Austin Corp. reported the following information for 2013 and 2014.Interest receivable, December 31, 2013 $1,100Interest receivable, December 31, 2014 1,400Interest income--2014 3,200How much cash was received for interest during 2014?A. $2,900B. $3,200C. $3,500D. $3,800

Answer:

1) 18 Red balls

2) 12 blue balls

3) [tex]\frac{5}{3}[/tex] green balls to red balls

Step-by-step explanation:

R  B  G

3:2:5

3+2+5 = 10

60/10 = 6

to find the number of red balls simply do

3 * 6 = 18

to find the number of blue balls do

2 * 6 = 12

to find the number of green balls do

5 *6 = 30

the ratio of green/red same as the original

5/3  

To find A's best response to B choosing L in normal form game, we can compare the payoffs for A choosing H and L when B chooses L.

If A chooses H and B chooses L, then A's payoff is 0 and B's payoff is 6.

If A chooses L and B chooses L, then A's payoff is 3 and B's payoff is 3.

Comparing the payoffs, we see that A gets a higher payoff if he chooses H when B chooses L. Therefore, A's best response to B choosing L is H.

To find B's best response to A choosing L, we can compare the payoffs for B choosing H and L when A chooses L.

If A chooses L and B chooses H, then A's payoff is 9 and B's payoff is 4.

If A chooses L and B chooses L, then A's payoff is 3 and B's payoff is 3.

Comparing the payoffs, we see that B gets a higher payoff if he chooses L when A chooses L. Therefore, B's best response to A choosing L is L.

So, the answer is (c) L;H. A's best response to B choosing L is H, and B's best response to A choosing L is L.

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The critical z-value for a 98% confidence level is 2.33.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

Statistics plays a significant role in various fields, including business, economics, social sciences, medicine, engineering, and many others.

To find the critical z value for a 98% confidence level, we need to look up the z-value associated with an area of 0.01 in the upper tail of the standard normal distribution table (since 98% of the area lies within the confidence interval, leaving 2% in the tails).

Using a standard normal distribution table, we can find that the z-value that corresponds to an area of 0.01 in the upper tail is approximately 2.33.

Therefore, the critical z-value for a 98% confidence level is 2.33.

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What will likely happen to the price of the toy after it lost popularity is that the price would go down, because demand decreased. That is option D.

The effect of decrease in the popularity of a product affects both it's demand and the cost price.

Since the product is less needed by the consumers and population at large the manufacturer would adjust the cost price to enhance its sales output at the end of each business month.

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The surface area of the rectangle prism is 96cm²

A prism is a solid shape that is bound on all its sides by plane faces. The surface area of a prism is expressed as;

SA = 2B +pH

where B is the base area and p is the perimeter of the base and h is the height of the prism.

Base area = 4× 2 = 8cm²

perimeter of the base = 2(4+2) = 2× 8 = 16cm²

height = 5cm

therefore the surface area of the prism

= 2×8 + 5×16

= 16+80

= 96cm²

therefore the surface area of the prism is 96cm²

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a) The fraction of all the meal combinations which have at least one vegan option is 1/8.

b) There are 168 different three-course meal combinations available.

A fraction is a way of representing a part or a ratio of a whole, using a numerator and a denominator separated by a slash ("/") or a horizontal line. The numerator represents the number of parts being considered, and the denominator represents the total number of equal parts that make up the whole.

According to the given information:

a) To work out the fraction of all the meal combinations which have at least one vegan option, we need to count the total number of meal combinations with at least one vegan option, and then divide it by the total number of meal combinations.

The vegan options in the table are:

Mozzarella salad (V)

Cheese pizza (V)

Aubergine curry (V)

There are a total of 4 salads (including the vegan salads) and 6 mains (including the vegan mains). So the total number of meal combinations without any restriction is 4 x 6 = 24.

Now, we can calculate the total number of meal combinations without any vegan option, which is 24 - 3 = 21 (since 3 options are vegan).

So, the fraction of all the meal combinations which have at least one vegan option is (total meal combinations - meal combinations without any vegan option) divided by total meal combinations:

= (24 - 21) / 24

= 3 / 24

= 1 / 8

Therefore, the fraction of all the meal combinations which have at least one vegan option is 1/8.

b) If diners also choose one of 7 dessert options, we can simply multiply the total number of meal combinations (24) by the number of dessert options (7) to get the total number of three-course meal combinations available:

24 x 7 = 168

So, there are 168 different three-course meal combinations available.

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The solution to the given problem of the unitary method comes out to be Plan A and Plan B thus lasting for a total of 1.25 hours each.

Finish the project using the tried-and-true basic methodology, the actual variables, and any pertinent knowledge you gain from the broad and specific questions. In response, customers might be given another opportunity to sample the expression the products. We'll miss out on important breakthroughs in programming comprehension if these changes don't take place.

Here,

Let's say that Plan A's duration is "a" hours and Plan B's duration is "b" hours.

=> Equation 1: 6a + 2b = 10.

=>  Equation 2: 3a + 5b = 10.

To get rid of "a," multiply Equation 1 by 3 and Equation 2 by 6 and you get:

=> Equation 3: 18a + 6b = 30

=> Equation 4: 18a + 30b = 60

Equation 3 minus Equation 4 results in:

=>  24b = 30

When we multiply both sides by 24, we get:

=> b=30/24=5/4=1.25 hours.

The value of "b" can now be reinserted into Equation 3 to find "a":

=> 18a + 6(1.25) = 30

=> 18a + 7.5 = 30

=> 18a = 30 - 7.5

=> 18a = 22.5

When we multiply both sides by 18, we get:

=> if a = 22.5/18 then 1.25 hours.

Plan A and Plan B thus last for a total of 1.25 hours each.

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Neither of the segments is the perpendicular bisector of the other.

To determine which segment is the perpendicular bisector of the other, we need to find the equations of the lines containing each segment and then check if one of the lines is perpendicular to the other and passes through the midpoint of the other segment.

Let's start by finding the midpoint of segment AT. The coordinates of A and T are not given, but we don't actually need them to find the midpoint.

So, the midpoint M of segment AT is:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2)

We don't know the actual values of AT_x1, AT_x2, AT_y1, and AT_y2, but we can find their expressions in terms of x using the segment lengths and the coordinates of the endpoints. We have:

AT_x2 - AT_x1 = BT_x2 - AT_x1 = (x + 5) - (2x + 3) = -x + 2

AT_y2 - AT_y1 = BT_y2 - AT_y1 = (BT - AT) = (x + 5) - (2x + 3) = x + 2

Therefore,

AT_x1 = AT_x2 + x - 2

AT_y1 = AT_y2 - x - 2

Now, we can substitute x=2 and the expressions for AT_x1 and AT_y1 into the midpoint formula to find the coordinates of M:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2) = ((AT_x2 + 2 - AT_x2)/2, (AT_y2 - 2 - AT_y2)/2) = (1, -1)

So, the midpoint of segment AT is M(1, -1).

Next, let's find the equations of the lines containing segments AT and DT. We can use the point-slope form of the equation of a line, which states that the equation of a line passing through a point (x1, y1) with slope m is y - y1 = m(x - x1).

For segment AT, we have:

m_AT = (AT_y2 - AT_y1)/(AT_x2 - AT_x1) = (x + 2)/(x - 1)

Let's substitute x=2 to find the slope of the line containing segment AT:

m_AT = (2 + 2)/(2 - 1) = 4

So, the equation of the line containing segment AT is:

y - AT_y1 = m_AT(x - AT_x1)

y - (22 + 3) = 4(x - 22 - 1)

y - 7 = 4(x - 5)

y = 4x - 13

For segment DT, we have:

m_DT = tan(m∠ATD) = tan(41x + 8)

Let's substitute x=2 and simplify:

m_DT = tan(82 + 8) = tan(90) = undefined

This means that the line containing segment DT is vertical and its equation is x = DT_x1 = 4*2 + 1 = 9.

Now, we need to check if one of these lines is perpendicular to the other and passes through the midpoint of the other segment.

First, let's check if the line containing segment AT is perpendicular to the line containing segment DT.  We have:

m_AT * m_DT = 4 * undefined = undefined

Since undefined is not equal to -1, the lines are not perpendicular, and we can rule out the possibility that the line containing segment AT is the perpendicular bisector of segment DT.

Next, let's check if the line containing segment DT is perpendicular to the line containing segment AT. We have:

m_AT = 4

So, the slope of the line perpendicular to the line containing segment AT is -1/4. We can use the point-slope form of the equation of a line again:

y - M_y = -1/4(x - M_x)

y - (-1) = -1/4(x - 1)

y + 1 = -1/4x + 1/4

y = -1/4x + 3/4

Now, we need to check if this line passes through point D, an endpoint of segment DT. We can substitute the coordinates of D into the equation of the line and check if the equation holds true:

DT_y1 = 4*2 + 1 = 9

DT_x1 = 9

9 = -1/4*9 + 3/4

9 = -9/4 + 3/4

9 = -6/4

This is not true, so the line containing segment DT does not pass through point D. Therefore, we can conclude that the line containing segment DT is not the perpendicular bisector of segment AT.

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Standard deviation is the best method for comparing the spread of frequency distributions for two groups, as it provides an accurate and sensitive measure of variability.

To compare the spread of the frequency distributions for two groups, we can use the measure of variability called the standard deviation. The standard deviation provides a measure of how much the data points are spread out around the mean.

A smaller standard deviation indicates that the data points are clustered closely around the mean, whereas a larger standard deviation indicates that the data points are more spread out from the mean.

The reason why standard deviation is a good measure of spread is that it is sensitive to the distance between data points and the mean. Therefore, it provides an accurate measure of how much the data is spread out, regardless of the shape of the distribution.

To calculate the standard deviation, we first need to calculate the mean of each group, and then the difference between each data point and the mean, squared.

We then take the average of these squared differences and take the square root to get the standard deviation.

For example, suppose we have two groups of test scores:

Group A: 75, 80, 85, 90, 95

Group B: 60, 70, 80, 90, 100

To calculate the standard deviation for Group A, we first calculate the mean:

(75 + 80 + 85 + 90 + 95) / 5 = 85

Then we calculate the difference between each data point and the mean, squared:

(75 - 85)² = 100

(80 - 85)² = 25

(85 - 85)² = 0

(90 - 85)² = 25

(95 - 85)² = 100

Next, we take the average of these squared differences:

(100 + 25 + 0 + 25 + 100) / 5 = 50

Finally, we take the square root of this average:

√(50) = 7.07

Therefore, the standard deviation for Group A is 7.07. We can repeat these steps for Group B and compare the two standard deviations to determine which group has a larger spread.

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99.57 units is the measurement of the hypotenuse for the given triangle.

In this case, the legs of the triangle are 7x+6 and 5x, so we have:

a = 7x+6

b = 5x

Substituting x = 11, we get:

a = 7(11) + 6 = 83

b = 5(11) = 55

Now we can use the Pythagorean theorem to find the length of the hypotenuse:

[tex]c^2 = a^2 + b^2\\c^2 = 83^2 + 55^2\\c^2 = 6889 + 3025\\c^2 = 9914[/tex]

Taking the square root of both sides, we get:

c = √9914 ≈ 99.57

Therefore, the length of the hypotenuse of the triangle is approximately 99.57 units.

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If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

The conversion factor that states [tex]1[/tex] gramme is about equivalent to [tex]0.035[/tex]ounces can be used to convert grammes to ounces.

we may multiply  [tex]5[/tex] by  [tex]0.035[/tex] to convert [tex]5[/tex] grammes to ounces:

[tex]5 grams \times 0.035 \ oz/gram = 0.175[/tex] ounces

It's vital to remember that the ratio of 1 gramme to  [tex]0.035[/tex] ounces is merely an estimate; the precise ratio is 1 gramme to [tex]0.03527396195[/tex] ounces.

However, utilizing the streamlined conversion factor of [tex]1[/tex] gramme to [tex]0.035[/tex] ounces is accurate enough for the majority of routine uses.

Therefore,If [tex]5[/tex] grammes are rounded to the closest tenth, that would be  [tex]0.175[/tex] ounces.

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Answer: 3x²-2x+5=0

You subtract the 2x and add 9 from both sides to get 3x²-2x+9=0

Answer:

3x^2−2x+5=0

Step-by-step explanation:

3x^2-4=2x-9

first you gotta add 9 to both sides

3x^2+5=2x

then you gotta subtract 2x from both sides

3x^2-2x+5=0

-SpoOky

Answer:

6^2 + 4(1/2)(6)(9) = 36 + 108 =

144 square meters

Answer: $63.40

Step-by-step explanation:

She starts out with $317  but she will only get 80%  which means she will lose 20%

100%-80%=20%

take 20% of 317

.2 x 317    convert 20% to decimal by moving decimal twice and multiply

=63.4

She will lose $63.40

Reason:

If she withdraws early, she can only withdraw 80% of what she put in. She takes a 20% penalty.

20% of 317 = 0.20*317 = 63.40 dollars is how much she loses.

Put another way:

She is able to withdraw 0.80*317 = 253.60 dollars if doing so early. She lost 317-253.60 = 63.40 dollars

Answer:

b

Step-by-step explanation:

we cannot simply write equation 5c + 3d as 8c, 8d, or 8cd.

A variable in mathematics is a symbol or letter that is used to indicate a quantity in a mathematical statement or equation that can have many values. It is a symbol that may be used to represent an arbitrary or undefined integer in algebraic expressions and equations.

In the equation 5c + 3c = 8c, we can combine the two terms on the left side because they have the same variable (c) and the same exponent (1).

However, in the expression 5c + 3d, the two terms have different variables (c and d) and cannot be combined in the same way. Therefore, we cannot simply write 5c + 3d as 8c, 8d, or 8cd.

If we want to simplify the expression 5c + 3d, we can only write it in its simplest form or factor it further if possible.

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B

Step-by-step explanation:

Answer:

blank is 4

Step-by-step explanation:

We can set up the equation:

[tex]\frac{1}{8} *x = \frac{1}{2}[/tex]

To solve, multiply both sides by 8.

[tex]\frac{1}{2}*8 = 4[/tex]

This checks out with the other statement.

Answer: its b

Step-by-step explanation: all coins have a heads and tails so that takes out c.

d is just for jokes

a.  a coin in a school problem is not gonna be wieghted.

The distance between the end of the water supply pipe and the sink should be 2 times the diameter of the supply pipe. Option B is the correct answer.

The distance between the end of the water supply pipe and the sink is determined by plumbing codes and standards to ensure safe and efficient water delivery.

The National Standard Plumbing Code requires a minimum distance of 2 times the diameter of the supply pipe between the end of the pipe and the nearest point of use, such as a faucet or sink.

This helps prevent any potential contamination from the supply pipe and ensures adequate flow and pressure for efficient operation.

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The simplified form of the given expression, can be found to be A. x² + 7x + 5.

Simplified expressions are algebraic expressions that have been reduced to their simplest form by applying the rules of arithmetic and algebra.

To simplify the expression, we add the corresponding terms from both expressions:

(-3x² + 2x - 4) + (4x² + 5x + 9)

Combine the x² terms: -3x² + 4x² = 1x² (or simply x²)

Combine the x terms: 2x + 5x = 7x

Combine the constants: -4 + 9 = 5

So, the simplified expression is:

x² + 7x + 5

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Answer: The outlier is 93 is an outlier. Since an outlier exists, median and IQR are the best measures of center and variation to represent this data set

If the researcher is interested in testing if a particular value is either greater or smaller than the hypothesized value, then a one-tailed test is appropriate

The decision of whether to use a one-tailed test or a two-tailed test when testing hypotheses depends on the nature of the situation and what the researcher is trying to demonstrate. . If the researcher is interested in testing if a particular value is simply different from the hypothesized value, then a two-tailed test is appropriate. The level of significance of the test is also an important consideration, but it is not the primary determinant of whether to use a one-tailed or two-tailed test.

what is demonstrate?

To demonstrate means to show or prove something convincingly with evidence or argument. It is a way of providing support for a claim or idea.

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The reasonable estimate of the median home cost in the US in 2025 is  $340,000

To assess the middle domestic taking a toll within the US in 2025, ready to utilize the verifiable drift and expect that the relationship between the middle domestic fetched and time (measured in a long time since 1975) is straight.

Let`s begin with calculating the rate of increment in median domestic fetched per year utilizing the information from 1975 to 2005. Ready to utilize the equation for the slant of a direct relapse line:

slant(slope) = (y2 - y1) / (x2 - x1)

where

y1 and y2 are the middle domestic costs in 1975 and 2005,

separately, and x1 and x2 are comparing a long time (0 and 30).

incline = ($240,000 - $40,000) / (30 - 0) = $6,000

This implies that the middle domestic taken a toll expanded by a normal of $6,000 per year amid this period.

Presently, ready to utilize this rate of increment to appraise the middle domestic taken a toll in 2025, which is 50 long times after 1975.

The year 2025 will be 50 a long time after 1975, so the number of a long time since 1975 will be x = 50. Utilizing the incline we fair calculated, able to assess the middle domestic fetched in 2025 as takes after 

y = y1 + slant(slope) * x = $40,000 + $6,000 * 50 = $340,000

Therefore, a sensible assessment of the middle domestic taking a toll within the US in 2025, based on the presumption that the slant watched from 1975 to 2005 proceeds, is $340,000. 

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Answer:

2l + 2w = 24, so l + w = 12

A(l) = l(12 - l)

According to the given data the length of the cable is 257.6ft.

An angle is formed by two rays, also called sides or arms, that extend from the vertex in different directions. The amount of turn between the two rays is the angle's measure, usually expressed in degrees or radians. A full turn, or a complete revolution, is 360 degrees or 2π radians.

To find the length of the cable, we can use trigonometry. Let "x" be the length of the cable. The tower height forms a right angle with the ground, so we can use the sine function:

sin(50) = opposite/hypotenuse

sin(50) = height/x

We know the height of the tower is 200 ft, so we can solve for x:

x = height/sin(50)

x = 200/sin(50)

x ≈ 257.6 ft

Therefore, the length of the cable is approximately 257.6 ft.

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The probability that point X is on segment DE is given as follows:

1/9.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The length of segment AE is given as follows:

28 - (-8) = 36 units.

The length of segment DE is given as follows:

28 - 24 = 4 units.

Hence the probability is given as follows:

p = 4/36

p = 1/9.

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Hence, it will take 2.6 hours for the two trains to be 520 miles apart.

Distance is a numerical or occasionally  qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

In everyday use and in kinematics, the speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity..

The two trains are moving  away from each other,

so we can  add their speeds to get their relative speed:

relative speed = 95 mph + 105 mph = 200 mph

Now ,we determine  the time it takes for the trains to be 520 miles apart,

so we can use the formula:

distance = speed × time

let t be the time  it takes for the trains to be 520 miles apart.

Then we get,

520 = 200 × t

Solving for t, we get:

t = [tex]\frac{520}{200}[/tex]

t = 2.6 hours

Therefore, it will take 2.6 hours for the two trains to be 520 miles apart.

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The equation r · sin θ = 10 in rectangular coordinates is equal to y = 10.

Herein we find the representation of a equation in polar coordinates, whose form in rectangular coordinates. This can be done by using the following definitions:

cos θ = x / r

sin θ = y / r

Where:

Then, the equation in polar coordinates is:

r · sin θ = 10

y = 10

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