What is PLATO?
People keep saying it but I don't know what it is.

Answer:

x and y =70

Step-by-step explanation:

The square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500 square mils.

To find the square mil area for a 2 inch wide by 1/4 inch thick copper busbar, we need to multiply the width and thickness of the busbar in mils.

1 inch = 1000 mils

So, the width of the busbar in mils = 2 inches x 1000 mils/inch = 2000 mils

And, the thickness of the busbar in mils = 1/4 inch x 1000 mils/inch = 250 mils

Therefore, the square mil area of the copper busbar = width x thickness = 2000 mils x 250 mils = 500,000 square mils.

Hence, the square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500,000 square mils.

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The statement that is true about the straight line angle is ∠ HLI = ∠ ILM.

The angle of the straight line

The measure of the angle of the straight line is equal to 180 degrees.

The line KLM is straight

Hence, the angle of the line KLM is equal to 180 degrees.

∠KLM = ∠KLH + ∠HLM

180 = 120 - ∠HLM

∠HLM = 60

Now in the angle HLM

∠HLM = ∠HLI + ∠ILM

60 = 30 + ∠ILM

∠ILM = 30

Angle HLI and angle ILM are both 30°

Hence they both are equal

∠ HLI = ∠ ILM.

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The question is incomplete the complete question is :

mAngleKLH = 120° and mAngleKLM = 180°, which statement about the figure must be true?

AngleHLM is bisected by Ray L J. AngleGLJ is bisected by Ray L H. MAngleKLG = mAngleHLJ mAngleHLI = mAngleILM.

Answer:

Dan scored 600 points

Step-by-step explanation:

let x = total points scored

(3/10)(4x/10) = 120

x = 1000

6*1000/10 = 600 points scored by Dan

Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

A standard normal distribution calculator is a statistical tool used to calculate probabilities associated with the standard normal distribution, which is a specific type of probability distribution.

Standard normal distribution is a continuous probability distribution that has a mean of 0 and a standard deviation of 1. It is commonly used in statistical analysis and hypothesis testing.

To use a standard normal distribution calculator, you typically input a value for which you want to calculate the probability, and the calculator will output the corresponding probability from the standard normal distribution. For example, if you want to calculate the probability that a standard normal random variable is less than 1.96, you would input 1.96 into the calculator, and it would output the probability of approximately 0.975.

Overall, a standard normal distribution calculator is a useful tool for performing statistical analysis and hypothesis testing involving the standard normal distribution. It can provide quick and accurate calculations of probabilities associated with the distribution, which can be useful for making informed decisions and drawing conclusions based on statistical data.

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You have the correct expression for the first answer box. It is s^3+12. Nice work.

The reasoning is that s^3 is the volume of the storage container on the left, and 12 is the volume of the storage container on the right. Adding the two container volumes gets the total volume.

-----------------------------------

For the second answer box, we'll plug in s = 4 to get

s^3 + 12 = 4^3 + 12 = 64 + 12 = 76

The total volume is 76 cubic feet.

So 76 is the answer to the second box

Answer

The sequence is geometric.

a = 1.5

r = -3

Explanation

Given:

The sequence given is: 1.5, -4.5, 13.5, -40.5

What to find:

If the sequence is geometric, also to find a, r.

Solution:

To check if it's geometric, we shall solve the following:

This shows that the sequence is geometric.

The first term, a, of the sequence is 1.5.

And the common ratio, r = (second term/first term) = (-4.5/1.5) = -3.

Hence, the sequence is geometric, a = 1.5 and r = -3.

The probability of choosing all five white balls correctly from a bowl of 69 white balls and the probability of choosing the correct red ball from a bowl of 29 red balls is \({}^{69}C_5/29\) .

The probability of choosing all five white balls correctly can be calculated using the formula for combinations, where the order does not matter and the balls are chosen without replacement. The probability is given by:

P(Choosing all 5 white balls correctly) = (Number of ways to choose 5 white balls correctly) / (Total number of possible combinations)

The number of ways to choose 5 white balls correctly is 1, as there is only one correct combination.

The total number of possible combinations can be calculated using the formula for combinations, where we choose 5 balls out of 69. It is given by:

Total number of combinations = \({}^{69}C_5\)

Next, we need to calculate the probability of choosing the correct red ball from a bowl of 29 red balls. Since there is only one correct red ball, the probability is 1/29.

Finally, to find the likelihood of being the winner of the Powerball lottery, we multiply the probability of choosing all five white balls correctly by the probability of choosing the correct red ball:

Likelihood = P(Choosing all 5 white balls correctly) * P(Choosing correct red ball)

=\({}^{69}C_5 \times 1/29\\\)

This gives us the probability of being the winner of the Powerball lottery.

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The sample space, S: {WW, WL, LW, LL} represent the experiment Playing a video game twice.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

1. Rolling a number cube twice

Drawing a possibility space allows us to see all the 36 outcomes of throwing a cube twice.

So, this is not the required case.

2. Rolling a number cube once

Drawing a possibility space allows us to see all the 6 outcomes of throwing a cube once.

So, this is not the required case.

3. Playing a video game twice

This case can be considered because it gives 4 outcome of Winning(W) and Losing(L).

4. Playing a video game twice

This case cannot be considered because it gives 2 outcome of Winning(W) and Losing(L).

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Answer:

yep its C :)

Step-by-step explanation:

I got it right on my quiz.

The formula that expresses the number of teachers in the school, \(n_t\), in terms of the number of students in the school, \(n_s\), is:

\(n_t = n_s / 11\)

In other words, the formula assumes a linear relationship between the number of teachers and the number of students, where the ratio of teachers to students is fixed at 1:11.

To express the number of teachers in the school, n_t, in terms of the number of students in the school, n_s, we can use the given information that for each teacher there are 11 students.

We can set up a proportion based on this relationship:

\(n_t / n_s = 1 / 11\)

To solve for \(n_t\), we can multiply both sides of the equation by \(n_s\):

\(n_t = (1 / 11) * n_s\)

Simplifying the equation, we have:

\(n_t = n_s / 11\)

Therefore, the formula that expresses the number of teachers in the school, \(n_t\), in terms of the number of students in the school, \(n_s\), is:

\(n_t = n_s / 11\)

Thus, the formula assumes a linear relationship between the number of teachers and the number of students, where the ratio of teachers to students is fixed at 1:11.

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Question:

A charter bus travels 225 miles in  4.5 hours. Assume the  distance travelled is directly  proportional to the time spent.

Write a direct variation equation.

Answer:

\(y = 50x\)

Step-by-step explanation:

Let:

y =  distance

x = time

So:

\(y = 225\)  and \(x = 4.5\)

Since, they are directly proportional: The following relationship exists

\(y = kx\)

Where

k = constant of variation

Substitute values for y and x

\(225 = 4.5 * k\)

Make x the subject

\(k = \frac{225}{4.5}\)

\(k = 50\)

Substitute 50 for k in \(y = kx\)

\(y = 50x\)

Answer:

3 yards because I looked it up

Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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The highest common factor (HCF) of the given polynomials is (x + 2).

To find the highest common factor (HCF) of the given polynomials, we need to factorize each polynomial and identify the common factors.

Polynomial: 2x + 4

This polynomial can be factored out by taking out the common factor of 2:

2(x + 2)

Polynomial: x^2 - 4

This is a difference of squares, which can be factorized as:

(x + 2)(x - 2)

Polynomial: x^2 - x - 6

To factorize this polynomial, we need to find two numbers that multiply to give -6 and add up to -1 (coefficient of x). The numbers are -3 and 2, so we can rewrite the polynomial as:

(x - 3)(x + 2)

Now, we can compare the factors of the three polynomials to determine the HCF. We identify the common factors by taking the minimum power of each common factor:

Common factors:

(x + 2)

Hence, the highest common factor (HCF) of the given polynomials is (x + 2).

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Complete question:

Find HCF - 2x + 4, x^2 - 4, x^2 - x - 6

Answer:

y = (x - 2) (x + 5)

Step-by-step explanation:

Answer:

1.335

Step-by-step explanation:

you have to do this equation .445 x 3 =1.335

Answer:

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite so just move it over to the opposite side

Step-by-step explanation:

For the given statement, we have to correctly rejecting the null hypothesis.

According to the statement

we have to find the outcome when hypothesis test evaluating a treatment that has a very large and robust effect.

For this purpose, we know that the

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.

And according to the given statement it is clear that the by this we have to rejected this hypothesis.

because this treatment and the large effects are not possible for the independent values of the hypothesis.

In other words, we can say that the we have to correctly rejecting the null hypothesis.

So, For the given statement, we have to correctly rejecting the null hypothesis.

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The bold statement does not pertain to either the independence of trials or the mutual exclusion of outcomes property of the binomial scenario.

The bold statement does not describe the independence of trials or the mutual exclusion of outcomes property of the binomial scenario.

In a binomial scenario, the independence of trials means that the outcome of one trial does not affect the outcome of another trial. Each trial is considered independent of the others. In this case, the researcher is testing a single individual, so there is no concept of multiple trials.

The mutual exclusion of outcomes property refers to the fact that in a binomial scenario, there are only two possible outcomes for each trial, and they are mutually exclusive. For example, if the outcomes are success (having diabetes) and failure (not having diabetes), an individual cannot have both outcomes simultaneously. However, the bold statement does not provide information about the possible outcomes or their exclusivity.

Therefore, the bold statement does not pertain to either the independence of trials or the mutual exclusion of outcomes property of the binomial scenario.

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Answer:

1/6

Step-by-step explanation:

Since there are 6 sides to a regular die, and there is only one number 1 on that die. The probability is 1/6 (one-sixth)

Answer: C \(0\leq y\leq 5\)

Step-by-step explanation:

Explanation

In the question, we are given that the difference of three times a number and six is nine. Using the variable x, we can write the equation as:

Answer 1:

We can then solve the equation below;

Answer 2: x=5

Answer:

(x-1)(x-2)(x-3)

Step-by-step explanation:

hy vọng nó giúp

The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

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The given statement is true.

Consider linearly independent vectors of \(R_{n}\)

Where n = 2

\(V = \[\begin{array}{ccc}4&\\2\end{array}\right]\)  

\(U = \[\begin{array}{ccc}5&\\6\end{array}\right]\)

Now product of these vectors

UV = 4x5 + 2x6

     = 32

Hence these vectors are not orthogonal.

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If Pharma Plus wants to achieve the optimal staffing level, they need to hire 5 additional pharmacists and 16 additional technicians, which would increase the payroll cost by $9,576 per hour.

a) To determine a minimum-cost staffing plan for Pharma Plus,

we have the following optimization problem:

Min 48P + 12T

Subject to:

P + T > 251 (Employees required)

2P - T > 0 (Service quality guideline)

P > 90 (Pharmacists employed)

Using the graphical method, we can graph the lines of each constraint:

Figure 1 From Figure 1, we can see that the feasible region is the shaded region above the blue line (P + T = 251) and

to the right of the orange line (2P - T = 0),

and to the right of the green line (P = 90).

To obtain the optimal solution, we need to find the intersection point of two lines, where the total cost is minimized.

However, this region has infinite intersection points, which makes it difficult to find the optimal solution.

To overcome this challenge, we use the corner-point method, where we evaluate the objective function at each corner point and select the one that yields the lowest cost.

In this case, the corner points are A (90, 161), B (115, 136), and C (165.5, 85.5).

Using the objective function, we obtain the following values:

At point A: 48(90) + 12(161)

= $3,624

At point B: 48(115) + 12(136)

= $4,008

At point C: 48(165.5) + 12(85.5)

= $7,308

Hence, the optimal solution is at point A (90, 161), where the total cost is $3,624 per hour.

Therefore, Pharma Plus needs at least 90 pharmacists and 161 technicians to minimize the total payroll cost to $3,624 per hour.

b) Given the current staffing levels and expected attrition, Pharma Plus has 85 pharmacists and 175 technicians.

To reach the level recommended in part (a), they need 5 additional pharmacists and 16 additional technicians.

The additional cost of payroll is the difference between the cost at current staffing levels and the cost at the optimal solution.

Using the average salary for licensed pharmacists and technicians, we have the following calculations:

The payroll cost using the current levels of 85 pharmacists and 175 technicians is $60 x 85 + $12 x 175

= $13,200 per hour.

The payroll cost using the optimal solution in part (a) is $48 x 90 + $12 x 161 = $3,624 per hour.

The increase in payroll cost is $9,576 per hour.

Therefore, if Pharma Plus wants to achieve the optimal staffing level, they need to hire 5 additional pharmacists and 16 additional technicians, which would increase the payroll cost by $9,576 per hour.

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Answer:

m=-1/2

Step-by-step explanation:

f(6)=-2 is (6,-2) and f(-4)=3 is (-4,3)

the equation for slope (m) is (y2-y1)/(x2-x1)

label the points:

x1=6

y2=-2

x2=-4

y2=3

now substitute into the equation:

m=(3--2)/(-4-6)

m=5/-10

m=-1/2

the slope is -1/2

hope this helps!

Answer:

Step-by-step explanation:

Answer:

\(\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} \)

Step-by-step explanation:

It is given that –

Slope of the first line is–

\(\sf\longmapsto \: m_{1} = 2\)

Let,

the slope of the Another line be –

\(\sf\longmapsto \: m _{2}\)

Now,

The angle between the two lines is 60°.

Let's start solving!

\(\sf\longmapsto \: \tan(60°) | \frac{ m_{1} - m_ {2} }{1 + m_{1} m_ {2}} | \)

\(\sf\longmapsto \: \sqrt{3} = | \frac{2 -m_{2} }{1 + 2m_{2}} | \)

\(\sf\longmapsto \: \sqrt{3} = ± \: \: ( \frac{2 -m_{2} }{1 + 2m_{2}} )\)

\(\sf\longmapsto \: \sqrt{3} = \frac{2 -m_{2} }{1 + 2m_{2}} \)

\(\sf\longmapsto \: \sqrt{3} (1 + 2m_{2}) = 2 - m_{2}\)

\(\sf\longmapsto \: \sqrt{3} + 2 \sqrt{3} m_{2} + m_{2} = 2\)

\(\sf\longmapsto \: m_{2} = \frac{2 - \sqrt{3} }{(2 \sqrt{3} + 1) } \)

The equation of line passing through point (2,3) and having a slope of –

\(\sf\longmapsto \: m_{2} = \frac{(2 - \sqrt{3} )}{2 \sqrt{3} + 1 } \)

is–

\(\sf\longmapsto \: (y - 3) = \frac{2 - \sqrt{3} }{2 \sqrt{3} + 1 } (x - 2)\)

\(\sf\longmapsto \: ( 2\sqrt{3} + 1)y - 3(2 \sqrt{3} + 1) = (2 - \sqrt{3} )x - 2(2 - \sqrt{3} \)

\(\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} \)

Hence the equation of the other line is -

\(\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} \)