O COUNTING AND PROBABILITY

Finding the odds in favor and against

Susana v

Espoo

Keith is at the grand opening celebration of a supermarket. He spins a wheel with 10 equal-sized slices, as shown below. The wheel has 7 black slices, 2 grey

slices, and I white slice. When the wheel is spun, the arrow stops on a slice at random. If the arrow stops on the border of two slices, the wheel is spun again.

23

(a) If the arrow stops on a black slice, then Keith wins a gift card. Find the

odds against Keith winning a gift card

to

X

Р

(b) If the arrow stops on a black slice, then Keith wins a gift card. Find the

odds in favor of Keith winning a gift card.

Explanation

Check

Answer:

  73 pages

Step-by-step explanation:

You want the number of pages required to hold 583 cards when each page will hold 8.

The number of pages required is ...

  (583 cards)/(8 cards/page) = 72 7/8 pages

The least integer greater than this number is 73

The number of pages needed to store 583 cards is 73.

Answer:

Area of the shape is 244.98cm² is B

Step-by-step explanation:

Area of shape=Area of semi circle+Area of trapezoid

A=1/2 πr² + 1/2(a+b)h

A=1/2×3.142×7² + 1/2(14+18)10.5

A=1/2×3.142×49 + 1/2×32×10.5

A=76.98+168

A=76.98+168

A=244.98cm²

Answer:

73/100

73 over 100

The given two ratios are not form a proportion.

Ratio is defined as the comparison of two quantities of the same kind by the method of division.

Proportion is an equation it is formed when two ratios are equivalent to each other.

The given two ratios are 4/8 and 1/7.

i.e., 4:8 and 1:7

By simplifying this ratio 4:8 we get 1:2

That is these two ratios are not equal.

proportion is formed only when the two ratios are equal.

Hence, the given two ratios are not form a proportion.

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Answer:

y=17

Please mark me as brainliest.

Answer: ⁕ The result is not always positive. ⁕

Why:  ♪ If you were to subtract two positive integers, 4 and 5, what would you get?  You would get -1.  Is -1 a positive integer?  No. ♪

Examples:

• 2-3 = -1 •

• 5-7 = -2 •

• 8-11 = -3 •

⟪ If you would like more help, please let me know below! ⟫

Symbols used: ⟪⟫•♪⁕

Answer: is not always positive

Answer: To solve for x in the equation x/9 = 7/15, we can cross-multiply to get:

15x = 9 * 7

Simplifying the right side, we get:

15x = 63

To solve for x, we can divide both sides by 15:

x = 63/15

Simplifying the fraction on the right side, we get:

x = 4 3/5 or x = 4.2 (rounded to one decimal place)

Therefore, the solution to the equation x/9 = 7/15 is x = 4.2 or x = 4 3/5.

Step-by-step explanation: kinda easy ngl lol but hope this helps :D

Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!

Answer:

One is 8 and the other is 17

Step-by-step explanation:

8+9=17

17+8=25

Answer:

c. a[b(b + 6)+7(a²-2)]

Step-by-step explanation:

look at the pic

The equivalent expression of the expression ab² + 6ab + 7a³ - 14a is

C. a [b (b + 6) + 7 (a² - 2)]

Option C is the correct answer.

We have,

To find the expression that is equivalent to ab² + 6ab + 7a³ - 14a, we can factor out common terms from the given expression.

The common terms in the expression are "a" and "(b + 7)".

Step 1:

Factor out "a" from the expression:

ab² + 6ab + 7a³ - 14a = a(b² + 6b + 7a² - 14)

Step 2:

Factor the quadratic expression inside the parenthesis:

b² + 6b can be factored as b(b + 6)

7a² - 14 can be factored as 7(a² - 2)

Step 3:

Putting it all together, the equivalent expression is:

a [b (b + 6) + 7 (a² - 2)]

Now let's check which option matches this expression:

a. (b + 7)(b + 6)(a² - 2) - Not equivalent

b. b(b + 6) + 7(a^2 - 2) - Not equivalent

c. a[b(b + 6) + 7(a² - 2)] - Equivalent

d. a[(b + 6)(b + 7a² - 14)] -Not equivalent

Thus,

The equivalent expression is

C. a [b (b + 6) + 7 (a² - 2)]

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Answer:

Step-by-step explanation:

Perimeter = 2L + 2W = 24

L+W = 12

(x+3)+(x/2) = 12

2x+6 +x = 24

x = 6 cm

L = x+3 = 9 cm

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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The minimum sample size required to construct a 95% confidence interval for the population mean is 16.

To determine the minimum sample size required to construct a 95% confidence interval for the population mean circumference of tennis balls within 0.05 inch, we need to use the formula for the margin of error:

Margin of error = Z* (σ/√n)

Where Z* is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Since we want a 95% confidence interval, Z* = 1.96 (from a standard normal distribution table).

We are given that σ = 0.10 inch and we want the margin of error to be 0.05 inch. Plugging in the values, we get:

0.05 = 1.96 * (0.10 / √n)

Solving for n, we get:

n = [(1.96 * 0.10) / 0.05]² = 15.36

We can't have a fractional sample size, so we round up to the nearest whole number. Therefore, the minimum sample size required is 16.

This means that the manufacturer needs to randomly select and measure the circumferences of at least 16 tennis balls to estimate the population mean circumference with 95% confidence and a margin of error of 0.05 inch.

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Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

The statement is true because :

Both these triangles are Congruent to each under the ASA congruence postulate . We say this because :

1) The two angles in both the triangles which are each other's corresponding part are equal ( 40° = 40° and 50° =50° )

2) There is one common side which is 12 . As both of the common sides are equal , these triangles are said to be congruent to each other .

Answer:

9.98- 2.53 = 7.45

7.68 + 13.07 = 20.75

100.03 - 16.28 = 83.75

Step-by-step explanation:

 9.98

- 2.53

_____

7.45

  1   1        - Process of carrying 10's

   7.68

+ 13.07

_______

 20.75

0000 13 ⇔ What the number becomes after carrying

↑↑↑↑↑

100.03

- 16.28

______

83.75

Happy New Year!

The relationship between the related rates dp/dt and dV/dt is -1.3kV^-2.3

Given :

When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the equation pV^1.3 = k, where k is a constant. Find the relationship between the related rates dp/dt and dV/dt.

p * V^1.3 = k

divide by v^1.3 on both sides

p *  V^1.3 /  V^1.3 = k /  V^1.3

p = k /  V^1.3

p = k *  V^-1.3

differentiate with respect to t on both sides

dp / dt = -1.3kV^-1.3 - 1 dv / dt

dp / dt / dv / dt = -1.3kV^-2.3

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Answer:

200 pounds

Step-by-step explanation:

4 televisions weigh 160 pounds

1 television weigh 40 punds

5 televisions weigh 200 pounds

Answer:

Logically 200 lbs

Step-by-step explanation:

160/4 = 40

1TV = 40 lbs

40 * 5 = 200

200lbs...

The value of x in the triangle is determined as 45.

The value of x in the triangle is calculated by applying the following formula,.

The measure of angle ABD = 0.2x + 52

The measure of angle CBD = 0.2x + 42

From the diagram, we can set-up the following equations;

x + 16 = 0.2x + 52

Simplify the equation above, by collecting similar terms;

x - 0.2x = 52 - 16

0.8x = 36

Divide both sides of the equation by " 0.8 "

0.8x / 0.8 = 36/0.8

x = 45

Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.

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3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

  x = 8

Step-by-step explanation:

The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...

  4 +7x = 60

  7x = 56 . . . . . . subtact 4

  x = 8 . . . . . . . . .divide by 7

Answer:

Step-by-step explanation:

Let the reading per day be d,

Carly total pages read: 8d + 40

Ashley total pages read: 10d

Here:

8d + 40 = 10d

40 = 10d - 8d

40 = 2d

d = 20

Answer:

Step-by-step explanation:

Answer:

57,000

Step-by-step explanation:

The cost of  one blueberry pie and one blackberry pie is $11.30 and $11.373 respectively.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:

Operands: The numbers used in an operation are called operands. Depending on the type of operation, different terms are applied to the operands.

Given Nathan sold 13 apples pies for $147,

cost of 13 apple pies  = $147

cost of 1 apple pie = 147/13 = $11.30

Lucy sold  7 blueberry pies and 11 apple pie $204.

7 blueberry  + 11 apple pie = $204

cost of 11 apple pie  = $124.384

cost of 7 blueberry = 204 - 124.384 = $79.615

cost of 1 blue berry = 79.615/7 = $11.373

Hence the cost of 1 apple pie is $11.30 and 1 blueberry is $11.373.

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Answer:

?

Step-by-step explanation:

Answer:

x² - 6x = 7

x² - 6x + 9 = 7 + 9

(x - 3)² = 16

x - 3 = ± 4

x - 3 = 4 and x - 3 = -4

x: {-1, 7}

Largest value of x = 7

Smallest value of x: -1

I hope this helps!

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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