Select the correct answer from each drop-down menu.
Alice is playing checkers against a computer and has won 8 games out of the 12 she's played so far.
Alice must win the next ✓consecutive games to reach a winning percentage of 80%. After that, losing
will bring her winning percentage down to 50%.
consecutive games

The domain is [tex]x \le 5[/tex] and the range of the function is [tex]f(x) \ge - 3[/tex]

The function is given as:

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

The radicand must be at least 0.

So, we have:

[tex]\sqrt{5 - x} \ge 0[/tex]

Square both sides

[tex]5 - x \ge 0[/tex]

Rewrite as:

[tex]5 \ge x[/tex]

Solve for x

[tex]x \le 5[/tex]

This means that the domain is [tex]x \le 5[/tex]

For the range, we have; [tex]\sqrt{5 - x} \ge 0[/tex]

This means that:

[tex]f(x) \ge 0 - 3[/tex]

[tex]f(x) \ge - 3[/tex]

Hence, the range of the function is [tex]f(x) \ge - 3[/tex]

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Primeter=10 + 4 +10 +7 = 31 ft

Answer:

QR = 15 cm

PQ = 20 cm

Step-by-step explanation:

Use the Pythagorean theorem. [tex]a^{2} +b^{2} =c^{2}[/tex]

Find QR first since you know QP are SR.

[tex]a^{2} +b^{2} =c^{2}\\12^{2} +9^{2} =c^{2}\\144+81=c^2 \\225=c^2\\\sqrt{225} = \sqrt{c^2} \\c = 15[/tex]

QR = 15 cm

Now you can find PQ. First find the length of PR by adding PS and SR together.

16 + 9 = 25

[tex]a^{2} +b^{2} =c^{2}\\a^{2} +15^{2} =25^{2}\\a^{2} +225 =625\\a^{2} +225-225 =625-225\\\a^{2} = 400\\\sqrt{a^2} =\sqrt{400} \\a = 20[/tex]

PQ = 20 cm

1. If the mean is used to determine Nathan's salary, he should choose Company A.

2. If the median is used to determine Nathan's salary, he should choose Company A.

3. The center of the data for Company B is more accurately described by the Median because the data is not uniformly scattered and has extreme values or outliers.

The Mean is the average value obtained after adding up a set of values and dividing the result by the number in the set.

The Median represents the middle value in an ordered list from smallest to largest.

Salaries   Company A   Company B

Year 1                10                   10

Year 2              20                  20

Year 3              30                  70

Year 4              40                  30

Year 5              50                  40

Year 6              60                  50

Year 7              70                  60

Total             280                280

Mean              40                  40

Median           40                  35 (30 + 40)/2

Thus, Nathan should choose Company A whether the Mean or the Median is used to determine Nathan's salary.

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Answer: Company B

Company A

Median

Skewed Right

Step-by-step explanation:

The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

The equation is given as:

f(x) = 3x + 3

Express f(x) as y

y = 3x + 3

Swap the positions of y and x

x = 3y + 3

Make y the subject

3y = x - 3

Divide by 3

y = 1/3x - 1

Replace y with the inverse function

f-1(x) = 1/3x - 1

Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

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Answer:

1.8 ounces

Step-by-step explanation:

Let :

⇒ weight of a can of juice = x

⇒ weight of an energy bar = y

=============================================================

Equations formed :

============================================================

Multiply Equation 1 by 2 :

⇒ 2 × (3x + 2y) = 2 × 33.6

⇒ 6x + 4y = 67.2 [Equation 3]

===========================================================

Subtract : Equation 3 - Equation 2

⇒ 6x + 4y - 4y - 2x = 67.2 - 27.2

⇒ 4x = 40

⇒ x = 10

===========================================================

Finding the weight of an energy bar :

⇒ 3(10) + 2y = 33.6

⇒ 2y = 3.6

⇒ y = 1.8 ounces

If the diameter is d = 8, then we divide that in half to get the radius of r = 4.

If the radius is r = 9, then we double it to get the diameter of d = 18

The formulas are:

I'll let you determine the others.

Answer:

Step-by-step explanation:

Diameter is twice the radius.  d = 2*r

Radius is half the diameter r = d÷2

 1) d = 8

      r = 8÷ 2

      r = 4

2) r = 9

   d = 2*r

       = 2*9

   d = 18

3) r = 24

   d = 24*2 =48

4) d = 36

   r = 36 ÷2 = 18

5) d = 52

      r = 52÷2 = 26

Answer:

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

Arc BC and Angle BWC are the same number of degrees.

When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.

Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.

180° - 120° is 60°

Angle BWC is 60° so Arc BC is 60°

Answer:

1 28/99

Step-by-step explanation:

When a number with 1-2 digits is divided by 99, it gets repeated with two digits. For example, 2/99=0.0202020202...

Another example would be 18/99=0.18181818...

Using this information, we can determine that 1.28282828 repeating would be 1 28/99

Let me know if you have any questions! :)

Answer:

10 m

Step-by-step explanation:

opposite = sin30° × 20 = [tex]\frac{1}{2}[/tex] × 20 = 10 m

Answer:

z = 30

Step-by-step explanation:

All angles of a triangle add up to 180:

z + 120 + 30 = 180

z + 150 = 180

z = 180 - 150

z = 30

Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

Equation 1

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

Equation 2

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

Solve by substitution

Substitute Equation 1 into Equation 2 and solve for x:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and solve for y:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

Conclusion

The dimensions of the rectangle are:

Therefore, the length of the longer side is 22 meters

The length of the longer side is 22 meters.

Let, one side of the rectangle is x meters.

According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the perimeter is 58 meters:

58 = 2 * (x + 4x - 6)

Now, let's solve for x:

58 = 2 * (5x - 6)

58 = 10x - 12

Add 12 to both sides:

58 + 12 = 10x

70 = 10x

Now, divide both sides by 10 to isolate x:

x = 70 / 10

x = 7

So, one side of the rectangle is 7 meters.

Now, we can find the length of the longer side:

Length of the longer side = 4x - 6

Length of the longer side = 4 * 7 - 6

Length of the longer side = 28 - 6

Length of the longer side = 22 meters

Therefore, the length of the longer side is 22 meters.

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Answer:

123 save some for me

Step-by-step explanation:

:0

Answer: 123

Step-by-step explanation: I did the math- lol-

AnswEr :

Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .

⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]

⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.

[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]

Therefore ,

When , x = 2 ,

When , x = –7 ,

Answer:

Hi,

Step-by-step explanation:

If the "is" means is equal to

Let's say a-1, a, a+1 the 3 consecutive integers.

[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]

[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]

The two sets are : (0,1,2) and (4,5,6).

Since I don't see the graphs:

 ⇒ I am going to answer by the general format of what you should see

The function has zeros at -3, 4:

 ⇒ which means that the function must interest the x-axis at x = -3 and

      x = 4

Hope that helps!

      ⇒look at the image I uploaded which shows a possible answer

Answer: 75 people

Step-by-step explanation:

1).

we have percentage of people who invested in 18-29 year category

=31%

we need

n=40 people

this is

30% of x =40

or

0.3x=40

x=40/0.3 =133.33 or 134 people

2).

in 65+ category

percentage =54%

we need

n=40

this is

54% of x =40

or

0.54x=40

or

x=40/0.54 =70.07 or 75 people

Answer: Commutative property

The statement "If the equation of a function is a rational expression the function is a rational" is true.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

If the equation of a function is a rational expression the function is a rational, the statement is true.

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The expression that represents Felipe's balance at the end of the year is 3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].

The equation that can be used to determine future value with compounding is:

FV = P (1 + r)^nm

3700 x [tex]( 1 + \frac{0.059}{4}) ^{4}[/tex] x [tex](1 + \frac{0.172}{8})^{8}[/tex].

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The value of side z will be equal to 99.32 cm.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

Given that:-

In ΔXYZ, x = 27 cm, y = 79 cm and ∠Z=142°

So by applying the formula given below:-

z²   =   x²  +  y²  -  2xyCos(142)

z²   =   79²  +   27²   -  2 ( 79 x 27  x  Cos142  )

z    =    99.32  cm

Hence the value of side z will be equal to 99.32 cm.

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The decimal degree of the angle 12' 8" is 0.2022

The angle measure is given as:

Angle = 12' 8"

As a general rule;

Where:

' represents minutes and " represents seconds.

So, we have:

Angle = 12/60 + 8/(60 * 60)

Evaluate the expression

Angle = 0.2022

Hence, the decimal degree of the angle 12' 8" is 0.2022

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Answer:

1. 5² is 25 yards

2. 7² is 49m

3. 8² is 64cm

4.draw a square, make one side 6 feet then do 6² which is 36feet

5. do the same thing then write 10 inches on one side and 10² is 100 inches.

6. 7x3= 21 ft

7. 5x4= 20 in.

8. 2x8= 16 yd

Step-by-step explanation:

common sense

Answer:

Step-by-step explanation:

D∩L={f}

D∪L={a,f,g,j,k}

Answer:

good and right and keep trying your best

Answer:

Ans= 6720 ways

Step-by-step explanation:

From Combination rule from Permutation and Combination, nCr

We use 8^C3 or 8C3,

8x7x6x5x4x3x2x1

--------------------------  =6,720

3x2x1

or

8x7x6x5x4x3! /3!, here the 3! cancels each other out, and we're left with 8x7x6x5x4, which equals 6720.