For the zero-sum game, solve the game, and find the value of the
game:
A
B
A
2
0
B
-3
2

a) Timothy's bike costs $20.It's important to note that the given percentage value represents a proportion or fraction of the original cost, allowing us to calculate the specific cost

To find the cost of Timothy's bike, we need to calculate 20% of Katie's bike cost.

20% of $100 can be calculated by multiplying $100 by 0.20:

20% * $100 = $20.

Therefore, Timothy's bike costs $20.

To calculate 20% of $100, we multiply $100 by the decimal equivalent of 20%, which is 0.20:

20% * $100 = 0.20 * $100 = $20.

In this scenario, Timothy's bike is priced at 20% of Katie's bike cost. This means that Timothy's bike is relatively less expensive compared to Katie's bike. It's important to note that the given percentage value represents a proportion or fraction of the original cost, allowing us to calculate the specific cost of Timothy's bike based on the given percentage relationship.

Based on the given information, Timothy's bike costs $20, which is 20% of Katie's bike cost.

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Question:

Solution:

Consider the following equation:

if l = 14 ft and w= 9ft and if we replace these values into the previous equation, we get:

we can conclude that the correct answer is:

The required volume of Famotidine is 4 mL.

To calculate the required volume in milliliters (mL) for the provided dosage of Famotidine, we can use the following formula:

Volume (mL) = (Dosage ordered / Available dosage) * Volume per dose

We have:

Dosage ordered = 40 mg

Available dosage = 20 mg/2 mL (This means there are 20 mg of Famotidine in 2 mL)

Volume per dose = 2 mL

Let's substitute these values into the formula:

Volume (mL) = (40 mg / 20 mg) * 2 mL

Simplifying the expression:

Volume (mL) = 2 * 2 mL

Volume (mL) = 4 mL

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The marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

The marginal utility simply refers to the change or extra satisfaction derived from the change in consumption.

Hence, the marginal utility of the fifth apple equals :

Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)

= (250 - 220) = 30

Hence, marginal utility per dollar: Marginal utility/price per apple

Price per apple = $0.5

Marginal utility of 5th apple = 30

Marginal utility of 5th apple = 30 / 0.5

Marginal utility of 5th apple = 60

Therefore, the marginal utility per dollar spent on the fifth apple is 60. The correct option is D.

Complete question :

If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:

a) 20

b) 30

c) 40

d) 60

Number of apples ____total utility

2__________________130

3__________________180

4__________________220

5__________________250

6__________________270

7__________________280

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7 inches

[25]^2-(24)^2=49

Г49=7

The cosine for the other acute angle will be 7 / 25.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The hypotenuse of a right triangle is 25 inches. The sine of one of the acute angles is 24/25.

sin θ = 24 / 25

We know that the sum of square of the sine and cosine of the angle will be equal to one. That is given as,

sin² θ + cos² θ = 1

Then the cosine for the other acute angle will be given as,

sin² θ + cos² θ = 1

(24 / 25)² + cos² θ = 1

576 / 625 + cos² θ = 1

cos² θ = 1 - 576 / 625

cos² θ = 49 / 625

cos² θ = (7 / 25)²

cos θ = 7 / 25

The cosine for the other acute angle will be 7 / 25.

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The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

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Answer:

304.5 cm2

Step-by-step explanation:

Think imaginatively, we got two congruent triangles and two rectangles with different dimensions.

S.A. of 2 triangles = 2*( 1/2 x B x H)

= 2*( 1/2 x 10.5 x 14) = 147 cm2

Rectangle 1 = 5*17.5 = 87.5 cm2

Rectangle 2 = 5*14 = 70 cm2

Total = 147 + 87.5 + 70 = 304.5 cm2

Answer: p(6) represents how the number of bacteria after 6 days.

Simply replace each x with 6 to go from the first sentence to the answer shown in bold above.

Answer:

2091 tiles

Step-by-step explanation:

(51/4×41/4)÷(1/4×1/4)

2091 tiles

Answer: i think its the second one, im sorry if its wrong :(

Step-by-step explanation:

I think it's the last one hoping it's correct : )

The average length encoding of a letter for a Huffman code of the letters and their given frequencies will be 245.

We have,

Frequencies:

a = 0.15 = 15,

b = 0.25 = 25,

c = 0.20 = 20,

d = 0.35 = 35,

e = 0.05 = 5,

So,

Now,

According to the question,

We will make Huffman tree,

i.e.

a = 0.15 = 15,

b + c = 25 + 20 = 45

d + e = 35 + 5 = 40,

Now,

a + b + c + d + e = 100

So,

a = 11 = 2 digits

b = 101 = 3 digits

c= 100 = 3 digits

d= 01 = 2 digits

e= 00 = 2 digits

And,

We know that,

Total bits required to represent Huffman code = 12.

So,

Now,

The average code length = a * 2 digits + b * 3 digits + c * 3 digits + d * 2 digits + e * 2 digits

i.e.

The average code length = 15 × 2 + 25 × 3 + 20 × 3 + 35 × 2 + 5 × 2

On solving we get,

The average code length = 245

Hence we can say that the average length encoding of a letter for a Huffman code of the letters and their given frequencies will be 245.

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Answer:

less than 90°

Step-by-step explanation:

Acute angles are less than 90°

Answer:

Less than 90 degree

Step-by-step explanation:

Because acute triangles are less than 90 degree.

And an acute triangle only include acute angles, no right angles (equal 90 degree) or obtuse angles (greater that 90 degree and less than 180 degree).

So... the answer is less than 90°! less than 90°! less than 90°! A! A! A!

Cheers! (￣▽￣)～■□～(￣▽￣)

Answer:

The transformation was the function went up 5 units, right two units, and a vertical stretch of 2.

Step-by-step explanation:

5/8•3/4

Step-by-step explanation:

it's gives you the same answer

Answer:

5/8•3/4

Step-by-step explanation:

That is very very easy

The solution set for the inequality 4x - 2 < 10 is x < 3.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
To solve the inequality 4x - 2 < 10, we need to isolate the variable x on one side of the inequality sign.

First, we add 2 to both sides of the inequality to get:

4x - 2 + 2 < 10 + 2

Simplifying, we get:

4x < 12

Next, we divide both sides of the inequality by 4 (since 4 is positive and we are not multiplying or dividing by a negative number) to get:

x < 3

Therefore, the solution set for the inequality 4x - 2 < 10 is x < 3.

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Answer:

y = 2x +5

Step-by-step explanation:

f(x) = y means that you want y to be on one side of the equation by itself.

so you need to isolate y.

2y - 4x = 10

first add 4x to both sides of the equation

2y = 4x + 10

then, divide by 2 on both sides to have y by itself

y = 4/2x + 10/2

finally, simplify:

y = 2x + 5

To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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Answer:

A) 3.996 inches

B) 0.01

C) option B

Step-by-step explanation:

Note: The diameter of the lid is between : 3.95 and  4.05

A) calculate the supplier set mean diameter

std = 0.02 inch

P( x < 3.95 ) = 1% = 0.01

= P ( Z < \((\frac{3.95 - u }{0.02})\) ) = P ( Z < -2.3263 ) = 0.01

therefore :

\((\frac{3.95 - u }{0.02})\)  = -2.3263

hence : u = 3.996 inches ( mean diameter )

B) At mean diameter = 3.98 calculate the value of std

P ( X < 3.95 ) = 0.01

= P ( Z < \(( \frac{3.95-3.98 }{std } )\) )  = P ( Z < -2.3263 ) = 0.01

therefore

\(( \frac{3.95-3.98 }{std } )\) = -2.3263

hence std = 0.01 inch

C) option B is preferable because its mean diameter is smaller and  the percent of lids too large to fit is considered more carefully using option B

Answer:

Step-by-step explanation:

Find x, considering the midsegment is half the parallel side:

Find z considering midsegment is connecting the midpoints of the sides:

Answer:

We could say that all of these equations (A, B, C, D, E, and F) could potentially be formulas for the graph.

Step-by-step explanation:

To determine which equations could possibly be a formula for the graph, let's briefly discuss the general shapes of these functions.

A. y = e^(-x): This is an exponential decay function, where the graph starts at a high value (when x is negative) and decreases to approach zero as x increases.

B. y = log(x): This is a logarithmic function, which starts at negative infinity for values close to 0 and increases slowly as x increases.

C. y = -e^(-x): This is a reflection of y = e^(-x) about the x-axis. The graph starts at a low value (when x is negative) and increases to approach zero as x increases.

D. y = -log(x): This is a reflection of y = log(x) about the x-axis, which starts at positive infinity for values close to 0 and decreases slowly as x increases.

E. y = ln(x): This is the natural logarithm function, which behaves similarly to y = log(x), starting at negative infinity for values close to 0 and increasing slowly as x increases.

F. y = -ln(x): This is a reflection of y = ln(x) about the x-axis, starting at positive infinity for values close to 0 and decreasing slowly as x increases.

Without knowing the specific graph, it's impossible to say which equations apply. However, all of these functions (A to F) are possible equations for different types of graphs.

Therefore, without any further information, we could say that all of these equations (A, B, C, D, E, and F) could potentially be formulas for the graph.

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Given function:

Given the general form of a quadratic equation:

The vertex form of the quadratic equation is:

Let us proceed to find the vertex of the quadratic equation:

We have

a = -3, b = 18, c = -21

The x-coordinate of the vertex:

The y-coordinate of the vertex:

Hence, the vertex of the equation is at (3, 6)

The equation in vertex form is thus:

Answer:

The statements that are correct are:

Option A and option E

Answer:

a and d

Step-by-step explanation:

The points (0, 0) and (3, -2) are solutions to the system of inequalities y≤-2x+6 and x−y<6 which are a correct options (A) and (C).

Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Given the system of inequalities as

y≤-2x+6 and x−y<6.

To determine the solutions, you first have to graph both of the lines in the problem.

y = -2x+6 and x − y = 6. Then, to shift them to inequality, you have to shade the half-plane that they represent.

The solution is the space that they have in common. In this case, it will be on the right side of the graph.

The points (0, 0) and (3, -2) are included in the shaded region they have in common.

Hence, the points (0, 0) and (3, -2) are solutions to the system of inequalities y≤-2x+6 and x−y<6.

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Answer:

10

Step-by-step explanation:

Let the missing side be 'x'.

Using Pythagorean Theorem, we can find the missing side.

Answer:

yes, phone companies, are only allowed to charge for the amount of data you use

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A straight line equals to 180 degrees. The example shown is a linear pair!

The number of degrees there are in the angle between the hour and the minute hands of the described clock is; 30°

The conventional analogue wall clock is numbered 1 to 12.

On this note, there are 12 unit subdivisions on the clock.

Each unit subdivision covers angle measure;

Since, at quarter past two; the hour arm of the clock is on 2 and the minute arm is on 3;

It follows that the degree measure of the angle subtended is; 30°.

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Once you have computed the expected value, you can mark your guess on the graph by finding the point where the curve is balanced. This is the point where the area to the left of the point is equal to the area to the right of the point.

A probability density function is a function that describes the likelihood of a random variable taking on a certain value. The area under the curve of a probability density function must be equal to 1. The normalizing constant, denoted by k, is a constant that is multiplied by the probability density function to ensure that the area under the curve is equal to 1. In other words, k is the value that makes the integration of the probability density function equal to 1.

To find the value of k, you would need to integrate the probability density function over its entire range and set the result equal to 1. Once you have found k, you can sketch the density function by plotting the function on the y-axis and the possible values of x on the x-axis.

The expected value of a random variable is a measure of the center of its distribution. It represents the average value that the variable would take if it were repeated many times. To compute the expected value of a continuous random variable, you would need to integrate the product of the random variable and its probability density function over its entire range.

Once you have computed the expected value, you can mark your guess on the graph by finding the point where the curve is balanced. This is the point where the area to the left of the point is equal to the area to the right of the point.

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