Mallick Corp. reported the following information for 2013 and 2014.Accounts receivable, December 31, 2013 $ 67,000Accounts receivable, December 31, 2014 63,000Sales (all on credit) -- 2014 745,000How much cash was collected from customers during 2014?A. $741,000B. $745,000C. $749,000D. $753,000

Answer:

x² - 4 = 0

Step-by-step explanation:

choices: x² - 4 = 0, x² = -4, 3x² + 12 = 0, 4x² = 16, 2(x-2)² = 0

to find x= -2, 2

x² - 4 = 0

(x + 2) (x - 2) = 0

x = -2, 2

If you use the normal distribution to estimate the probability that score exceeds 100, the answer would be zero.

This is because a normal distribution is a continuous probability distribution, and the probability of any individual score, no matter how high or low, is always zero.

However, this answer contradicts the assumption of a normal distribution for scores because it implies that scores cannot exceed 100, which is not true. Scores can theoretically range from negative infinity to positive infinity, and in practice, there may be some scores above 100, especially if the measurement instrument is imprecise or the test is very difficult.

Therefore, if we observe scores that are higher than 100, it suggests that the assumption of a normal distribution may not be appropriate for the data, and we may need to use a different distribution or statistical model to estimate probabilities or make inferences about the scores.

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The table that shows a relation that represents a function is: table D in the options given.

To determine if a relation is a function, we need to check if each value of x corresponds to a unique value of y.

A. In this relation, x = 3 is paired with two different values of y (-2 and -1) which means this relation is not a function.

B. In this relation, each value of x does not corresponds to only one value of y, so this relation is not a function.

C. In this relation, -3 and 1 are paired with two different values of y (-3 and 1), which means this relation is not a function.

D. In this relation, each value of x corresponds to only one value of y, so this relation is a function.

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Answer: The 8 oz steak is a better buy as it has a lower unit price at $1.06 per ounce compared to $1.14 per ounce for the 14 oz steak.

Step-by-step explanation: To determine which is a better buy, we can calculate the unit price of each steak.

The unit price is the price per ounce of steak.

For the 8 oz steak:

Unit price = price ÷ quantity = $8.50 ÷ 8 = $1.06 per ounce

For the 14 oz steak:

Unit price = price ÷ quantity = $16.00 ÷ 14 = $1.14 per ounce

Therefore, the 8 oz steak is a better buy as it has a lower unit price at $1.06 per ounce compared to $1.14 per ounce for the 14 oz steak.

The circumference of a circle is proportional to its diameter. The constant of proportionality for this relationship is pi (π). Therefore, we can use the equation C = πd (where C is the circumference and d is the diameter) to determine the circumference of a circle.

Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159, but its decimal representation goes on infinitely without repeating.

The radius of a circle is half the length of its diameter. Therefore, the relationship between diameter and radius is that the diameter is twice the length of the radius, or d = 2r.

If given the diameter of a circle, you can calculate its radius by dividing the diameter by 2 (r = d/2). Conversely, if given the radius of a circle, you can calculate its diameter by multiplying the radius by 2 (d = 2r).

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Answer:

Table:

Domain: {-1, 3, 6}

Range: {4, 5, 6}

Set of coordinates:

Domain: {-4, -3, 1}

Range: {1, 3, 4}

The number of each type of basket made is as follows:

2-point basket = 19

3-point basket = 9

The team made 28 baskets and scored 65 points. Some baskets were 2-point baskets, and some baskets were 3-point baskets.

let

x = number of 2-point basket

y = number of 3-point basket

Therefore, using equation

x + y = 28

2x + 3y = 65

multiply equation(i) by 2

2x + 2y = 56

2x + 3y = 65

subtract he equation

y = 9

Therefore,

x = 28 - 9

x = 19

Therefore, the team made 19 2-point basket and 9 3-point basket.

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Answer:

there is no Modal number because all the numbers appears only once

Therefore , the solution of the given problem of area comes out to be  the pizza only occupies 0.24 square inches of the box's bottom.

The object's overall size can be determined by figuring out how much room would be required to completely enclose the object's exterior. When selecting an analogous item with a tubular form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

Assume that the square box's side length is "s" inches.

The pizza's size is specified as 254.47 in2. The area of the pizza would be equal to the area of the square box because it fits tightly inside of it.

=> s² = 254.47

=> s = √(254.47)

=> s = 15.95 inches

If you round to two decimal places, the area of the square box minus the area of the pizza is equal to (15.95)2 - 254.47, or 0.24 in2.

Therefore, the pizza only occupies 0.24 square inches of the box's bottom.

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Answer:

Step-by-step explanation:

8600

Answer:

8,600

Step-by-step explanation:

"nearest hundred", meaning 643 and since the tens place is under 50 it is closer to 600 then 700 making it 8,600

The probability that Claire spinning an 8 is around 0.078, or 7.8%.

We may use the strategy of calculating favorable results over total outcomes to get the likelihood that Claire spins a sum of 8. We must specifically determine how many possibilities there are to reach a sum of 8 when spinning the two spinners and divide that number by the total number of possible outcomes.

To illustrate, we can use a table to display all of the possible results for spinning two spinners labeled 1-8, and then compute the sum of each outcome:

There are 64 possible outcomes (8 spinners 1 choice times 8 spinner 2 choices), and we can see that there are 5 methods to reach a sum of 8: (2,6), (3,5), (4,4), (5,3), and (6,2). As a result, the likelihood of getting an 8 is:

P(sum of 8) = number of favorable outcomes / total number of outcomes

            = 5 / 64

            = 0.078125

So the likelihood of Claire spinning an 8 is around 0.078, or 7.8%.

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Answer:

ight, whats good.

To calculate the percentage of students who brought lunch from home, we can use the following formula:

Percentage = (Number of students who brought lunch from home / Total number of students) * 100

Given:

Number of students who ate school lunch = 114

Number of students who brought lunch from home = 266

Total number of students = Number of students who ate school lunch + Number of students who brought lunch from home = 114 + 266 = 380

Plugging in these values into the formula:

Percentage = (266 / 380) * 100 = 70%

So, 70% of the students brought lunch from home.

Answer:

If the expected value of the game is 5.6, this means that on average you can expect to earn 5.6 points per game if you were to play the game many times. However, since the point values available in the game are 20, 10, and 2, you cannot earn exactly 5.6 points in any single game.

Instead, over many games, the average number of points you would earn per game would approach the expected value of 5.6. For example, if you played the game 100 times, you might earn 2000 points if you got 20 points every time, 1000 points if you got 10 points every time, or 200 points if you got 2 points every time. But if you averaged your points across all 100 games, the average should be close to the expected value of 5.6 points per game.

The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.

Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.

The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.

It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.

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The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -[tex](p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3[/tex]

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -[tex](p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)[/tex]

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression [tex]-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3[/tex] subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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B) the use of L-dopa can reduce schizophrenic symptoms.

There is evidence to suggest that schizophrenia that has association with an overactive dopamine system in certain parts of the brain.

L-dopa is a medication commonly used to treat Parkinson's disease, which is characterized by low dopamine levels. However, studies have shown that L-dopa can also reduce symptoms of schizophrenia, providing further support for the link between dopamine and this disorder.

Option A is incorrect as lower dopamine activity is not associated with the removal of schizophrenic symptoms.

Option C is incorrect as antipsychotic drugs are used to treat symptoms of schizophrenia, not Parkinsonian symptoms. Option D is incorrect as the research on dopamine-receiving synapses in persons with schizophrenia is still ongoing and there is no clear consensus on their activity levels.

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The link between dopamine and schizophrenia is supported by the finding that  The use of L-dopa can reduce schizophrenic symptoms. So the correct option is B .

There is evidence to suggest that schizophrenia that has association with an overactive dopamine system in certain parts of the brain.

L-dopa is a medication commonly used to treat Parkinson's disease, which is characterized by low dopamine levels. However, studies have shown that L-dopa can also reduce symptoms of schizophrenia, providing further support for the link between dopamine and this disorder.

Option A is incorrect as lower dopamine activity is not associated with the removal of schizophrenic symptoms.

Option C is incorrect as antipsychotic drugs are used to treat symptoms of schizophrenia, not Parkinsonian symptoms. Option D is incorrect as the research on dopamine-receiving synapses in persons with schizophrenia is still ongoing and there is no clear consensus on their activity levels.

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The slant height of the Teepee is 32.76 feet.

The square footage of one of the rooms is 44 square feet.

Check the attached for the sketch of the cone. From the image, the slant height is labelled l. Note that the base diameter is 14 feet, so the base radius will be 7 feet.

(a) Thus, the slant height can be found by considering one of the right triangles in the cone. That is:

l² = 32² + 7²   (Pythagoras Theorem)

l²  = 1024 + 49

l = √1073

l = 32.76 feet

(b) The shape of base is a circle.

Area of circle = πd

where d is the base diameter

Area of circle = 22/7 * 14

Area of circle = 44 square feet

Thus, the square footage of one of the rooms is 44 square feet

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Answer:

A full-time employee at a large company who has been there for years would typically have the best employee benefits.

Large companies often have more resources to provide extensive employee benefits packages, including health insurance, retirement plans, paid time off, and other perks. Full-time employees who have been with the company for years may be eligible for additional benefits, such as higher matching contributions to retirement plans and increased vacation time.

New hires at both small and large companies may not have access to as many benefits initially, as they may need to work for a certain period before becoming eligible. Part-time employees may also have limited access to benefits, depending on the company's policies.

Overall, the length of time an employee has been with the company and the size of the company are two important factors in determining the quality and quantity of employee benefits.

The number of  individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5% is at least 246.

To determine the sample size needed for a 90% confidence interval with a margin of error no more than 5%, we can use the formula:

n = ([tex]z^{2}[/tex] * p * q) / [tex]E^{2}[/tex]

where:
n = sample size
z = z-score for the desired confidence level (in this case, 1.645 for 90%)
p = proportion of individuals who believe global warming is not a problem (0.8)
q = 1 - p (0.2)
E = margin of error (0.05)

Plugging in these values, we get:

n = ([tex]1.645^{2}[/tex]* 0.8 * 0.2) / [tex]0.05^{2}[/tex]
n ≈ 246

Therefore, at least 246 individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5%. The answer is at least 246.

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A bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 200 and a standard deviation of 50.

We will find the score that separates the lower 60% of ratings from the top 40% of ratings.

Let x be the score that separates these two portions. We can find the corresponding z-scores using the standard normal distribution, since the ratings are normally distributed with mean 200 and standard deviation 50.

The z-score corresponding to the 60th percentile is the value z such that

P(Z ≤ z) = 0.6

With the help of standard normal tables, we can find that z = 0.25. Therefore, we have

(x - 200)/50 = 0.25

For x, we get

x - 200 = 0.25 * 50

x - 200 = 12.5

x = 212.5

Similarly, the z-score corresponding to the 40th percentile is the value z such that

P(Z ≤ z) = 0.4

With the help of standard normal tables, we can find that z = -0.25. Therefore, we have

(x - 200)/50 = -0.25

For x, we get

x - 200 = -0.25 * 50

x - 200 = -12.5

x = 187.5

Hence, the score that separates the lower 60% from the top 40% is between 187.5 and 212.5.

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Answer:

The numbers in order from biggest to smallest are: 0.925, 0.9, 0.871, 0.87, 0.637, 0.62, 0.125, 0.012, and 0.01.

Step-by-step explanation:

To order these numbers from biggest to smallest, I compared the digits in each decimal place starting from the tenths place. For example, the number with the largest digit in the tenths place is 0.9. If two or more numbers have the same digit in the tenths place, I then compared the digits in the hundredths place and so on until I found which number was larger.

Answer: To determine whether the condition of equal standard deviations is met in this case, we can perform a quick check by comparing the sample standard deviations of each group. If the sample standard deviations are roughly equal, then we can assume that the condition of equal standard deviations is met.

Alternatively, we can use Levene's test for equality of variances, which tests the null hypothesis that the population variances are equal across all groups. If the p-value of the test is greater than the significance level (usually 0.05), then we can assume that the condition of equal standard deviations is met.

Without the data or the sample standard deviations, it is not possible to determine whether the condition of equal standard deviations is met in this case.

Step-by-step explanation:

A) Let the side length of the square base be x, and the height of the box be h. Then, the volume of the box is given by:

V = [tex]x^2[/tex] * h = 8500

Solving for h, we get:

h = 8500 / [tex]x^2[/tex]

The surface area of the box can be expressed as:

S = 2x^2 + 4xh

Substituting the value of h obtained above, we get:

S = [tex]2x^2[/tex] + 4x(8500 / [tex]x^2[/tex]) = 2[tex]x^2[/tex]+ 34000 / x

Thus, the surface area of the box can be expressed as a function of x.

B) To graph the function, plot the surface area (S) on the y-axis and the side length of the square base (x) on the x-axis. Since x cannot be negative, the domain of the function is (0, infinity). As x gets very large or very small, the surface area approaches infinity, so we should only graph the function for values of x that make sense in the context of the problem.

C) The minimum amount of cardboard required to construct the box is equal to the surface area of the box. To find the minimum surface area, we need to find the minimum of the function S(x) obtained in part A.

D) To find the dimensions of the box that minimize the surface area, we need to find the value of x that minimizes the function S(x). We can do this by taking the derivative of S(x) with respect to x, setting it equal to zero, and solving for x. This gives us:

dS/dx = 4x - 34000/[tex]x^2[/tex] = 0

Multiplying both sides by [tex]x^2[/tex] and solving for x, we get:

x = (8500/2[tex])^(1/3)[/tex] ≈ 18.3

Therefore, the dimensions of the box that minimize the surface area are a square base with side length of approximately 18.3 inches, and a height of:

h = 8500 / [tex]x^2[/tex] ≈ 26.2 inches

E) UPS might be interested in designing a box that minimizes the surface area because it can reduce the amount of cardboard used in each box, resulting in cost savings and a reduced environmental impact. Additionally, minimizing the surface area of a box can make it more efficient to stack and transport, reducing shipping costs and making the overall process more sustainable.

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A) The Surface Area = [tex]X^2 + 34000/X[/tex]

B) The y-axis and the side length X on the x-axis.

C) The minimum amount of cardboard required to construct the box is approximately 1649.39 square inches.

D) The dimensions of the box that minimize the surface area are X = 20.5 inches and Y = 16.87 inches.

E)  Smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

A) Express the surface area of the box as a function of X:

Let the side length of the square base be X and the height of the box be Y. Then, we know that the volume of the box is 8500 cubic inches, so:

[tex]X^{2Y} = 8500[/tex]

To find the surface area of the box, we need to add up the area of each face. There are 5 faces in total (the bottom square and 4 identical rectangular sides), so:

Surface Area = [tex]X^2 + 4XY[/tex]

We can substitute the value of Y from the equation for volume, giving:

Surface Area = [tex]X^2 + 4X(8500/X^2)[/tex]

Surface Area = [tex]X^2 + 34000/X[/tex]

B) Graph the function found in part a:

To graph this function, we can plot the surface area on the y-axis and the side length X on the x-axis. The graph will have a minimum value, which we can find using calculus or by using a graphing calculator.

C) What is the minimum amount of cardboard that can be used to construct the box:

The minimum amount of cardboard required to construct the box is the surface area of the box. To find this minimum value, we need to find the minimum point on the graph in part b. From the graph or by using calculus, we can see that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. Substituting this value into the equation for surface area, we get:

Surface Area = [tex]20.5^2 + 4(20.5)(8500/20.5^2)[/tex]= 1649.39 square inches

D) What are the dimensions of the box that minimize the surface area:

From part c, we know that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. To find the height of the box, we can substitute this value of X into the equation for volume:

[tex]X^2Y = 8500[/tex]

[tex](20.5)^2 Y = 8500[/tex]

[tex]Y = 8500/(20.5)^2 = 16.87[/tex] inches

E) Why might UPS be interested in designing a box that minimizes the surface area:

UPS and other parcel delivery services are always looking for ways to reduce their costs and increase efficiency. By designing a box that minimizes the surface area while still containing the same volume of goods, they can reduce the amount of cardboard used for each shipment. This would save them money on materials and shipping costs, while also reducing their environmental impact. Additionally, smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

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The percent rate of change of students graduating within 4 years from 1995 to 2009 =   8.17%

Here,  the percent of studenst graduated in 1995 = 57. 5%

and the percent of studenst graduated in 2009 = 52. 8%

First we find the relative change.

Let a represents the initial value and b represents the findal value

a =  57.5 and b =  52.8

so, the relative rate of change of students would be,

r = (b - a)/a

r = |(52.8 -  57.5)| /  57.5

r =  0.0817

And the percent rate of change of students graduating within 4 years from 1995 to 2009 would be,

p = r × 100

p =  0.0817 × 100

p =  8.17%

Therefore, the required percent is   8.17%

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Answer:

(2x+6),(2x-6)

Step-by-step explanation:

This instance is DOTS or the difference of 2 squares so (2x+6),(2x-6). it states [tex]a^{2} - b^{2} = (a+b)(a-b)[/tex]

From the similar triangle, y=8.7, and x=4

From the similar triangle,

First lets find the angle both triangles share

to determine the value , solving on the bigger triangle,

cosθ= adjacent/hypothenus

cosθ= 5/10

cosθ= 0.5

θ= 60

Therefore, to obtain y,

sin 60= y/10

y=10 sin 60

y=8.7

from the smaller triangle,

to determine x

cos 60=2/x

x cos 60=2

x=2/cos60

x= 4.

Therefore, y=8.7, and x=4.

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As the probability of flooding any given year is 0.05, the probability of not flooding in the next year is 0.95 or 95%.

The probability of flooding in a region once every 20 years means that the probability of flooding any given year is 1/20 or 0.05.

Given that the probability of flooding in any one year is greater than zero, we know that the probability of not flooding is less than 1.

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The measure of angle a is 30° , angle b is 60° and angle c is 105°  calculated from the properties of angles and of triangle.

When two straight lines intersect each other at some angle, say line AB intersect line CD, then the opposite angles formed by the two lines are called vertically opposite angles. A pair of vertically opposite angles are equal to each other.

Angle a is formed at the intersection of the two straight lines, say AB and CD. The angle opposite to angle is 30°.

Thus from the definition of vertically opposite angles we get,

Angle a = 30° , since pair of vertically opposite angles are equal to each other.

In a right angle triangle one of three angles is 90° and the other two angles are acute angles. The sum of all the angles of a triangle is 180°.

Say  ΔMNO is a right angle triangle where angle a is one of the other two acute angles (where angle a = 30°).

The third angle (acute) is b.

Thus from the sum of triangle we get,

Angle a + Angle b + 90° = 180°

⇒ 30° + Angle b + 90° = 180°

⇒ Angle b = 60°

Here angle c is an angle labelled in a triangle (on the left of the previous triangle, say ΔMNO).

Two angles are said to be adjacent angles when they have a common vertex and side. The pair of adjacent angles sum to 180° , that is they are supplementary angles.

The adjacent angle of Angle c is 75°.

Thus, Angle c + 75° = 180°

⇒ Angle c = 105°

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The domain of the function g(4) is equal to 16, which makes the option (1) correct.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function g(4) as follows:

Given g(x) = 5f(x) +1, from the table of values for f(x), f(4) = 3 so;

g(4) = 5(f(4)) + 1

g(4) = 5(3) + 1

g(4) = 15 + 1

g(4) = 16

Therefore, the domain of the function g(4) is derived to be equal to 16.

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