Directions: Based on the information given in the following problem, compute the gross pay.

Annual pay: $14,900. Calculate monthly pay.

Round your answers to two decimal places.

gross pay: $
per month

The given expression can be written as in the simplified form, 5/3

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

[tex]1 + \frac{1}{1+ \frac{1}{1+1} }[/tex]

It can be solved by various steps,

First step,

1/(1+1) can be written as 1/2

[tex]1 + \frac{1}{1+ \frac{1}{2} }[/tex]

Second step,

1 + 1/2 can be written as 3/2

[tex]1 + \frac{1}{\frac{3}{2} }[/tex]

Now, 1/(3/2) can be written as 2/3

[tex]1 + \frac{2}{3}[/tex]

Further, it can be written as,

5/3

Hence, the simplified form is 5/3

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Answer:

Step-by-step explanation:

y=10

David paid a total amount of 19.05 in dollars.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Cost of the food = $15

Sales tax = 7%

Cost of food with sales tax = 15 + (7% × 15) = $16.05

He tipped the waiter 20% of the cost of the food.

Total cost = $16.05 + (20% × 15) = $16.05 + 3 = $19.05

Hence the total amount is $19.05.

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The surface area of a solid object is defined as the area that the object occupies. To find the surface area we must find the total area of its faces.

Here, we are given a triangular prism and we are asked to find its surface area.

We can find the area of a triangular prism using the following formula (as shown in the attached image, Please note that "b" and "s2" have the same defined length) :

(S + b + h)L + bh

Where

Here, we are given the length of the base(8in), the height(15in) and the length of the prism(21in); however we are not given the slant length. so we must find it.

If we ignore the prism itself and look at the base, we notice that the base is a right angled triangle. Within the triangle we have its base length and height and we need to find the hypotenuse. We can do so by using the Pythagorean theorem: a² + b² = c² where a and b = length of legs and c = hypotenuse.

Here a and b = 15 and 8.

By plugging in these values we acquire:

==> 15² + 8² = c²

==> 225 + 64 = c²

==> 289 = c²

==> 17 = c

So the hypotenuse (or slant length) = 17

Now that we have identified all the variables we can finally plug in the values to get the surface area.

We have

Plugging this into (S + b + h)L + bh, we acquire

==> (17 + 8 + 15)21 + 8(15)

==> 40(21) + 8(15)

==> 840 + 8(15)

==> 840 + 120

==> 960

The surface area is 960 in²

When digitizing a recording of a musical performance, two strategies that will result in a more accurate digital representation of the original music are:

Increasing the sampling rate of the music being digitized: The sampling rate is the number of samples of the analog audio waveform taken per second. The higher the sampling rate, the higher the frequency range that can be captured, resulting in a more accurate representation of the original sound.

Increasing the bit depth of the music being digitized: The bit depth is the number of bits used to represent each sample of the audio waveform. The higher the bit depth, the greater the number of possible levels of amplitude that can be captured, leading to a more accurate representation of the original analog waveform and a clearer, more dynamic digital audio file.

Increasing the volume of the music being digitized and increasing the speed of the music that is being digitized do not necessarily result in a more accurate digital representation of the original music.

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Consider a situation where we are typing data it in to an Excel worksheet and accidentally type 762 instead of 726. This type of inaccuracy is referred to as "transposing."

A vertical range containing cells is converted into a horizontal range, alternatively vice versa, via the TRANSPOSE function.

Consider a situation where we are typing data it in to an Excel worksheet and accidentally type 762 instead of 726.

Thus, this type of inaccuracy is referred to as "transposing."

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Because of gravity, the item accelerates continuously. The ball took 2 seconds to reach the ground, hence option (d) is accurate.

The metric system and the International Systems in Units both use the metre (m), also spelt as meter, as the basic unit of length (SI). Inside the British Imperial & American Customary systems, it is equivalent to around 39.37 inches.

Metric is the preferred word outside of North America for the measuring unit that is equivalent to about 1.094 yards, with American spelling being meter. Metric in American English and Metric everywhere else are terminology used in music and poetry respectively.

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If we feed the dog with same amount of food and with , without water , then the independent variable is " presence or absence of added water" .

The Independent Variable is the factor that is manipulated or varied in an experiment in order to observe the effect on the dependent variable.

In this case, the dependent variable would be the amount of food consumed by the dog.

By adding or not adding water to the food and keeping all other conditions constant ; such as:  using the same bowls, feeding the dog at the same time of day ,

the experiment aims to determine the effect of the independent variable (added water) on the dependent variable (amount of food consumed).

Therefore , the independent variable in this situation  is " presence or absence of water" .

The given question is incomplete , the complete question is

You try feeding your dog the same amount of food both with and without added water while using the same bowls at the same time of day.

What is the independent variable ?

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If Sam and Tyrone are running on a trail. Sam reaches the 4th mile marker at the same time that Tyrone reaches the 1st mile marker. The number of minutes that  Sam and Tyrone meet is: B) 45 minutes .

Speed = Distance/Time  

Sam speed = 1/10 mile/minute

Tyrone speed = 1/6 mile/minute

Time distance covered by Tyrone= (4-1) + x

Time taken= t

Hence,

x/(1/10)   =  (3 + x)/(1/6)

10x  =   6(3 + x)

10x  =  18 + 6x

4x  = 18

x  = 9/2

Time ( t) =x/(1/10)   =  (3 + x)/(1/6)

Time ( t)  =  (9/2)/(1/10)

Time ( t)  = 45 minute

Therefore the correct option is  B.

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Answer:

140 for both

Step-by-step explanation:

An exterior angle and its adjacent interior angle are supplementary angles, so they add to 180°.

so Part A = 180-40=140

Part B

The exterior angle theorem states that: The measure of an exterior angle of a triangle is supplementary to its adjacent interior angle.  The sum of the remote interior angles must equal the measure of the exterior angle of the triangle.

It's also 140

The equation of the line through the points (-1, -2) and (4, 3) is y = x + 3.

The equation of a line can be found using the point-slope form, where the slope of the line is determined from the two given points and the equation is written in the form y = mx + b, where m is the slope and b is the y-intercept.

Given the points (-1, -2) and (4, 3), the slope of the line can be calculated as (3-(-2))/(4-(-1)) = 5/5 = 1.

Plugging in the coordinates of one of the points and the slope into the point-slope form, we have:

y - -2 = 1(x - -1)

Simplifying, we get:

y = x + 3 is the required equation of the line.

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When one alternative stochastically dominates another, it means that the first alternative has a higher probability of leading to a better outcome than the second alternative, regardless of the decision maker's attitude towards risk.

In other words, one alternative stochastically dominates another when, for any level of payoff that the decision maker might find acceptable, the first alternative has a higher probability of achieving that level of payoff than the second alternative.

This concept is often used in decision-making under uncertainty, such as in the field of economics. It can help decision makers to compare different alternatives and choose the one that is more likely to lead to a desirable outcome. Stochastic dominance is a concept that is commonly used in decision theory and is based on the idea of probability. It refers to the relationship between two alternatives with respect to their probability distributions.

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- 4.2 explain in your own words what it means when one alternative stochastically dominates another?

If you roll a fair six-sided die, you will receive the indicated number of points. After one roll, 3.5 points should be expected.

A six-sided cube with the digits 1-6 printed on the faces is the most popular type of die. The value of the roll is indicated by the number of "spots" that are visible at the top. The opposite faces on the six-sided die are positioned so that they always add up to seven. The word "die" is derived from Old French and Latin datum, which means "anything provided or played." The names of the numbers are preferable, but some seasoned gamblers still refer to the different sides of the dice by using the terms ace, deuce, trey, cater, cinque, and dice.

Add up all of the die's pips., [tex]1+2+3+4+5+6=21[/tex].

The likelihood of a specific face being up on any roll of a single die is [tex]1/6[/tex].

After one roll, the anticipated number of points is [tex]21/6= 3.5[/tex]

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A group can choose two musicals, three dramas, and four thrillers out of eleven musicals, eight dramas, and seven thrillers by using the formula 11C2 × 8C3.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A={1,6} has a permutation of 2, which is {1,6}, {6,1}. There is no other way to organize the components of set A, as you can see. Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Next, combination determines how many ways we can choose two numbers from each group.

11C2 × 8C3

11*10/2*1=110/2=55

8c3=8*7*6/3*2*1

55×56 = 3080

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The first hypothesis is acceptable because it is testable. The second hypothesis is not acceptable because it is a statement of opinion. The third hypothesis is not acceptable because it is not testable and measurable. The fourth hypothesis is acceptable because it is testable.

The hypothesis " the new formula of puppy chow makes puppies grow 57% faster than the original formula of puppy chow " is a good hypothesis since it is testable and falsifiable.

"Chris Sale was the best pitcher in Chicago baseball history," is an opinion that cannot be verified or disproven via scientific investigation. This hypothesis is not acceptable because it is a statement of opinion.

The phrase "ghosts really do exist" is also neither testable or falsifiable, and hence is not an admissible hypothesis.

The statement "dogs are happy when fed steak" is a broad generalization that may not apply to all dogs, but it may be tested through controlled experiments. So it is also acceptable.

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The solution of the system of equation are y=4/9x-5 and 1/9x-2y=-4 is x=18 and y=3.

Two or more expressions with an Equal sign is called as Equation.

The system of equation are:

y=4/9x-5..(1)

1/9x-2y=-4..(2)

Substitute 1 in equation 2

1/9x-2(4/9x-5)=-4

1/9x-8/9 x+10=-4

x/9(1-8)+10=-4

x/9(-7)+10=-4

Substitute 10 on both sides

-7x/9=-4-10

-7x/9=-14

-7x=-126

Divide both sides by 7

x=126/7

x=18

Now plug in x value in equation 1

y=4/9(18)-5

y=8-5

y=3

Hence, the solution of the system of equation are y=4/9x-5 and 1/9x-2y=-4 is x=18 and y=3.

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The lead time for the first row in the data frame Onlineta City Hotels v2 is 65.

The lead time for the first row in the data frame Onlineta City Hotels v2 is calculated as follows: Take the difference of the checkout date (88) and the booking date (23) to get 65.

Lead Time = Checkout Date - Booking Date

Lead Time = 88 - 23

Lead Time = 65

Lead time is the time difference between when a customer books a hotel room and when they check out of the hotel. This lead time is important for a hotel, as it allows them to plan ahead and anticipate the demand for their rooms. Knowing the lead time helps a hotel manager to manage the availability of their rooms, ensure that they have enough staff on hand to accommodate guests, and plan for any other services that may be needed. It is also important for marketing purposes, as it allows a hotel to target customers who may be more likely to book a room in advance.

The lead time for the first row in the data frame Onlineta City Hotels v2 is 65.

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Answer:

The lead time in the first row of the onlineta_city_hotels_v2 data frame is 88. By using a filter with ggplot2, you are able to select specific segments of your data and plot them using R. Going forward, you can use filters and facets to compare visualizations of different aspects of the same data to gain even deeper insights from your analyses.

Step-by-step explanation:

Answer:

The y-intercept is the point where the graph crosses the y- axis.  The line crosses the y-axis at (0,-6). So, the y-intercept is -6.

A. The y-intercept is 3,500. (0,3500)

B. The y-intercept represents the height of the glider when it starts falling.

Step-by-step explanation:

Answer:

See the attached image.

Step-by-step explanation:

The y-intercept is the point on a line when it touches the y-axis.

When the horizontal axis is time (t), this point at t = 0 represents when no time has passed since some point in time.

Answer:

The number 9.3488 rounded to the nearest tenth is; 9.3

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

The proportional equation that represents the salary of each person after the raise is given as follows:

y = 1.12x.

The raise to the salary of each staff member is given as follows:

12%.

Hence the percentage of the salary after the raise is given as follows:

100 + 12 = 112%.

Meaning that the multiplier is of:

1.12.

Then the equation is given as follows:

y = 1.12x.

In which:

The problem asks for the proportional equation that represents the salary of each person after the raise.

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The correct response is C. If 56% of the houses take more than three months to sell, there is 1.4% chance that a random sample proportion would be as high as or higher than the one they obtained.

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Population model: Y = β0 + β1X + ε, where Y is the SAT score, X is the number of hours spent in the preparation course, β0 is the intercept, β1 is the causal effect (the effect of hours on SAT), and ε is the error term.

To estimate the causal effect of hours of preparation on the SAT score, we would structure a controlled experiment as follows:

Population model: Y = β0 + β1X + ε, where Y is the SAT score, X is the number of hours spent in the preparation course, β0 is the intercept, β1 is the causal effect (the effect of hours on SAT), and ε is the error term. This model assumes that the causal relationship between hours and SAT score is linear and that the effect of hours on SAT score is constant for all students in the population.

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Answer:

the largest possible value for x is 6

the smallest possible value for x is 1

Step-by-step explanation:

Amounts that have with Lisa, Aldo, and Miguel in their wallets are $35, $25, and $100 respectively.

Lisa, Aldo, and Miguel have a total of $160 in their wallets.

Miguel has 4 times what Aldo has.

Lisa has $10 more than Aldo.

Let the amount that the Aldo has to be $x

Then according to the given question.

The amount that the Lisa has $(x+10)

The amount that the Miguel has $(4x)

So the total amount can be resulted as the sum of the amounts of the three each individual.

x + x + 10 + 4x = 160

6x + 10 = 160

6x = 160 - 10

6x = 150

x = 25

Therefore the amount in the Aldo wallet is $25

Hence, the amount in the Lisa's wallet is:

x + 10 = 25 + 10 = $35

Hence, the amount in the Miguel's wallet is:

4x = 4(25) = $100

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Lisa, Aldo, and Miguel have a total of $160 in their wallets. Miguel has 4 times what Aldo has. Lisa has $10 more than Aldo. how much does each have?

any cylindrical shape that has the r²h equal to 160 will have an equal volume.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, Right circular cylinder A has a volume of $160pi cubic feet.

The product of a cylinder's base area and height provides the formula for calculating the cylinder's volume. A cylinder's volume is equal to πr²h cubic units.

Where r is the radius

and h is the height

In our case volume = 160 * pi

By comparing,

r²h = 160

So we can state that any cylindrical shape that has the r²h equal to 160 will have an equal volume.

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The uniform probability distribution is used with  option (d) a continuous random variable.

The uniform probability distribution is used for a continuous random variable, meaning that a variable can take on any value within a specified range, and the likelihood of any value within that range is equal. This distribution is often represented by a rectangle with height equal to the uniform probability density, and width equal to the range of the variable. In other words, if the range of a continuous random variable is from a to b, and we define the uniform distribution over this range, then the probability of any value between a and b is equal to (b-a)^-1. The uniform distribution is useful in various applications where the lack of knowledge of the underlying process leads to equal probabilities for all outcomes in a given range.

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The expression for F in terms of d is F = 108 / d².

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s. If these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s.

Inversely proportional means, when one quantity increases, other decreases.

Given that,

The force of attraction, F Newtons, between two magnets is inversely proportional to the square of the distance, d cm, between the magnets.

F ∝ 1 / d²

This can be written as, for some constant k,

F = k (1 / d²)

When d = 1.5, F = 48.

48 = k (1 / (1.5)²)

48 = k / 2.25

k = 48 × 2.25

k = 108

So the expression relating F and d can be written as,

F = 108 / d²

Hence the required expression is F = 108 / d².

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It is crucial to note that a correlation coefficient of 0 does not imply that there is no link between the variables; rather, it indicates that the relationship is not linear.

A correlation coefficient is a statistical measure of the extent to which changes in one variable predict changes in another. The value of a positively linked variable rises or falls in lockstep. Correlation coefficients, in summary, are used to determine the strength and direction of linear correlations between pairs of variables. Pearson's correlation coefficient should be used when both variables are normally distributed; otherwise, Spearman's correlation coefficient should be used. Pearson's correlation coefficient is calculated by dividing the covariance of two variables by the product of their standard deviations.

Here,

A correlation value of 0 denotes that no linear relationship exists between two variables. It indicates that whether one variable rises or decreases, the other variable does not change. In other words, no relationship exists between the two variables.

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