A mathematics professor gives two different tests to two sections of his college algebra courses. The first class has a mean of 56 with a standard deviation of 9 while the second class has a mean of 75 with a standard deviation of 15. A student from the first class scores a 62 on the test while a student from the second class scores an 83 on the test. Compare the scores. Which student performs better

Answer:

$11.30

Explanation : 11.3= 1.10(8)+2.5

The required orders are Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.

An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation. In Hannah's example, the equation holds true for the value of x equal to 10, but not for other values, such as 1. The equation is a conditional equation as a result.

Let we consider the number of orders Kara served as x.

Then, Harry served x + 10 orders and Erin served 4x orders.

The total number of orders they served is x + x + 10 + 4x = 86 orders.

So, 6x + 10 = 86

6x = 76

x = 12.5

Kara served 12.5 orders, Harry served 22.5 orders, and Erin served 50 orders.

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Answer:

Step-by-step explanation:

Let the orders served by Kira be k.

Orders served by Henry= 10 less than Kira

                                       = k-10

Orders served by Erin= 4 times of Kira

                                   = 4k

Total orders served= 86

     Kira+Henry+Erin= 86

               k+k-10+4k= 86

                       6k-10= 86

                            6k= 86+10

                            6k= 96

                              k= 96/6

                              k= 16

Kira= k= 16

Henry= k-10= 16-10= 6

Erin= 4k= 4x16= 64

∴ Kira served 16 orders, Henry served 6 orders & Erin served 64 orders

Answer:

$6,760

Step-by-step explanation:

With $10.50 per hour and 40 hour weeks.

$10.50 * 40 = $420

So Linda made $420 a week and with 52 weeks in a year.

$420 * 52 = $21,840

She made $21,840 annually at her old job.

With a bi-weekly salary she makes $1,100 every 2 weeks.

There are 52 weeks in a year, so divide that by 2 to get 26 bi-weeks thus 26 pay periods a year.

$1,100 * 26 = $28,600

or divide $1,100 in half ($1,100 / 2 = $550)

$550 * 52 = $28,600

Now find the difference by subtracting the new pay rate by the old one. (Subtract the old from the new one, if you prefer that phrasing.)

$28,600 - $21,840 = $6,760

So Linda's new job pays $6,760 more than her old one.

The speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.

The drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.

The drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.

(To determine the speed of the water drop and the speed of the car when the drop strikes the hood,

use the kinematic equations of motion.

First, we can find the time it takes for the drop to fall 10m using the kinematic equation:

distance h = 10m,

\(h = 1/2 at^2\)

where

h is the vertical distance,

a is the acceleration due to gravity (9.8m/s²), and t is the time.

Substituting the values, we have;

\(10 = 1/2 (9.8) t^2 \\

t^2 = 20/9.8 \\

t ≈ 1.43 seconds\)

Next, find the final velocity of the drop using the kinematic equation:

\(v = vo + at\)

where v is the final velocity,

vo is the initial velocity (which is 0m/s for the drop),

a is the acceleration due to gravity, and

t is the time we just calculated.

Substituting the values, we have

v = 0 + (9.8)(1.43)

v ≈ 14.0 m/s downward

Finally, find the speed of the car when the drop strikes the hood using the kinematic equation:

\(v = vo + at\)

v = 25 + (3)(1.43)

v ≈ 29.3 m/s to the east

Therefore, the speed of the water drop when it strikes the hood is approximately 14.0 m/s downward, and the speed of the car at that moment is approximately 29.3 m/s to the east.

To determine the velocity and acceleration

The velocity of the water drop with respect to the passenger in the car is simply the vector difference between the velocity of the water drop and the velocity of the car:

v_drop,p = v_drop - v_car

where v_drop is the velocity of the water drop (14.0 m/s downward) and

v_car is the velocity of the car (29.3 m/s to the east).

Substituting the values, we get:

v_drop,p = (0, -14.0, 0) - (29.3, 0, 0)

v_drop,p = (-29.3, -14.0, 0) m/s

Thus, the drop appears to have a velocity of approximately 29.3 m/s to the west and 14.0 m/s downward with respect to the passenger in the car.

The acceleration of the water drop with respect to the passenger in the car is simply the vector difference between the acceleration of the water drop and the acceleration of the car:

a_drop,p = a_drop - a_car

where a_drop is the acceleration due to gravity (9.8 m/s² downward) and

a_car is the acceleration of the car (3 m/s² to the east).

Substituting the values, we have,

a_drop,p = (0, -9.8, 0) - (3, 0, 0)

a_drop,p = (-3, -9.8, 0) m/s²

Therefore, the drop appears to have an acceleration of approximately 3 m/s² to the west and 9.8 m/s² downward with respect to the passenger in the car.

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The total number of times 7 can occur as the sum on rolling two cubes for 180 times is 30. It is gained by applying the knowledge of probability to the given problem.

What is probability?

Probability depicts the number of possibilities of how many times an event can occur. The probability of happening of an event invariably lies between 0 and 1. For a sure event, it is always 1. Its formula is given as P(E) = No. of favourable outcomes / Total no. of outcomes

Calculation of the total number of times 7 can appear as a sum on rolling two cubes for 180 times

Number of cubes rolled = 2

Total number of outcomes on rolling two cubes = 36

Total possibility of getting 7 as sum = 6

The probability of getting 7 as a sum on rolling two dice only once is given by P(E1)

P(E1) = 6 / 36

         = 1 / 6

She repeated the process 180 times  so the needed probability, P(E) is obtained by multiplying 180 by P(E1)

P(E) = 180 × (1 / 6)

P(E) = 30

Hence, the required probability of getting 7 as the sum is given by 30.

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For the given continuous random variable x:

(a) p(x < 4) = -8/27.

(b) p(3 ≤ x < 4) = -5/27

The continuous random variable x that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 x)/27.

(a) To find p(x < 4), we need to integrate the density function from x = 2 to x = 4:

p(x < 4) = ∫24 2(1 x)/27 dx

= (2/27) ∫24 (1 - x) dx

= (2/27) [(x - x2/2)]24

= (2/27) [(4 - 42/2) - (2 - 22/2)]

= (2/27) [(4 - 8) - (2 - 2)]

= (2/27) [(-4) - 0]

= (2/27) (-4)

= -8/27

So, p(x < 4) = -8/27.

(b) To find p(3 ≤ x < 4), we need to integrate the density function from x = 3 to x = 4:

p(3 ≤ x < 4) = ∫34 2(1 x)/27 dx

= (2/27) ∫34 (1 - x) dx

= (2/27) [(x - x2/2)]34

= (2/27) [(4 - 42/2) - (3 - 32/2)]

= (2/27) [(4 - 8) - (3 - 4.5)]

= (2/27) [(-4) - (-1.5)]

= (2/27) (-2.5)

= -5/27

So, p(3 ≤ x < 4) = -5/27.

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The possible degree sequences for a simple graph are: b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2) c. (5, 4, 4, 4, 3, 2)

To determine which of the given degree sequences are possible for a simple graph, we can apply the Handshaking Lemma.

The Handshaking Lemma states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

Let's analyze each degree sequence:

a. (5, 3, 3, 3, 3, 2)

To check if this degree sequence is possible, we sum up all the degrees: 5 + 3 + 3 + 3 + 3 + 2 = 19. According to the Handshaking Lemma, the sum of the degrees should be twice the number of edges. Therefore, the number of edges should be 19/2 = 9.5, which is not an integer. Since the number of edges must be a whole number, this degree sequence is not possible for a simple graph.

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2)

Summing up the degrees: 6 + 5 + 5 + 5 + 4 + 4 + 3 + 2 + 2 + 2 = 38. According to the Handshaking Lemma, the number of edges should be 38/2 = 19. The number of edges being an integer, this degree sequence is possible for a simple graph.

c. (5, 4, 4, 4, 3, 2)

Summing up the degrees: 5 + 4 + 4 + 4 + 3 + 2 = 22. The number of edges should be 22/2 = 11. Since the number of edges is an integer, this degree sequence is possible for a simple graph.

d. (9, 7, 3, 3, 3, 2, 2, 1, 1)

Summing up the degrees: 9 + 7 + 3 + 3 + 3 + 2 + 2 + 1 + 1 = 31. The number of edges should be 31/2 = 15.5, which is not an integer. Therefore, this degree sequence is not possible for a simple graph.

Based on the analysis above:

a. (5, 3, 3, 3, 3, 2) is not possible.

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2) is possible.

c. (5, 4, 4, 4, 3, 2) is possible.

d. (9, 7, 3, 3, 3, 2, 2, 1, 1) is not possible.

Therefore, the possible degree sequences for a simple graph are:

b. (6, 5, 5, 5, 4, 4, 3, 2, 2, 2)

c. (5, 4, 4, 4, 3, 2)

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Answer:

b its a trinominal with a degree of 2

The polynomial, 3x - 4 + 5x², is a trinomial with a degree of 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

We have the polynomial,

3x - 4 + 5x²

To find the degree of a polynomial:

We take the highest powered variable, and the order of that variable is equal to the degree of the polynomial.

Here, the highest power is 2.

So, the degree is 2.

And the polynomial has three terms.

So, the polynomial is trinomial.

Therefore, it is a trinomial with a degree of 2.

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the Nash equilibrium is not necessarily the best or most desirable outcome for the players involved. It simply represents a stable state where no player has an incentive to unilaterally deviate from their chosen strategy.

To determine the Nash equilibria in a game, we need to analyze the strategies of each player and identify the combinations of strategies where no player has an incentive to unilaterally deviate.

Given the options:

1. (P1=Shot, P2=Shot)

2. (P1=No shot, P2=No shot)

3. (P1=Shot, P2=No shot)

4. (P1=No shot, P2=Shot)

Let's analyze each combination:

1. (P1=Shot, P2=Shot):

If both players choose to shoot, they both face the risk of being shot and getting injured. Neither player has an incentive to deviate from this strategy, as changing to "No shot" would expose them to the risk of being shot without being able to retaliate. Therefore, (P1=Shot, P2=Shot) is a Nash equilibrium.

2. (P1=No shot, P2=No shot):

If both players choose not to shoot, they avoid the risk of being injured. Again, neither player has an incentive to unilaterally deviate from this strategy, as changing to "Shot" would expose them to the risk of being injured without gaining any advantage. Therefore, (P1=No shot, P2=No shot) is a Nash equilibrium.

3. (P1=Shot, P2=No shot):

If Player 1 chooses to shoot while Player 2 chooses not to shoot, Player 1 has an advantage and can potentially eliminate Player 2 without being injured. In this scenario, Player 2 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=Shot, P2=No shot) is not a Nash equilibrium.

4. (P1=No shot, P2=Shot):

Similarly, if Player 1 chooses not to shoot while Player 2 chooses to shoot, Player 2 has an advantage and can potentially eliminate Player 1 without being injured. In this scenario, Player 1 may have an incentive to deviate from "No shot" and switch to "Shot" to protect themselves. Therefore, (P1=No shot, P2=Shot) is not a Nash equilibrium.

Based on the analysis, the Nash equilibria in this game are:

- (P1=Shot, P2=Shot)

- (P1=No shot, P2=No shot)

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The correct option is B.

5 pound

The number (5.3) after Decimal is <5 so it round off to 5.

It is the same to round a number to one decimal place as to the nearest tenths. At this instance, it is known which numeral is in the hundredths position. When the number in the hundredths place is higher than or equal to 5, the tenths digit is raised by one unit.

A typical rule of thumb is to glance at the digit immediately to the right of the place value you want to round to and make your choice. For instance, rounding 5.1837 to the closest hundredth would result in 5.18 (because 3<5), whereas rounding 5.184 to the nearest thousandth would result in 5.184 (because 7>5).

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I understand that the question your are looking for is:

A scale measured a 4.5-pound brick as weighing 5.3 pounds. which measurement is more accurate but less precise than 5.3 pounds?

A. 4.98 pounds

B. 5 pounds

C. 5.52 pounds

D. 6 pounds

Answer:

Solve in parenthesis first(exponents:

(3 x 10^6) + (3 x 10^6)

Will be:

(3 x 1,000,000) + (3 x 1,000,000)

Multiply in the parenthesis:

(3,000,000) + (3,000,000)

Add them:

= 6,000,000

Standard form:

6 x 6^10

Use the order of

Answer:

I don't know isisuwhvqb

Answer:

she will need 2/3 more jars

The height of the pole mounted on top of the cliff is 7.6 meters,

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the height of the cliff, hence:

tan(58) = h/14

h = 22.4 meter

Let h' be the height of the cliff and pole, hence:

tan(65) = h'/14

h' = 30 meter

height of pole = 30 - 22.4 = 7.6 meter

The height of the pole mounted on top of the cliff is 7.6 meters,

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Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

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The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

Answer:

6

Step-by-step explanation:

Note the rules for signs directly next to each other:  

If there is two positive signs, the result will be positive.

If there is one positive and one negative sign, the result will be negative.

If there is two negative signs, the result will be positive.

In this case, there is a positive and a negative sign. You are, therefore, subtracting 10 with 4:

10 + (-4) = 10 - 4 = 6

6 is your answer.

~

Answer:

\(x^2+3x+8\)

\(15936\)

Step-by-step explanation:

\(\left(x+2\right)^2-\left(x-4\right)\)

\(\left(x+2\right)\left(x+2\right)-\left(x-4\right)\)

\(x^2+2x+2x+4-(x-4)\)

\(x^2+4x+4-\left(x-4\right)\)

\(x^2+4x+4-x+4\)

\(x^2+3x+8\)

\(1000^2-992^2\)

\(1000000-984064\)

\(15936\)

Answer:

Step-by-step explanation:

There are two options as below.

1. JL/JK = 5 : 1

Find the coordinates of L:

The point is L(8, - 10)

2. JL/JK = 1 : 5

Find the coordinates of L:

The point is L(0, 6)

ckgcujcfyfxgxhfccvcchf

Answer:

Hey angel i have missed talking to you on padlet and i hope we are still friends

Step-by-step explanation:

Step-by-step explanation:

subtract 9x from both sides

y = -9x+8

Answer:

Hence, The time of a commercial plane ride at this rate is:

280 Minutes or (4 hours and 40 minutes)

First Step-by-step explanation:

Let the speed of the commercial Airplane be

X km/min

The speed of the jet plane is

2x km/min

Multiply both the left & Right sides of the equation by 2x:

1730 / x - 1730 / (2x) = 140

1730 * 2 - 1730 = 140 * 2x

1730 = 280x

x = 1730 / 280

x = 173 / 28

1730 / 173 /28 = 280 (min)

Hence, the time of a commercial plane ride at this rate is:

280 (minutes).

Second  Step by Step explanation:

Make a plan:

x km/h.  

2x km/h.

time = distance/speed

Solve the problem:

x km/h

2x km/h

1730/2x - 1730/x = 7/3 (using the ground truth)

x = 346 km/h (using the ground truth)

1730/2 * 346 = 5/2 hours (using the ground truth)

1730/346 + 140/60 - 5/2 = 5 hours

The time of a commercial plane ride on this route is Five (5) hours.

Hope this helps!

Answer:

631

thx for points

The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

An equation is an expression that shows the relationship between two or more numbers and variables.

Solving the polynomial using completing the square:

2x² - 4x - 3 = 0

First divide through by 2:

x² - 2x - 3/2 = 0

add 3/2 to both sides:

x² - 2x - 3/2 + 3/2 = 0 + 3/2

x² - 2x = 3/2

add the square of half the coefficient x to both sides:

x² - 2x + 1 = 3/2 + 1

(x - 1)² = 2.5

taking square root:

x - 1 = ±√2.5

x = 1 ± √2.5

The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

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Answer: Step 3

Step-by-step explanation: this is the right answer on the edge, hope this helps!

The prevalence rate per 100,000 is 99.8%

We know that the prevalence rate is the proportion of persons in a population who have a particular disease over a specified period of time.

In this question, we have been given a data on breast cancer for the past year:

number of new cases: 1,774;

number of total cases: 4,192;

population: 5,977,906

We need to find the prevalence rate per 100,000

The total number of infected people = 1,774 + 4192

                                                             = 5966

Chance of infection in the whole population would be,

5,977,906/ 5966 ≈ 1002

This means, chances of having breast cancer is 1 in every 1002 people.

A prevalence rate is calculated by dividing total number of infected people by the total population. The result is then multiplied by 100,000

Now we calculate the prevalence rate per 100,000

= (5966 / 5,977,906) × 100,000

= 0.000998 × 100,000

= 99.8 %

Therefore, the prevalence rate per 100,000 is 99.8%

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Answer:

\(\huge\bf\underline{\underline{\pink{A}\orange{N}\red{S}\green{W}\purple{E}\blue{R}}}\)

\( 60\% \: of \: 80 \\ = \frac{60}{100} \times 80 \\ = \frac{4800}{100} = 48\)

\(\color{purple}{HOPE}\) \(\color{purple}{THIS}\) \(\color{purple}{WILL}\) \(\color{purple}{HELPS}\) \(\color{purple}{YOU}\)

Above triangle is an equilateral triangle.

This means that

\(y + 3 = 2y - 5\)

Lets us solve for y.

\(y - 2y = - 5 - 3 \\ - y = - 8 \\ \frac{ - y}{ - 1} = \frac{ - 8}{ - 1} \\ y = 8\)

All three angles are equal in an equilateral triangle.

this means that if given that one angle is 10x° then all the other 2 angles are equal to 10x°

\(10x + 10 x+ 10x = 180 \\\)

Sum of all interior angles of a triangle is 180°

Let us solve for x

\(30x = 180 \\ \frac{30x}{30} = \frac{180}{30} \\ x = 6\)

x=6°

GOODLUCK

Answer:

\(\huge\boxed{\sf x = -2/3}\)

Step-by-step explanation:

3x + 2 = 0

Subtract 2 to both sides

3x = 0 - 2

3x = -2

Divide 3 to both sides

x = -2/3

\(\rule[225]{225}{2}\)

Answer: 6 square inches

Step-by-step explanation:

Since the pizza is 16 inches and there is 8 slices divide.

16 inches ÷ 8 slices = 2 inches per slice

Each slice is 2 inches.

Since each slice is 2 inches multiply by 3 slices to get how many square inches she ate.

2 inches per slice x 3 slices = 6 square inches

Therefore she ate 6 square inches of pizza.

In the transformation ABC A'B'C', the preimage of B' is B.

It's a triangle, ABC. ABC is changed so that the resulting image is A'B'C'. It should be noted that there are many other forms of transformations, including dilation, vertical shift, horizontal shift, rotation about a point, reflection on a line, etc.

Corresponding vertices will be matched in all transformations. In other words, A will change to A', B to B', and C to C'.Preimage of B' would just be B itself due to the transformation's ability to maintain image similarity and convert vertices appropriately.

In conclusion, it is B.

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In the transformation ABC A'B'C', the preimage of B' is ____