Make b the subject of the formula [tex]a=\sqrt{b + 6[/tex]

[tex] \underline{ \boxed{ \sf{✰\: Option\:D. \:81✓ }}}[/tex]

Refer to the attachment for solution ☘️

Hope it helps

Answer:

A. 1/220   B. 1/22   C. 3/11

Step-by-step explanation:

This question uses combinations -- counting the number of ways a selection can be made from a set of objects (without arranging them after the selection is done).

Notations for combinations:

The number of ways to select  r  things from a set of  n  things is

[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]  where the exclamation points mean factorial.

[tex]n!=1\cdot2\cdot3\ldots\cdot n[/tex]  and 0! is defined to be 1.

There are two other commonly used symbols for this:

[tex]_nC_r[/tex]  and  [tex]n \choose x[/tex].

In all three parts, the number of ways to choose 3 balls from a set of 12 is

[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot4\cdot3\cdot2\cdot1}{(3\cdot2\cdot1)(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}[/tex]

Notice that 9 factors in the denominator cancel 9 factors in the numerator, leaving

[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10}{3\cdot2\cdot1}=220[/tex]

A. The number of ways to choose 3 red balls from the 3 red balls is C(3, 3) = 1, so the probability is 1 / 220.

B)  The number of ways to choose 3 green balls from the set of 5 green balls is [tex]C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{5\cdot 4}{2}=10[/tex]  out of 220, so the probability is 10/220 = 1/22.

C)  The number of ways to choose 1 red is C(3, 1) = 3.  Choose 1 green in C(5, 1) = 5 ways.  Choose 1 white in C(4, 1) = 4 ways.

The probability is  [tex]\frac{3\cdot 5 \cdot 4}{220}=\frac{60}{220}=\frac{3}{11}[/tex]

Answer:

a) 1/220

b) 1/22

c) 3/11

Step-by-step explanation:

Check the attachment.

Answer:

30

Step-by-step explanation:

the beginning of the box is the first quartile the middle is the median the end it the third quartile

Answer:

Step-by-step explanation:

Area of the door = area of the rectangle + area of the semicircle

                            = 7 × 4                            +  (3.14 × 2²)/2

                            = 28                                + (3.14 × 4)/2

                            = 28                                + 3.14 × 2

                           = 28                                 + 6.28

                           = 34.28

Answer:

15%

Step-by-step explanation:

number 8 is 15% because you divide 42 by 280 the number of people to get the pecent you ha e which is 15%

Answer:

5×6=30

24÷50=0.49....following long division method

56+72+x =180 ( therefore sum of angle in a triangle)

128+x=180

x=180-128

x=52

Answer:

THE MISSING ANGLE = 52°

Step-by-step explanation:

Sum of all angles = 18°0

Let the missing angle be x°

56° + 72° + x° = 180°

x° = 180° - 72° - 56°

x° = 52°

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The value a = -1 < 0 represents the translation -1 units to the left and

b = 9 > 0 represents the translation 9 units up is correct.

The rule of transformation is defined as,

( x , y ) → ( x + a , y + b ) (equation - 1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units right and if a<0, then the graph shifts a units left.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

Based on the given conditions, formulate,

(x, y) → (x-1, y+9) (equation - 2)

From (1) and (2) equations,

We get,

a = -1 , b = 9

The value a = -1 < 0 represents the translation -1 units to the left and

b = 9 > 0 represents the translation 9 units up.

Therefore,

Description of the rule is,

The value a = -1 < 0 represents the translation -1 units to the left and

b = 9 > 0 represents the translation 9 units up is correct.

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sum of three number= 98

the second number.

Let the three numbers be x, y and z

Sum of the numbers is 98.

x + y + z = 98………………(i)

The ratio of the first to the second is 2/3.

x/y = 2/3

x= 2/3 × y

x= 2y/3

The ratio of the second to the third is 5/8.

y/z= 5/8

z/y= 8/5

z= 8/5 × y

z= 8y/5

Put the value of x = 2y/3 and z = 8y/5 in (i).

2y/3 + y + 8y/5= 98

49y/15= 98

49y= 98 × 15

49y= 1470

y= 1470/49

y= 30

Therefore, the second number is 30.

answer= option c.

Answer:

[tex]x = 13 ~~ \text{and}~~ y= 10[/tex]

Step-by-step explanation:

[tex]~~~~~~2.31 \times 10^x = 2200 \times 1.05 \times 10^y\\\\\implies 2.31 \times 10^x = 2310 \times 10^y\\\\\implies \dfrac{10^x}{10^y} = \dfrac{2310}{2.31}\\\\\implies 10^{x-y}=1000\\\\\implies 10^{x-y} = 10^3\\\\\implies x - y = 3[/tex]

[tex]\text{If x = 13 and y = 10 then the difference will be 3.}[/tex]

Step-by-step explanation:

If we convert

[tex]r = - 10 \cos(x) [/tex]

to a Cartesian equation,

[tex] {r}^{2} = - 10 r \: \cos(x) [/tex]

[tex] {x}^{2} + {y}^{2} = - 10x[/tex]

[tex] {x}^{2} + 10x + {y}^{2} = 0[/tex]

[tex] {x}^{2} + 10x + 25 + {y}^{2} = 25[/tex]

[tex](x + 5) {}^{2} + {y}^{2} = 25[/tex]

So we have a circle with center (-5,0), with a diameter of 10.

Answer:

2411.52

Step-by-step explanation:

D = r x 2

R = d/2

16/2 = 8

A = πr^[tex]\pixr^{2}[/tex]

A = 3.14 x 8x8

A = 3.14 x 64

A = 200.96

V = A x H

V = 200.96 x 12

V = 2411.52

Answer:

3

340?Step-by-step explanation:

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Answer:

The answer is 47796816366096114154433241462805777065938231744772710

Step-by-step explanation:

hope this helps you

Answer:

226.19

Step-by-step explanation:

A= 2πrh+ 2πr2= 2·π·4·5+2·π·42≈226.19467

or

S = (2 * pi * r^2) + (2 * pi * r * h)

S = (2 * pi * 4^2) + (2 * pi * 4 * 5)

S = (32 pi) + (40 pi) = 72pi = 226.08 ANS.

Answer:

251.333 (Repeating)

Step-by-step explanation:

First, you need to find the area of the circle at the top, which is [tex]\pi r^{2}[/tex]

Next, you multiply it by the height. (I did also use actual pi)

This is if it's total area, not lateral.

Answer:

Sorry I can't answer this.

But you may use the protacter to find the angle

? = 73°

There are 7 sides in this polygon

Calculate total interior angles using (n-2) * 180    

                                                                  ["n" denotes number of sides]

The missing angle inside the polygon:

900° - 130° -119° -130° -154° -130° -130°

900° - 793°

107°

A straight line has total 180°

? + 107° = 180°

? = 180° - 107°

? = 73°

Answer:

3/8 of the area is shaded

Step-by-step explanation:

this can be determined by deviding the total shape into parts and determining those parts

so we see the top right 1/4 of the shape has a square that is shaded, with the triangle only covering 1/2 of this shape becuase the hypotenuse ((diagnal edge of a right triangle)) devides the square in half

beings that 1/2 of the 1/4 square is shaded, we know that in reation to the whole shape that the small shaded area is equal to 1/8 ((1/2 ÷ 1/4 = 1/8))

same can be said for the bottum shape, with the bottum half of the whole shape half covered we can determine its total shaded area in relation to the shape ((1/2 ÷ 1/2 = 1/4))

the left top shape is completely unshaded so we wont need to calculate any shadded area into the equation

with the total shape covered by 1/4 + 1/8 we can find the least common denominator between the two fractions to get a simplifide answer for the total shaded area

1/4 = 2/8
2/8 + 1/8 = 3/8

this leaves 5/8 of the shape unshaded

3/8 fraction of the square is to be shaded.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In the top right 1/4 of the shape has a square that is shaded, with the triangle only covering 1/2 of this shape because the hypotenuse divides the square in half.

1/2 of the 1/4 square is shaded, we know that in relation to the whole shape that the small shaded area is equal to 1/8.

same can be said for the bottom shape, with the bottom half of the whole shape half covered we can determine its total shaded area in relation to the shape.

1/4 = 2/8

2/8 + 1/8 = 3/8

Hence, 3/8 fraction of the square is to be shaded.

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Answer:

Exact form = 1/49

Step-by-step explanation:

Decimal form = 0.02

Hope this helps! :)

Answer:

[tex]\frac{1}{7}^{2} = \frac{1}{49}[/tex]

Step-by-step explanation:

The power of the 2 means to multiply it two times itself.

Example: 7^2 = 7 * 7 = 49

Apply that to a faction.

[tex]\frac{1}{7}^{2} =\frac{1}{7} *\frac{1}{7} = \frac{1}{49}[/tex]

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Step 1:  Determine the equation

So we know that our equation does not have a y-intercept which means that it doesn't intersect ANYWHERE on the y-axis.  Therefore, this means that our equation will be a straight vertical line that doesn't move side to side and just goes straight up and down.  We also know that our point is (3, 6) which means that our x-value will be 3 and this is where the equation will be located.  

There are several ways to display our answer where x = 3 is the most common way which basically means give me all of the y-values for the same x value of 3.  Another way of saying it is x - 3 = 0 which either way when adding 3 to both sides gives you x = 3 which is what I usually go with.

Answer: [tex]x = 3[/tex]

Answer:

x = 3 or x - 3 = 0

Step-by-step explanation:

Given

Solving

Step-by-step explanation:

The store buys a remote control robot for $60 plus it marks up by 30%.

First, we need to convert 30% to a decimal of 0.30.

Then we multiply 60 by 0.30.

60*0.30=18

We know we have to add the original price of $60 with an $18 markup.

60+18=78

We now get $78 as the selling price.

Answer:

$1.15

Step-by-step explanation:

6 pairs of socks cost $6.90.

so every sock is at least one dollar. one dollar per sock, then you take the .90 and divided between the 6 socks and you get 15, so one dollar and 15 cents per sock.

Hope this helps, have a nice day!

Answer:

r = 17

Step-by-step explanation:

calculate: 2r=35-1

divide both sides: 2r=34

Answer:

prices of food and games and tickets

Answer:

i already did i the previous one

btw can you send this full page of work in pdf if you could

15.

[tex] \frac{89.32}{48.50} \times 100[/tex]

Answer:

The answer should be A.

Step-by-step explanation:

Well, to determine how two triangles are similar you first look at the image of what they give you.

As you can see the images shows only degree angles.

Looking at your option to see degree angles.

In some options, there is a side length of a triangle, but we aren't given a side length on both triangles so that answer does that apply.

Our last option is between A and D.

D is false as we determine the triangles are similar to each other.

RCW and VCB are vertically opposite meaning their 25° are the same to each other.

We know that every triangle adds up to 180.

Answer:

C. 15800 to spare

Step-by-step explanation:

All you have to do is add up the total money he has to spend  money, then you add up the total cost, and subtract the total money he has to spend by the total cost, and you're left with he has 15,800 left to spare. ;)

He should make a loan from the investors about 4.6%..

To determine the volume or chance of commodity in terms of 100, use the chance formula. Per cent simply means one in a hundred. With the chance formula, a number between 0 and 1 can be expressed. A number that's expressed as a bit of 100 is what it is. It's substantially used to compare and determine rates and is represented by the symbol.

Total quantum plutocrat Korey have

= Saving plutocrat heritage plutocrat

= $,500$,000

= $,500

Total quantum of charges

= Store Fixtures amount + Computer and Cash Register amount + Inventory  amount +Rent amount + Insurance amount

=  $2700 + $1200 + $17400 +$10800 + $3000

= $35100

So, Fund taken through loans and investor

= Total quantum of charges -Total quantum plutocrat Korey have

= $ 35100-$ 33500

= $ 1600

and, the percentage is

= 1600 x 100 / 35100

= 4.6%

He should make a loan from the investors about 4.6%.

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Answer:

Step-by-step explanation:

Isolate the variable of y from one side of the equation.

-14=5(3y-10)-5y

First, switch sides.

[tex]\sf{5\left(3y-10\right)-5y=-15}[/tex]

Use the distributive property.

DISTRIBUTIVE PROPERTY:

A(B-C)=AB-AC

5(3y-10)

Multiply by expand.

5*3y=15y

5*10=50

15y-50-5y

15y-5=10y

= 10y-50

10y-50=-15

Add by 50 from both sides.

10y-50+50=-15+50

Solve.

10y=35

Then, you divide by 10 from both sides.

10y/10=35/10

Solve.

Divide the numbers from left to right.

35/10=7/2

y=7/2

Divide is another option.

7/2=3.5

[tex]\Longrightarrow: \boxed{\sf{y=\dfrac{7}{2}}}[/tex]

I hope this helps. Let me know if you have any questions.

The expression  that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).

First step

Monthly interest rate = (Annual percentage rate ÷ Number of months in a year)

Monthly interest rate= 0.12 ÷ 12

Monthly interest rate= 0.01

Second step

Amount left = Amount charged - Amount paid

Amount left = $450 - $150

Amount left = $300

Third step

Amount of interest=Monthly rate ×Amount left

Amount of interest=(0.01) (300 dollars)

Amount of interest=$3

Therefore the expression  that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).

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Considering the area of a rectangle, it is found that the area of Bob's remaining plot of land is of 12.5 acres.

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, that is:
A = lw.

In this problem, both the length and the width are divided in half, hence the proportion remaining is given by:

A = 0.5l x 0.5w = 0.25lw = 25% of the initial area.

Hence:

0.25 x 50 = 12.5.

The area of Bob's remaining plot of land is of 12.5 acres.

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