There are 4 colas, 1 ginger, 7 root beers, and 6 cherry sodas in a cooler. What are the odds of choosing a ginger ale? Give your answer in a proportion in lower terms.

Answer:

[tex]\sqrt{2}[/tex] or 1.414

Step-by-step explanation:

1) Find the mean. 1+2+3+4+5 = 15. 15/5= 3

2) For each data point, find the square of its distance to the mean. (4, 1, 0, 1, 4)

3) Sum the values from Step 2. 10

4) Divide by the number of data points. 10/5= 2

5) Take the square root. [tex]\sqrt{2}[/tex]

Answer:

the answer square root of 2! just did the test and got it right :)

Step-by-step explanation:

Answer:

It would take 6 days for 500 students to be affected.

Step-by-step explanation:

Given that:

1. Seven kids returned with the virus.

2. The aggressive virus spreads at 130% each day.

We want to find how many days until 500 students are infected by the virus.

First day:

7 students have the virus, 130% of 7 student will contract the virus again.

130% of 7 = (130/100) × 7

= 1.3 × 7 = 9.1 ≈ 9

9 new students are affected

New total affected = 7 + 9 = 16 students.

Day 2:

Affected = 1.3 × 16 = 20.8 ≈ 20

New total affected = 20 + 16 = 36

Day3

Affected = 1.3 × 36 = 46.8 ≈ 46

New total affected = 36 + 46 = 82

Day4

Affected = 1.3 × 82 = 106.6 ≈ 106

New total affected = 106 + 82 = 188

Day5

Affected = 1.3 × 188 = 244.4 ≈ 244

New total affected = 244 + 188 = 432

Day6

Affected = 1.3 × 432 = 561.6 ≈ 561

New total affected = 561 + 432 = 993

Therefore, it would take 6 days for 500 students to be affected.

Answer:

0.577

Step-by-step explanation:

inv. sin (0.5) = 30

tan (30) = 0.577

The value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Tan[tex](Sin^{-1}(1/2))[/tex]

[ Sin 30° = 1/2 ]

= Tan([tex]sin^{-1}sin30)[/tex])

= Tan 30°

= 0.58

Thus,

0.58 is the value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

Learn more about trigonometric identities here:

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Answer:

[tex]4x^2-21x-2[/tex]

Step-by-step explanation:

Given that:

Difference of two trinomials is [tex]x^2 - 10x + 2[/tex]

One of the two trinomials is  [tex]3x^2 - 11x - 4[/tex]

To find:

The other trinomial = ?

Four options are:

[tex]2x2 - x - 2 \\2x2 + x + 6 \\4x2 + 21x + 6\\ 4x2 - 21x - 2[/tex]

Solution:

Let the two trinomials be A and B.

Given A - B = [tex]x^2 - 10x + 2[/tex]

B = [tex]3x^2 - 11x - 4[/tex]

We have to find the other trinomial A.

A - B = [tex]x^2 - 10x + 2[/tex]

A - ([tex]3x^2 - 11x - 4[/tex]) = [tex]x^2 - 10x + 2[/tex]

[tex]\Rightarrow[/tex] A = [tex]x^2 - 10x + 2[/tex] + ([tex]3x^2 - 11x - 4[/tex])

[tex]\Rightarrow[/tex] A = [tex]4x^2-21x-2[/tex]

So, the correct answer is [tex]4x^2-21x-2[/tex].

Answer:

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Step-by-step explanation:

Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:

[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]

[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]

Thus,

[tex]f(x) = 7\cdot x + 10[/tex]

The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.

Answer:

Step-by-step explanation:

[tex]a^{m}*a^{n} =a^{m+n}\\\\\\2^{3}*2^{5} = 2^{3+5} =2^{8}\\\\\\3^{2}*3^{4}=3^{2+4} = 3^{6}\\\\\\a^{2}*a^{5}=a^{2+5}=a^{7}[/tex]

Answer:

a) irrational

b) irrational

c) rational

d) rational

e) irrational

Note:

rational numbers are numbers that can be expressed in fractions.

irrational numbers are numbers that cannot be expressed in fractions i.e. they are never-ending-non-repeating decimals. examples √2, pi etc.

Answer:

Hope it helps U can still ask me if u have confusions

Answer:

  60+16√30 cm² ≈ 147.64 cm²

Step-by-step explanation:

You can figure the height of the object from ...

  V = Bh

  120 cm^3 = (30 cm^2)h

  4 cm = h . . . . . divide by 30 cm^2

However, this is insufficient to tell you the surface area.

__

If you assume that the base is square, then its side length is

  A = s^2

  s = √A = √(30 cm^2) = (√30) cm

The lateral surface area can then be found from the perimeter of the base and the height

  LA = Ph = (4√30 cm)(4 cm) = 16√30 cm^2

The total surface area will be the sum of this lateral area and the area of the two bases:

 total area = 16√30 cm^2 +2·30 cm^2

 total area = (60 +16√30) cm^2 ≈ 147.64 cm^2

__

For any other shape, the total area will be larger. It can be arbitrarily large, unless limits are put on the dimensions of the object.

Answer:

30 cm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 6 and h = 10 , thus

A = [tex]\frac{1}{2}[/tex] × 6 × 10 = 3 × 10 = 30 cm²

and 7² = 7 × 7 = 49

Answer:

1)        30 cm²

2) Seven squared equals seven times 7

Step-by-step explanation:

Base = 6 cm

Height = 10 cm

Area of triangle = [tex]\frac{1}{2}[/tex]*base * height

                          = [tex]\frac{1}{2} * 6 * 10[/tex]

                         = 3 * 10

                          = 30 cm²

2) 7² = 7 * 7

Answer:

0.375

Step-by-step explanation:

0.125 x 3 = 0.375

Answer:

0.375

Step-by-step explanation:

3 x 125

8 x 125

=

375

1000

=

0.375

Other sample problem:

5 = 5×125 = 625 = 0.625

8         8×125         1000

Hope this helps, have a good day :)

Step-by-step explanation:

because of the revenue it recieves from North sea oil and gas

Answer:

B) 3

Step-by-step explanation:

Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline.

In 300 miles journey the gallon of gasoline consumed will be

300/26= 11.54 gallons

Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline.

In 300 miles journey the gallon of gasoline consumed will be

300/36= 8.33 gallons

The amount of gasoline saved= 11.54-8.33

The amount of gasoline saved= 3.21

approximately 3 gallons of gasoline

Answer:

B. 110

Step-by-step explanation:

z is supplemental to 70°, so the add up to 180°

z+70°=180°

z=180°-70°

z=110°

Option B is correct. The required value of z is 110 degrees

Supplementary angles are angles summing up to 180 degrees. According to the circle geometry, we can see that z and 70 degrees lie on the same line, this shows that both angles are supplementary.

Since supplementary angles sum up to 180degrees, hence;

[tex]z + 70 = 180\\[/tex]

Subtract 70 from both sides

[tex]z+70-70=180-70\\z=110^0[/tex]

Hence the value of z is 70 degrees

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Answer:

1. Apples, Cauliflower, Green beans

2. Apples, Cauliflower, Salmon

...

27. Grapes, Corn, Almonds

Step-by-step explanation:

There are 3x3x3 = 27 combinations possible. You can enumerate them systematically.

Answer:

There are 27 combinations possible.

Hope this helps!

Answer:

-1

Step-by-step explanation:

Answer:

The simplest form of the given expression is 8.

Step-by-step explanation:

(-11/2x + 3) - 2(-11/4x - 5/2)

Distribute 2 to (-11/4x - 5/2)

(-11/2x + 3) - (-11/2x - 5)

Now, combine like terms. The terms with the x value will cancel each other out because a negative plus a positive of the same number will equal zero. For example, -2 + 2 = 0.

So, the expression in the simplest form is going to be 8. The x values have cancelled each other out so all there is left is the constant number which is 8.

The table represents a function because each input (x-value) corresponds to exactly one output (y-value)

If we had repeated x values, then that is a sign we don't have a function. So for instance, if we had the two points (1,5) and (1,6) then we don't have a function because the input x = 1 corresponds to outputs y = 5 and y = 6 simultaneously.

Note: the y values are allowed to repeat and we still have a function, but this function is not one-to-one because of the repeated value y = 2.

Answer:

No idea dude

Step-by-step explanation:

I just need points

Answer:

6 and -120

Step-by-step explanation:

The first 3 positive integers are 1, 2 and 3 and their product is 6, the first 5 negative integers are -1, -2, -3, -4 and -5 and their product is -120.

Answer:

C.) 4(750c-700t) ; D.) 2800t - 3000c

Step-by-step explanation:

Time taken :

Tatenda = t sec/m^2

Ciara = c sec/m^2

Tatenda = 700m^2 per week

Ciara = 750m^2 per week

Which expressions can we use to describe how many more seconds Tatenda spends than Ciara spends mowing lawns during 4

Total Time taken over four weeks :

Tatenda = 4(t * 700) = 4(700c)

Ciara = 4(c * 750) = 4(750c )

Number of seconds Tatenda spends more than Ciara : meaning Tatenda spends more seconds than

Tatenda - Ciara

4(700t) - 4(750c) = 4(700t - 750c)

4(700t - 750c)

Or

4(700t - 750c) = 2800t - 3000c

2800t - 3000c

Answer: D

Step-by-step explanation:

The common difference is  -2/3  so using the last term which is -8/27 multiply it by -2/3 to find the next terms.

[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]    

[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]  

[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]  

Answer:

9

Step-by-step explanation:

We can set up a systems of equations to find the value of the third side.

Let's assume that [tex]x[/tex] is the length of both sides 1 and 2. Let's also assume that [tex]y[/tex] is the length of the third side.

We know that [tex]x + x + y = 23[/tex], and looking at the first clue we can make the equation [tex]y = 2x-5[/tex].

We can substitute y into the equation [tex]x + x + y = 23[/tex].

[tex]x + x + (2x-5) = 23\\\\2x + 2x-5 = 23\\4x-5 = 23\\4x = 28\\x = 7[/tex]

So the length of the side that is the same as the second is 7.

Now we can plug this into the equation [tex]y = 2x-5[/tex] to find [tex]y[/tex].

[tex]y = 2(7) - 5\\\\y = 14-5\\\\y = 9[/tex]

Hope this helped!

Answer:

9 cm

Step-by-step explanation:

Let's say that the length of the 2 equal sides is x.

That means:

Side 1 = x

Side 2 = x

We know that the third side is 5 less than twice the length of the 2 equal sides, or 2x-5

Side 3 = 2x-5

The perimeter is all sides together.

Side 1 + Side 2 + Side 3

We know the length of each side, so let's put that in instead.

x + x + 2x-5

Let's simplify this expression:

x + x + 2x - 5

2x + 2x - 5

4x - 5

We know the perimeter, 4x-5, is 23 cm.

4x - 5 = 23

4x = 28

x = 7

The third side is 2x-5. If x is 7...

2*7 - 5 = 14-5 = 9

Answer: 9 cm

Answer:

we would be facing the North West

Answer:

B. Only line B is a well-placed line of best fit.

Step-by-step explanation:

A good line of best fit is a line drawn to represent, as much as possible, all data points. As long as the data points are clustered along the line, and are not farther from each other, the line is a best fit for such data points.

Therefore, from the two lines drawn by Maggie, Line B seems to be the only well-placed line of best fit, as virtually all the data points are clustered along the line, compared to Line A. Line A only runs across 2 data points. The rest data points are scattered far apart from the line.

Therefore, the statement that best describes the placement of the line of best fit drawn by Maggie is: "B. Only line B is a well-placed line of best fit."

Answer:

Only line B

Step-by-step explanation:

Line A is too low on the graph to be best fit for the plot

Answer:

5.84 x10.^4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the  

10

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

first answer

Step-by-step explanation:

(8x³ - 22x² - 4) / (4x - 3)

when you do long division you get the first answer

Answer:

3. Fifth degree polynomials are also known as quintic polynomials. Quintics have these characteristics: One to five roots. Zero to four extrema.

4. x = -5 or x = 0 or x = 5

Step-by-step explanation:

Solve for x:

6 x^5 - 150 x^3 = 0

The left hand side factors into a product with four terms:

6 x^3 (x - 5) (x + 5) = 0

Divide both sides by 6:

x^3 (x - 5) (x + 5) = 0

Split into three equations:

x - 5 = 0 or x^3 = 0 or x + 5 = 0

Add 5 to both sides:

x = 5 or x^3 = 0 or x + 5 = 0

Taking cube roots gives 0 times the third roots of unity:

x = 5 or x = 0 or x = 0 or x = 0 or x + 5 = 0

Subtract 5 from both sides:

x = 5 or x = 0 or x = 0 or x = 0 or x = -5

There are {2} duplicate solutions:

Answer: x = -5 or x = 0 or x = 5

Answer:

1) Real Number

2)Whole Number

3)Irrational Number

4)Rational Number

5)Integers

6)Natural Numbers

Answer:

Step-by-step explanation:

1) Diagonal bisect the angles of Rhombus

∠CAB = ∠CAD

∠CAB = 71

2) ∠DAB = ∠CAB + ∠CAD

 ∠DAB = 71 + 71 = 142

In Rhombus, adjacent angles are supplementary

∠DAB + ∠ABC = 180

142 + ∠ABC = 180

           ∠ABC = 180 - 142

         ∠ABC = 38

3)  In rhombus, opposite angles are congruent

∠ADC = ∠ABC

∠ABC = 38

In rhombus, diagonal bisect angles

∠BDC = (1/2)*∠ADC

∠BDC= 38/2

∠BDC = 19

4) Diagonals bisect each other at 90

∠DEC = 90

5) Diagonals bisect each other

BE = DE

BE + DE = DB

7x -2 +7x -2 =24   {add like terms}

        14x - 4 =24

              14x = 24+4

              14x = 28

                 x = 28/14

                 x = 2 m

6) AB = 13m

BE = 7x - 2 = 7*2 -2 = 14 -2 = 12 m

In right angle ΔAEB,  {use Pythagorean theorem}

AE² + BE² = AB²

AE² + 12² = 13²

AE² + 144 = 169

         AE² = 169 - 144

         AE² = 25

         AE = √25

        AE = 5 m

Diagonals bisect each other

AE = EC

AC = 2*5

AC = 10 m

7)Side = 13 m

Perimeter = 4*side

                  = 4*13

 Perimeter = 52 m

8) d1 = AC = 10 m

   d2 = DB = 24 m

Area = [tex]\frac{d_{1}*d_{2}}{2}[/tex]

         [tex]=\frac{10*24}{2}\\[/tex]

          = 10 *12

          = 120 m²

Answer:

No, all of her work is correct.

Step-by-step explanation:

Answer:

No, all of her work is correct.

Step-by-step explanation:

All of her work is correct.

The first step is showing factorization of √50

The second step is simplifying the factorization

The third step is simplifying the entire radical.

When you take a square root of a square, they cancel out, so:

√5² = 5

We multiply it with our leftover √2 and we get:

5√2