Part 3
sales tax is 8%
basketballs are 20% off
you have two customers john and david. john has $250 and
david has $150. john is coaching a baseball team and wants
to buy 10 baseball bats for his team. david wants to buy 3
pairs of running shoes for his kids. will each person be able
to buy the items that they want? explain.
baseball bats are 5% off
running shoes are 15% off
i
tax
with
discount
total
cost
john
david

Hence, The percentage of households in the town with one or more cars = 75.8%, a standard error to the estimate= 1.92%

Total sample households  = 500

Households in the town with one car = 172

Households in town with two or more cars  =207

Households in the town with one or more cars = 172 + 207

                                                                            = 379

The percentage of households in the town with one or more cars =

(379 / 500)*100 = 75.8%.

A standard error to the estimate  = 1.92%.

Hence, The percentage of households in the town with one or more cars = 75. , a standard error to the estimate= 1.92%

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The probability that James will take the same mode of transportation twice is 1/9.

To find the probability that James will take the same mode of transportation twice, we need to calculate the probability of each individual transportation option and then multiply them together.

In the morning, James has 3 transportation options: bus, cab, or train. Since he randomly chooses his ride, the probability of selecting any particular option is 1 out of 3 (assuming all options are equally likely).

Therefore, the probability of James selecting the same transportation mode in the morning and evening is 1/3.

Hence, the probability that James will take the same mode of transportation twice is 1/3 multiplied by 1/3:

P(same mode of transportation twice) = 1/3 * 1/3 = 1/9.

Therefore, the probability that James will take the same mode of transportation twice is 1/9.

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The system with an input-output relation y(u) -x() cos(2T fo), where fo is a constant, is linear but not time-invariant.

To determine whether the system defined by the input-output relation y(u) = x(t) cos(2πf0 t) is linear or time-invariant, we need to apply the superposition principle and the time-invariance test.

Linearity:

A system is linear if it satisfies the superposition principle, which states that the response to a sum of inputs is equal to the sum of the individual responses to each input. Mathematically, this can be expressed as:

y(u) = a1x1(u) + a2x2(u)

where a1 and a2 are constants, x1(u) and x2(u) are two arbitrary input signals, and y(u) is the corresponding output.

Let's apply this principle to the given system:

y1(u) = x1(t) cos(2πf0 t)

y2(u) = x2(t) cos(2πf0 t)

y(u) = y1(u) + y2(u) = x1(t) cos(2πf0 t) + x2(t) cos(2πf0 t)

This is a sum of two inputs, and the output is the sum of the individual responses to each input. Therefore, the system is linear.

Time-Invariance:

A system is time-invariant if its behavior does not change over time. In other words, if the input signal is shifted in time, the output signal is also shifted by the same amount of time.

Let's test the time-invariance of the given system:

Assume the input signal is x1(t), and the corresponding output is y1(t) = x1(t) cos(2πf0 t).

Now, let's shift the input signal by a time τ to get a new input signal x2(t) = x1(t-τ). The corresponding output is y2(t) = x2(t) cos(2πf0 t) = x1(t-τ) cos(2πf0 t).

Let's compare the two outputs:

y2(t) = x1(t-τ) cos(2πf0 t)

y1(t-τ) = x1(t-τ) cos(2πf0 (t-τ))

We can see that y2(t) and y1(t-τ) are not equal, which means the system is not time-invariant.

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Answer:

\(cos \theta = 0.6\)

Step-by-step explanation:

Draw a line from point ( 0.6, 0.8 ) to the X - axis, forming a right triangle with hypotenuse = r = 1 , adjacent = 0.6,  opposite = 0.8

\(cos \theta = \frac{adjacent}{hypotenuse} , \ where \ adjacent = 0.6 ,\ hypotenuse \ = r= 1\)

\(cos \theta = \frac{0.6}{1}\\\\cos \theta = 0.6\\\\\theta = cos^{-1} \ 0.6\\\\\theta = 53.13^\circ\)

The value of cos θ is,

⇒ cos  θ = 0.6

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Now, We can Draw a line from point ( 0.6, 0.8 ) to the X - axis, forming a right triangle with hypotenuse = r = 1 , adjacent = 0.6,  opposite = 0.8

Hence, We can formulate;

⇒ cos θ = 0.6 / 1

⇒ θ = cos ⁻¹ 0.6

⇒ θ = 53.13°

Thus, The value of cos θ is,

⇒ cos  θ = 0.6

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Answer:

$20.01

Step-by-step explanation:

Simply subtract $29.99 from $50.00 so, your problem should be set up like this:

You substitute the numbers with 10s, but there cannot be more than one.

Answer:

$20.01

Step-by-step explanation:

You should subtract 50.00 and 29.99, and since there are three zeros, you have to borrow from the five, making it a four. Then, you make the first zero into a 10, then borrow from that one, making it a nine, same with the second zero. Then, for the third zero, you only borrow one from the second zero, turning the second one into a nine and the third on into a 10. You then start the subtracting process. This is the first part to the problem:

50.00 - 29.99 = ?

Then, this is what you should have after:

49.91(0) - 29.99 = ?

This is what you get after:

20.01

Then, add the dollar sign. You will get:

$20.01

Hope it helped!

Answer:

4:3

Step-by-step explanation:

if we take 44:33 and simplify by dividing by 11 we get 4:3

\(44:33 \\ ⇒ \frac{44}{33} \\ ⇒ \frac{4}{3} \\ = 4:3\)

- BRAINLIEST answerer

Answer: 50%

Step-by-step explanation:

The sample size of the data which has a sample mean of 0.7 is 20.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

Cathy has obtained a sample mean of 0. 7 and , but she cannot remember if the sample size was 20 or 25,

Calculate the sample size as shown below,

As we know that the variance would be positive,

s² ≥ 1 / (n - 1) \([\Sigma _{i =0}^nx_i^2 - n\bar x^2]\)

0 ≥ 1 / (n - 1) \([\Sigma _{i =0}^nx_i^2 - n\bar x^2]\)

[10 - n × x × 0.7²] ≥ 0

n × x × 0.7² ≤ 10

n ≤ 10 / (0.7)²

n ≤ 20.408

Thus, the sample size is 20.

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Answer:

Step-by-step explanation:

Sorry I do not know?

The optimal solution for the given linear programming problem using the graphical solution procedure is at (A, B) = (6, 2) with the objective function value of -4.

To find the optimal solution graphically, we plot the feasible region determined by the constraints. In this case, the feasible region is a polygon bounded by the lines 2A + 3B = 12, A + 4B ≤ 21, 2A + B ≥ 7, 3A + 1.5B ≤ 21, and -2A + 6B ≥ 0. We then evaluate the objective function -2A - B at the vertices of the feasible region to determine the optimal solution. The vertex that gives the minimum value of the objective function is the optimal solution. By calculating the objective function at each vertex, we find that the minimum value of -4 is obtained at (A, B) = (6, 2). This means that the optimal solution is to set A = 6 and B = 2, and the objective function value at this point is -4. For part (b), to determine the amount of slack or surplus for each constraint, we evaluate the constraints at the optimal solution (A, B) = (6, 2). For the constraint 1A + 4B ≤ 21, the left-hand side is 1(6) + 4(2) = 14, which indicates a slack of 7 (21 - 14). For the constraint 2A + 1B ≥ 7, the left-hand side is 2(6) + 1(2) = 14, which indicates a surplus of 7 (14 - 7). For the constraint 3A + 1.5B ≤ 21, the left-hand side is 3(6) + 1.5(2) = 20, which indicates a slack of 1 (21 - 20). Lastly, for the constraint -2A + 6B ≥ 0, the left-hand side is -2(6) + 6(2) = 4, which indicates a surplus of 4 (4 - 0). These slack and surplus values represent the amount by which the left-hand side of each constraint falls short or exceeds the right-hand side at the optimal solution. A positive slack indicates that the constraint is not fully utilized, while a positive surplus indicates that the constraint is exceeded.

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18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

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Step-by-step explanation:

Hint : we will check for each option whether it is an experiment or not by using the concepts of probability first we will check then if a coin is tossed then it is an experiment or not ? then we will check that if a dice is rolled is it an experiment or not and then we will repeat the same process for choosing a marble from a jar

complete step by step answer and event is a set of outcomes of an experiment to which probability is assigned as take an example when we and I the possibility of 5 appearing on the die is an event if for tossing a coin we do not know the result when a coin is tossed in can give any result whether it will be a head or tails so this is an example for a random experiment if a six-sided dice will be rolled then we do not know what is about to come there result can be anything from 126 so it is also an example for random experiment choosing a marble from a jar is also an experiment because we are choosing one marble from the jar and experiment is a work in which a result can be anything hence option d is the correct option not probability is how likely something is about to happen when a coin is tossed there are two possibility outcomes heads or tails show the probability of an outcome 1

( number of ways it can happen )÷

( total number of outcomes)

so when a coin is tossed the total number of outcomes are to solve the probability of a current head is 1/2

The volume of the rectangular prism with a height of 7m, width of 6m, and length of 7m is 294 cubic meters.

To calculate the volume of a rectangular prism, we multiply the length, width, and height together. In this case, the height is 7m, the width is 6m, and the length is 7m.

Using the formula for the volume of a rectangular prism:

Volume = Length × Width × Height

Substituting the given values:

Volume = 7m × 6m × 7m

Calculating the product:

Volume = 294m^3

Therefore, the volume of the rectangular prism is 294 cubic meters.

The volume of a three-dimensional object represents the amount of space it occupies. In the context of a rectangular prism, the volume tells us how much three-dimensional space is enclosed within its boundaries. The unit for volume is cubic meters, which signifies a measure in three dimensions (length, width, and height) all expressed in meters.

In this specific case, with a height of 7m, width of 6m, and length of 7m, the resulting volume is 294 cubic meters. This means that the rectangular prism occupies a space equivalent to 294 cubes with each side measuring 1 meter.

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To summarize: If points a and b are in a straight line, the distance traveled and the displacement will be the same. If points a and b are not in a straight line, the distance traveled will be greater than the displacement.

The distance traveled refers to the total length covered during the journey, regardless of the direction taken. On the other hand, displacement refers to the change in position from the starting point to the ending point, taking into account the direction of travel.

Neglecting the curvature of the corners implies that the path taken is a straight line. In this case, the distance traveled and the displacement will be the same if the points a and b are in a straight line.

If points a and b are not in a straight line, then the distance traveled will be greater than the displacement. This is because the distance traveled considers the entire path covered, while displacement only considers the change in position.

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The time period after which they will cross the start line together is  after 32 minutes as per the given data.

After either has completed a certain number of full laps in the exact same amount of time as the other has finished an integer number of full laps, they will both cross the starting line together.

That time will be the least common multiple (LCM) of their lap times, 128 seconds and 120 seconds.

LCM

LCM(120, 128) = 120×128/GCD(120, 128)

LCM = 120×128/8 = 1920

Converting this to minutes, we get

(1920 s)/(60 s/min) = 32 min

They will next cross the start line together after 32 minutes.

LCM of any two is the value that is evenly divisible by the two given numbers. The full form of LCM is Least Common Multiple. It is also called the Least Common Divisor (LCD). For example, LCM (4, 5) = 20. Here, the LCM 20 is divisible by both 4 and 5 such that 4 and 5 are called the divisors of 20.

It is also used to add or subtract any two fractions when the denominators of the fractions are different. While performing any arithmetic operations such as addition, subtraction with fractions, LCM is used to make the denominators common. This process makes the simplification process easier.

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3150 miles in 14 hrs

225 mph

hope this helps!

Suppose that triangles ABC and DFE are similar. Therefore, the ratio between their corresponding sides is constant. Let x and y be

Then,

Triangle DFE is impossible, the lengths of its sides are impossible to construct in such a manner that the result is a right triangle whose hypotenuse is 3. DFE is an impossible triangle, the hypotenuse of a right triangle is always its largest side.

However, we can algebraically find x and y, although it would not make any sense geometrically speaking.

Solving for x,

Similarly, solving for y,

Answer:

\(x=11\)

Step-by-step explanation:

The sum of all the angles in a triangle is always 180 degrees.

Hence,

\((7x-17)+42+78=180\)

Remove the brackets:

\(7x-17+42+78=180\)

Add/Subtract the numbers:

\(7x+103=180\)

Subtract 103 from both sides:

\(7x+103-103=180-103\)

\(7x=77\)

Divide both sides by 7:

\(\frac{7x}{7}=\frac{77}{7}\)

\(x=11\)

Answer:

X = 11

Step-by-step explanation:

This triangle will add up to 180 degrees

Our angles we have right now our 42 and 78 I add those up so I know how much the missing angle will have to equal to add up with the others to equal 180 so 42 + 78 = 120

So our other angle will have yo equal 60 so we have to find out what multiplied by 7 subtracted by 17 equals 60 well 7 x 11 = 77 and 77 - 17 = 60 so x = 11

2 intersecting lines are shown. A line with points T, R, and W intersects a line with points S, R, and V at point R.  the value of x  is  mathematically given as

x=20

This is further explained below.

In most cases, two lines that cross one other are shown. In this example, line TW and line SV meet at point R.

The angles are as follows, starting at the top and moving clockwise:

Angels \(3x\textdegree \ and\ (x+40 \textdegree)\) are considered horizontal angles because of the description (opposite when two lines intersect). Vertical angles are equivalent, therefore

x=20

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Answer:

Step-by-step explanation:

25% it means 1/4 of the total

1/4 of 80 is 20 (80/4=20)

answer B

As per the concept of probability, the rationale behind statistical process control is to understand and control the sources of variation in a manufacturing process to change the six sigma calculations and alpha error score (option d).

Statistical Process Control (SPC) is a methodology used in manufacturing industries to monitor and control a process by measuring and analyzing the process variables over time.

The results of previous corrective actions on the existing process are important in determining the effectiveness of those actions and whether further adjustments are needed.

Acceptable variation within probability limits is a key aspect of SPC. By understanding the probability distribution of the process variables, we can determine the acceptable range of variation and use control charts to monitor the process and identify any deviations from this range.

Six sigma calculations and alpha error score are also important aspects of SPC. Six sigma is a statistical measure that indicates the level of quality in a process, and the alpha error score is the probability of rejecting a true null hypothesis.

Hnce the option (d) is correct.

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Answer:

1200

Step-by-step explanation:

1,500-300=1200

The 98% confidence interval estimate of the standard deviation of body temperature for all healthy humans, based on a simple random sample of 105 body temperatures with a sample mean of 98.20 °F and a sample standard deviation of 0.64 °F, is (0.78 °F, ∞) with the lower bound rounded to two decimal places.

To construct the confidence interval estimate of the standard deviation, we can use the chi-square distribution. Since the sample follows a normal distribution and the sample size is relatively large, we can use the chi-square distribution to estimate the population standard deviation.

First, we need to determine the chi-square critical values for a 98% confidence level. Looking up the critical value in the chi-square distribution table with 104 degrees of freedom (105 - 1), we find that the critical value is approximately 128.42.

Next, we calculate the confidence interval:

Confidence Interval = [sqrt((n - 1) * s^2) / sqrt(chi-square upper value), sqrt((n - 1) * s^2) / sqrt(chi-square lower value)]  

Confidence Interval = [sqrt((104) * (0.64^2)) / sqrt(χ^2 upper value), sqrt((104) * (0.64^2)) / sqrt(χ^2 lower value)]

Confidence Interval = [sqrt(43.52) / sqrt(128.42), sqrt(43.52) / sqrt(χ^2 lower value)]

Confidence Interval ≈ [0.78 °F, ∞]

Therefore, the 98% confidence interval estimate of the standard deviation of body temperature for all healthy humans is (0.78 °F, ∞), with the lower bound rounded to two decimal places.

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Answer:

y2

Step-by-step explanation:

"y3"   was replaced by   "y^3".  1 more similar replacement(s).

Simplify: y5 by y3

1.1    y5 divided by y3 = y(5 - 3) = y2

Final answer:

y2

y³y⁻⁵ can be written in the form of positive exponent is 1/y².

An expression is combination of variables, numbers and operators.

The given expression is y³y⁻⁵

y power three times of y power minus five.

We need to simplify the expression using only positive exponents

From properties of exponents we have, when bases are same then the powers will be added

y³⁻⁵

y⁻²

This can be written as 1/y² as positive exponent.

Hence,  y³y⁻⁵ can be written in the form of positive exponent is 1/y².

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The table represents the exponential function:

y = 4*(5)^x

Clearly this is an exponential function of the form:

y = A*(b)^x

First, notice that we have the point (0, 4), which means that:

4 = A*(b)^0

4 = A*1

4 = A

Then we can write:

y = 4*(b)^x

And using the second ponit (1, 20) we can write:

20 = 4*(b)^1

20 = 4*b

20/4 = b

5 =b

then the exponential function is:

y = 4*(5)^x

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Answer:

Step-by-step explanation:

The quadratic expression can be factored into two binomials if it has two real roots.

Two real roots possible with non-negative discriminant:

As D = b² - 4ac, we get the following inequality

This is true for any value of k

Answer:

(-∞, ∞)  or  \(k \in \mathbb{R}\)

Step-by-step explanation:

Binomial:  two terms connected by a plus or minus sign.

Discriminant

\(b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0\)

\(\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}\)

\(\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}\)

\(\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}\)

If a quadratic expression factors into two binomials, it will have two real roots.  Therefore, the discriminant will be greater than zero.

Given quadratic expression:

  \(3x^2+kx-8\)

\(\implies a=3, \quad b=k, \quad c=-8\)

Substitute the values of a, b and c into the discriminant, set it to > 0:

\(\implies k^2-4(3)(-8) > 0\)

\(\implies k^2+96 > 0\)

As k² ≥ 0 for all real numbers,

\(\implies k^2+96 \geq 96\)

Therefore, the values of k are (-∞, ∞)  or  \(k \in \mathbb{R}\)

Answer:

Width = 44 yards

Length = 171 yards

Step-by-step explanation:

given data

length of the field = 5 yards

Perimeter of the rectangular field = 430 yards.

solution

we consider here length of the field = L

and width of the field = W

as we know length of the field 5yards less than quadruple the width

so here

L = 4W - 5       .....................................1

and  

Perimeter (P) will be here

P = 2(L + W)      ............................................2

put here equation 1 value

430 = 2(4W - 5 + W)  

solve it we get

W = 44

so here put value in eq 1 we het

L = 4W - 5          

L = 4(44) - 5

L = 171

so, length of the field is 171 yards