\triangle} = \dfrac{1}{2}\times (base)\times (height)}}[/tex]

Let's find the altitudes now ,

Altitude on side of 18 units :-

[tex]\bf \implies Area = \dfrac{1}{2} \times (base)(height) \\\\\bf \implies 36\sqrt{6} unit^2 = \dfrac{1}{2} \times 18 \times h_1 = 36\sqrt{6} u^2 \\\\\bf\implies h_1 =\dfrac{ 36\sqrt6 \times 2 }{18} \\\\\boxed{\bf\implies h_1 = 4\sqrt6 units }[/tex]

Altitude on side of 24 units :-

[tex]\bf \implies Area = \dfrac{1}{2} \times (base)(height) \\\\\bf \implies 36\sqrt{6} unit^2 = \dfrac{1}{2} \times 24 \times h_1 = 36\sqrt{6} u^2 \\\\\bf\implies h_1 =\dfrac{ 36\sqrt6 \times 2 }{24} \\\\\boxed{\bf\implies h_1 = 3\sqrt6 units }[/tex]

Altitude on side 30 units :-

[tex]\bf \implies Area = \dfrac{1}{2} \times (base)(height) \\\\\bf \implies 36\sqrt{6} unit^2 = \dfrac{1}{2} \times 30 \times h_1 = 36\sqrt{6} u^2 \\\\\bf\implies h_1 =\dfrac{ 36\sqrt6 \times 2 }{30} \\\\\boxed{\bf\implies h_1 = 2.4\sqrt6 units }[/tex]