Put the quadratic


y=2x^2-4x+2


into the quadratic formula


enter the number that belongs in the green box.

Answers

Answer 1

The quadratic formula for solving quadratic equations of the form ax^2 + bx + c = 0 is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

To put the quadratic equation y = 2x^2 - 4x + 2 into this formula, we need to identify the values of a, b, and c.

In this case, we have a = 2, b = -4, and c = 2. Substituting these values into the quadratic formula, we get:

x = (-(-4) ± sqrt((-4)^2 - 4(2)(2))) / (2 * 2)

x = (4 ± sqrt(16 - 16)) / 4

x = (4 ± 0) / 4

Simplifying this expression, we get:

x = 1 or x = 1/2

Therefore, the solutions to the quadratic equation y = 2x^2 - 4x + 2 are x = 1 and x = 1/2.

To explain this solution in more detail, we first need to understand the quadratic formula and how it can be used to solve quadratic equations. The quadratic formula is a formula that provides the solutions to any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.

In this case, we were given a specific quadratic equation, y = 2x^2 - 4x + 2, and we needed to find its solutions. To do this, we identified the values of a, b, and c and substituted them into the quadratic formula. We then simplified the expression to obtain the solutions, which were x = 1 and x = 1/2.

It is important to be able to use the quadratic formula to solve quadratic equations because many real-world problems can be modeled using quadratic equations. By being able to solve these equations, we can find important information such as the roots, or solutions, of the equation, which can help us make predictions and solve problems.

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Related Questions

The teacher could buy the shirt online 3.50 each she would also pay a fee of 9.50 for shipping the shirts.

Answers

The function that represents the total cost (y) of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y

Cost of each shirt = $3.50

The fee for shipping the shirts is = $9.50

Total number of shirts bought by shirt online = x

The total cost of buying x shirts is represented by y

The total cost will be the sum of each cost of the shirt and shipping charges

y = 3.50x + 9.50

Hence, the function that represents the total cost y of buying x shirt online of $3.50 each and shipping charges of $9.50 is 3.50x + 9.50 = y

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The question is incomplete complete question is :

The teacher could buy the shirt online at 3.50 each she would also pay a fee of 9.50 for shipping the shirts. Write a function that can be used to find y the total cost in dollars of buying x shirts online.

A car is purchased for $35,000. The owner finances the car at an interest rate of 4.6%, continuously compounded, for 6 years. What is the monthly payment on the car? Group of answer choices $640.62 $46,124.68 $35,046.00 $743.95

Answers

The monthly payment on the car is approximately $640.62. The correct option is A

To solve this problem

The formula for the monthly payment on a continuously compounded loan can be expressed as:

P = (r * A) / (1 - (1 + r)^(-n))

Where

P is the monthly payment r is the yearly interest rateA is the principal (i.e., the original amount borrowed) n is the number of payments (i.e., the number of years multiplied by 12)r is the annual interest rate (stated as a decimal and constantly compounded)

Plugging in the given values, we get:

P = (0.046 * 35000) / (1 - (1 + 0.046/12)^(-6*12))

P ≈ $640.62

Therefore, the monthly payment on the car is approximately $640.62.

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you are given that 4a - 2b = 10 and a + c = 3

write an expression in a,b and c that is equal to 23

give your answer in it's simplest form

Answers

Answer:

3a - 2b - c + 16 = 23

Step-by-step explanation:

so we want to write an equetion which containe a, b and c so we have given

4a - 2b = 10 and a + c = 3

so we are going to differentiate 10 to 7 + 3 it will be

4a - 2b = 10

4a - 2b = 7 + 3 ...then we insert a + c in place of 3 b/c they are equal

4a - 2b = 7 + a + c .... we take to the left side of the equal sighn

4a - a - 2b - c = 7

3a - 2b - c = 7

thrn if we want to write the equetion =23 we add 16 both side 3a - 2b - c + 16 = 23 .

Rectangle abcd was dilated to create rectangle a’b’c’d’. the area of rectangle abcd is 16in^2 and the area of the rectangle a’b’c’d’ is 64in^2. which scale factor was used to dilate the rectangle?
help asap please!!!!!

Answers

If the area of rectangle abcd is 16in² and the area of the rectangle a’b’c’d’ is 64in², the scale factor used to dilate the rectangle was 2.

When a rectangle is dilated, its dimensions are multiplied by a common factor known as the scale factor. The scale factor is the ratio of the corresponding sides of the original rectangle and the dilated rectangle.

Let the scale factor be represented by k. The area of the original rectangle is 16 in², so we can write:

length x width = 16

Let L and W represent the length and width of the original rectangle, respectively. Therefore, we have:

LW = 16

After dilation, the area of the new rectangle is 64 in². The length and width of the new rectangle are kL and kW, respectively. Therefore, we can write:

(kL)(kW) = 64

Simplifying the above equation, we get:

k²LW = 64

Substituting the value of LW from the first equation, we get:

k²(16) = 64

Solving for k, we get:

k = √4 = 2

This means that the length and width of the new rectangle are twice the length and width of the original rectangle.

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WHATS THE AREAA OF THE PARALLELOGRAM

Answers

Answer:16 + (1/2) × 8 = 16 + 4 = 20 unit2

Step-by-step explanation:

Find the surface area of the net below in square centimeter 12,9,9

Answers

using the formula for the surface area of a box(cuboid) .
formula is
'(height x width) + 2(height x length) + 2(wi
2(h*w)+2(h*|)+2(w*|)
here we will take the word used in the question
"deep" to be its width..
-2(9*9) + 2(12*9) + 2(9*12)
=594cm?
Thank me later
o
У 3

Suppose f'(x) = 833 + 12x + 2 and f(1) = -4. Then f(-1) equals (Enter a number for your answer)

Answers

To find f(-1), we can use the fact that the derivative of a function f(x) gives us the slope of the tangent line to the graph of f(x) at any point x. We can use this information along with the given value of f(1) to find the equation of the tangent line at x=1, and then use that equation to find the value of f(-1).

First, we find the equation of the tangent line at x=1:
- The slope of the tangent line at x=1 is f'(1) = 833 + 12(1) + 2 = 847
- The point (1, f(1)) lies on the tangent line, so we can use the point-slope form of the equation of a line to write the equation of the tangent line:
y - (-4) = 847(x - 1)
y + 4 = 847x - 847
y = 847x - 851

Now we can use this equation to find f(-1):
- The point (-1, f(-1)) also lies on the tangent line, so we can substitute x=-1 and solve for y:
f(-1) + 4 = 847(-1) - 851
f(-1) + 4 = -1698
f(-1) = -1702

Therefore, f(-1) = -1702.
To find f(-1), we first need to determine the function f(x). We know f'(x) = 833 + 12x + 2. To find f(x), we need to integrate f'(x) with respect to x:

∫(833 + 12x + 2) dx = 833x + 6x^2 + 2x + C

Now, we use the given condition f(1) = -4 to find the constant C:

-4 = 833(1) + 6(1)^2 + 2(1) + C

Solve for C:

C = -4 - 833 - 6 - 2 = -845

Now we have the function f(x) = 833x + 6x^2 + 2x - 845. To find f(-1), plug in x = -1:

f(-1) = 833(-1) + 6(-1)^2 + 2(-1) - 845

f(-1) = -833 + 6 - 2 - 845

f(-1) = -1674

So, f(-1) equals -1674.

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What is the measure of an angle of it is 160 less than 4 times it’s complement

Answers

The measure of the angle is 40 degrees.

Let x be the measure of the angle and y be its complement.

The sum of an angle and its complement is 90 degrees, so we have:

[tex]x+y=90[/tex]

Also, we know that "the measure of an angle of it is 160 less than 4 times its complement", which can be written as:

[tex]x=4y-160[/tex]

Now we can substitute the first equation into the second equation:

[tex]4y-160+y=90[/tex]

Simplifying and solving for y, we get:

5y = 250

y = 50

Substituting y = 50 into the first equation gives:

x + 50 = 90

x = 40

Therefore, the measure of the angle is 40 degrees.

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Jasmine deposited $400 in a bank that paid her 2. 15% interest every year. Assuming no deposits or withdrawals were made. How much money will she have in 5 years? round to nearest.




Help

Answers

Answer:

$444.89

Step-by-step explanation:

PV = $400

i = 2.15%

n = 5

Compound formula:

FV = PV (1 + i)^n

FV = 400 (1 +2.15%)^5

FV = $444.89 (round to nearest cents)

15√2 = x√2please help me, how do i solve this? i'm in 9th grade and i completely forgot how to do this.

Answers

The equation 15√2 = x√2 can be solved, the value of x that satisfies the equation is 15.

To solve the equation 15√2 = x√2, you can divide both sides by √2 since the square root of 2 is a common factor on both sides of the equation. This gives:

15√2 / √2 = x√2 / √2

On the left side of the equation, the √2 and the denominator cancel out, leaving:

15

On the right side of the equation, the √2 and the denominator also cancel out, leaving:

x

So the solution to the equation is:

x = 15

Therefore, the value of x that satisfies the equation is 15.

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Find an equivalent expression using the Distributive Property.

25w+30x
Find an equivalent expression using the Distributive Property.

25w+30x

Answers

Answer: 5(5w+6)

Step-by-step explanation:

Factor out a 5: 5(5w+6)

To check our work distribute: 25w+30

Answer: 5(5w+6)

Answer:

5 ( 5w + 5x )

Step-by-step explanation:

Just find a common factor in both terms: 5

5 ( 5w + 5x )

If you multiply again, you will see that the values of both expressions are the same.

Evaluate the following expressions. Your answer must be an angle -z/2 S 0 S in radians, written as a multiple of r. Note that r is already
provided in the answer so you simply have to fil in the appropriate multiple. E.g. if the answer is /2 you should enter 172. Do not use decimal answers.
Write the answer as a fraction or integer
Sin^-1(sin((-5t-6)

Answers

The given expression is sin⁻¹ (sin((-5t-6)). Since the argument of sin⁻¹ and sin is the same, we can simplify the expression as follows:
sin⁻¹ (sin((-5t-6))) = -5t-6
OR, -5t-6 = (-2π/π)(-5t-6/2) = -2π(2.5t+3)/π = -5π/2(2.5t+3)
Therefore, the answer is -5π/2(2.5t+3).

Given the expression: sin^-1(sin(-5t-6))
To find the angle -z/2, we can use the following properties:
1. sin⁻¹ (sin(x)) = x, if -π/2 ≤ x ≤ π/2 (i.e., x is in the range of the principal branch of the inverse sine function).
2. The sine function has a periodicity of 2π. Therefore, sin(x) = sin(x + 2nπ), where n is an integer.

Given angle: -5t - 6
We need to add 2nπ to this angle to bring it into the range of -π/2 to π/2:
⇒ -5t - 6 + 2nπ, where n is an integer.

Now, we apply the sine and inverse sine functions:
sin⁻¹ (sin(-5t - 6 + 2nπ))

Since sin^-1(sin(x)) = x when x is in the range of the principal branch, our final expression becomes:
-z/2 = -5t - 6 + 2nπ

In this expression, -z/2 represents the angle in radians, written as a multiple of r. To find the multiple, you simply have to solve for -z/2 in terms of r.
Therefore, the answer is: -z/2 = -5t - 6 + 2nπ.

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part of a multiplication table is below. complete the pattern in the multiplication table. click each dot on the image to select an answer. a partial multiplication table with 3 rows and 3 columns. the first row reads 40, 45, 50. the second row reads an unknown number, 54, 60. the third row reads 56, an unknown number, 70. stuck?.

Answers

the completed multiplication table is:  40  45  50  ,72  54  60 and 56  90  70 .by using common factor  logic we can solve this question.

what is  common factor ?

A common factor is a number that divides evenly into two or more other numbers. For example, the common factors of 12 and 18 are 1, 2, 3, and 6, because all of these numbers divide evenly into both 12 and 18.

In the given question,

From the given table, we can see that:

The first row reads 40, 45, 50 (which are multiples of 5).

The second row has an unknown number (let's call it x), 54, and 60.

The third row reads 56, an unknown number (let's call it y), 70 (which are also multiples of 7).

To find the missing numbers, we can use the fact that multiplication is commutative, meaning that the order of the factors does not matter. Therefore, we can fill in the missing numbers by looking for factors that are common to both the row and column headers.

Starting with the second row, we can see that the common factor between x and 54 is 9, since 9 x 6 = 54 and 9 x x = ?. So, the missing number in the second row is 9 x 10 = 90.

Moving on to the first column, we can see that the common factor between 40 and 56 is 8, since 8 x 5 = 40 and 8 x 7 = 56. So, the missing number in the second row, first column is 8 x 9 = 72.

Finally, we can find the missing number in the first row, second column by finding the common factor between 45 and 60, which is 15, since 15 x 3 = 45 and 15 x 4 = 60. So, the missing number in the first row, second column is 15 x 5 = 75.

Therefore, the completed multiplication table is:

40  45  50

72  54  60

56  90  70

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Nine hundred thirty six student's, 65% of the entire student body, attended the football game. find the size of the student body.

Answers

The size of the student body is approximately 1440 students.

To determine the size of the student body, we'll use the given information that 936 students represent 65% of the total number of students. We can set up a proportion to solve for the unknown total (let's call it "x"):

(65% of x) = 936

To express the percentage as a decimal, divide 65 by 100, which equals 0.65:

0.65 * x = 936

Next, to find the value of x, divide both sides of the equation by 0.65:

x = 936 / 0.65

x ≈ 1440

So, the size of the student body is approximately 1440 students. In this problem, we used the concept of percentage to find out the total number of students in the student body, knowing that 936 students (65%) attended the football game.

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the population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day. How many people are left after 1 week

Answers

The number of people left after one week is approximately 157286.

How to find the number of people left?

The population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day.

Therefore, each day, 20% of the people are killed by the virus.

Hence, let's find the number of people left as follows:

Therefore,

7 days = 1 week

number of people left = 750,000(1 - 20%)⁷

number of people left = 750,000(1 - 0.2)⁷

number of people left = 750,000(0.8)⁷

number of people left = 750,000(0.2097152)

number of people left = 157286.4

Therefore,

number of people left after 1 week =  157286.4

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A


Fill in the blank. If one line has a slope of 0. 5 and another distinct line has a


slope of those two lines are


A. Parallel


B. Not correlated


C. Perpendicular


e


D. Undefined


Is urgent , no link plis

Answers

If one line has a slope of 0. 5 and another distinct line has a slope of those two lines are Parallel. The correct answer is A.

Two lines are parallel if and only if they have the same slope. If two distinct lines have different slopes, then they cannot be parallel. In this case, one line has a slope of 0.5 and the other line's slope is unknown, so we cannot determine whether they are parallel or not just by looking at their slopes.

However, if the other line's slope is perpendicular to 0.5, then the lines would be perpendicular. Two lines are perpendicular if and only if the product of their slopes is -1. Therefore, if the other line's slope is -2, then the lines would be perpendicular (0.5 * -2 = -1).

If the other line's slope is undefined (i.e., the line is vertical), then the lines would not be parallel or perpendicular, but rather they would be skew lines.

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In AABC, m ZA=62° and m ZB = 39º.


In AXYZ, m ZY=39° and mZz= 79º.


Julie says that the triangles are congruent because all the


corresponding angles have the same measure.


Ramiro says that there is not enough information given to


determine whether the triangles are similar, congruent, or


neither.


Is either student correct? Explain your reasoning.


Answer in complete sentences and include all relevant calculations.

Answers

we cannot determine whether the triangles are congruent or similar based on the given information .

Neither student is correct.

To determine whether two triangles are congruent or similar, we need to compare all three pairs of corresponding angles and all three pairs of corresponding sides.

In this case, we are given two pairs of corresponding angles: angle A in triangle ABC is congruent to angle Z in triangle XYZ, and angle B in triangle ABC is congruent to angle Y in triangle XYZ. However, we do not know the measure of angle C in triangle ABC or angle X in triangle XYZ, so we cannot compare the third pair of corresponding angles.

Furthermore, we are not given any information about the lengths of the sides of the two triangles, so we cannot compare the corresponding sides.

Therefore, we cannot determine whether the triangles are congruent or similar based on the given information.

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The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin10,000 times and obtained 5067 heads. (2pts)a) Is this significant evidence at the 5% level that the probability that Kerrich’scoin comes up heads is not 0. 5?Remember to specifythe null and alternative hypotheses, the test statistic, and the P-value. B) Give a 95% confidence interval to see what probabilities of heads are roughlyconsistent with Kerrich’s result

Answers

a) We can reject the null hypothesis and cthat theronclude is significant evidence that the probability of Kerrich's coin coming up heads is not 0.5. b) we get a confidence interval of 0.495 to 0.517.

a) To test the hypothesis that the probability of Kerrich's coin coming up heads is not 0.5, we can use a one-sample proportion test at the 5% level of significance. The null hypothesis is that the true proportion of heads is 0.5, and the alternative hypothesis is that it is not equal to 0.5.

The test statistic can be calculated as (5067-0.510000)/(sqrt(100000.5*0.5)) which simplifies to 5.401. The corresponding P-value can be found using a standard normal distribution table or a calculator to be approximately 3.3x10^-8, which is much smaller than 0.05. Therefore, we can reject the null hypothesis .

b) To construct a 95% confidence interval for the true proportion of heads, we can use the formula p ± z*sqrt((p(1-p))/n), where p is the sample proportion, z is the z-score corresponding to a 95% confidence level (which is 1.96), and n is the sample size. Substituting the values, we get a confidence interval of 0.495 to 0.517, which means that we can be 95% confident that the true proportion of heads falls within this range.

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1. Given XY and ZW intersect at point A Which conjecture is always true about he giver statement? A. XA = AY B. XAZ is acute C. XY is perpendicular to XY D. X, Y, Z and W are noncolinear. ​

Answers

The conjecture "X, Y, Z and W are noncolinear" is always true when given that line segments XY and ZW intersect at point A. So option D is the correct answer.

When line segments XY and ZW intersect at point A, it means that X, Y, Z, and W do not all lie on the same line. Since they do not all lie on the same line, they are considered non-collinear.

The conjecture "XA = AY" is not always true. It is only true if the lines XY and ZW are perpendicular bisectors of each other. The conjecture "XAZ is acute" is not always true. It is only true if angle ZAY is obtuse, in which case angle XAZ would be acute. The conjecture "XY is perpendicular to XY" is not a valid conjecture because it is a statement that XY is perpendicular to itself, which is always true but not informative.

So the correct answer is option D. X, Y, Z and W are noncolinear. ​

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The diameter of om is 68 cm and the diameter of oj is 54 cm. if the length of jk is 8 cm, what is the length of lm? lm​

Answers

The length of lm is 10 cm.

To find the length of lm, we need to use the fact that om and oj are both diameters of their respective circles. We can start by finding the radius of each circle:

- The radius of om is half of its diameter, so it's 34 cm.
- The radius of oj is half of its diameter, so it's 27 cm.

Next, we can use the fact that jk is perpendicular to lm to create a right triangle:

- One leg of the triangle is jk, which we know is 8 cm.
- The other leg is half of the difference between the radii of the two circles, since lm connects the two circles. That means the other leg is (34 - 27)/2 = 3.5 cm.

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

lm² = jk² + (radius difference/2)²
lm² = 8² + 3.5²
lm² = 70.25
lm = 10 cm

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Please please help ASAP. See photo below

Central / Inscribed Angles (Algebraic)

Answers

The calculated value of x in the circle is 12.3

Calculating the value of x in the circle

From the question, we have the following parameters that can be used in our computation:

The circle

∠QRS = 7x - 21

QS = 130

Using the theorem of intersecting chords, we have the following equation

∠QRS = 1/2 * QS

Substitute the known values in the above equation, so, we have the following representation

7x - 21 = 1/2 * 130

Evaluate

7x - 21 = 65

Evaluate the like terms

7x = 86

Divide by 7

x = 12.3

Hence, the value of x in the circle is 12.3

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i need help !!!!!!!!!!!!!!!!!!

Answers

Answer:

  [tex]\displaystyle\textsf{a) }\binom{8}{4}\\\\\textsf{b) }\binom{-8}{4}[/tex]

Step-by-step explanation:

Given a translation vector ...

  [tex]\displaystyle \binom{g}{h}[/tex]

moves g to the right and h up, you want the vectors for 8 right, 4 up, and for 8 left, 4 up.

Substitution

When we have g = units to the right, and we want 8 units to the right, we know that g = 8. Similarly, h = units up, and we want 4 units up, so h = 4.

Putting these values in the vector form, we have ...

a)   8 right, 4 up matches vector ...

  [tex]\displaystyle \boxed{\binom{8}{4}}[/tex]

b)  Left is the opposite of right, so 8 units left will be represented by ...

  g = -8

As before, 4 units up means h = 4.

  [tex]\displaystyle \boxed{\binom{-8}{4}}[/tex]

<95141404393>

Compute the variances in dollar amount and in percentage. (round to the nearest whole percent.) indicate whether the variance is favorable (f) or unfavorable (u).


budgeted amount - expense $106.00


actual amount $100.00


dollar variance $



percent variance


%


f or u

Answers

This is an unfavorable variance.

To calculate the dollar variance, we subtract the actual amount from the budgeted amount:

Dollar variance = Budgeted amount - Actual amount = $106.00 - $100.00 = $6.00 (favorable)

The dollar variance of $6.00 suggests that the actual expenses were less than the budgeted expenses, which is a favorable variance.

To calculate the percentage variance, we use the following formula:

Percentage variance = (Budgeted amount - Actual amount) / Budgeted amount x 100%

Substituting the values, we get:

Percentage variance = ($106.00 - $100.00) / $106.00 x 100% = 5.66% (rounded to the nearest whole percent)

The percentage variance of 5.66% suggests that the actual expenses exceeded the budgeted expenses by 5.66%, which is an unfavorable variance.

It's important to note that the dollar variance and percentage variance provide different perspectives on the variance, and they should be considered together to fully understand the implications of the variance. In this case, the dollar variance is favorable, indicating that the company spent less than expected.

However, the percentage variance is unfavorable, indicating that the company's expenses were higher than budgeted. The company may use this information to identify areas where they can reduce expenses in the future or adjust their budgeting process to be more accurate.

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An instructor graded 200 papers and found 80 errors. If a paper is picked at


random, find the probability that it will have exactly 4 errors

Answers

The probability of a paper having exactly 4 errors can be calculated using the binomial probability formula, which is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

What is the probability of selecting a paper at random from 200 papers and instructor found 80 errors and the probability that a paper has exactly 4 errors?

In binomial probability formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

n is the number of trials (in this case, the number of papers graded)

k is the number of successes (in this case, the number of papers with exactly 4 errors)

p is the probability of success (in this case, the probability that a paper has an error, which can be calculated by dividing the total number of errors by the total number of papers graded)

Calculate the probability of a paper having an error

p = 80/200 = 0.4

Calculate the probability of a paper having exactly 4 errors

P(X = 4) = (200 choose 4) * 0.4^4 * (1-0.4)^(200-4) ≈ 0.153

Therefore, the probability of picking a paper at random and finding exactly 4 errors is approximately 0.153 or 15.3%.

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Light travels 9.45 \cdot 10^{15}9.45⋅10
15
9, point, 45, dot, 10, start superscript, 15, end superscript meters in a year. There are about 3.15 \cdot 10^73.15⋅10
7
3, point, 15, dot, 10, start superscript, 7, end superscript seconds in a year.

Answers

The distance which this light travel per second is equal to 3 × 10⁸ meters per seconds.

What is speed?

In Mathematics and Science, speed is the distance covered by a physical object per unit of time.

How to calculate the speed?

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

By making distance the subject of formula, we have:

Distance, d(t) = speed × time

Distance = (9.45 × 10¹⁵ meters per year) × (1 year/ 3.15 × 10⁷ seconds)

Distance = 3 × 10⁸ meters per seconds.

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Complete Question:

Light travels 9.45 × 10¹⁵ meters in a year. There are about 3.15 × 10⁷ seconds in a year. How far does light travel per second?

WEATHER Suppose during springtime it rains about 40% of the time when school is dismissed for the day, Describe a model that could be used to simulate whether it will be raining when school is dismissed on a particular day during springtime. ​

Answers

One way to model this situation is by using a probability distribution, such as the binomial distribution. The binomial distribution models the probability of a certain number of successes (in this case, rain) in a fixed number of trials (in this case, school days during springtime).

Let's say we want to simulate whether it will be raining when school is dismissed on a particular day during springtime. We can define a success as rain and a failure as no rain. Then, the probability of success (rain) is 0.4, and the probability of failure (no rain) is 0.6.

To simulate whether it will be raining on a particular day, we can use a random number generator to generate a value between 0 and 1. If the value is less than or equal to 0.4, we can consider it a success (rain) and if it's greater than 0.4, we can consider it a failure (no rain).

We can repeat this process for a large number of trials (school days during springtime) to simulate the probability of rain over a given period of time. By keeping track of the number of successes (rainy days) and failures (non-rainy days), we can estimate the probability of rain during springtime when school is dismissed.

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Jenelle draws one from a standard deck of 52 cards. Determine the probability of drawing either a two or a ten? Write your answer as a reduced fraction. Answer= Determine the probability of drawing either a two or a club? Write your answer as a reduced fraction. Answer=

Answers

The probability of drawing either a two or a ten is (4+4)/52, which simplifies to 2/13.
The probability of drawing either a two or a club is (3+13)/52, which simplifies to 4/13.


For the first question: In a standard deck of 52 cards, there are four 2s and four 10s. The probability of drawing either a two or a ten is the number of successful outcomes (drawing a 2 or a 10) divided by the total number of possible outcomes (52 cards). So, the probability is (4+4)/52 = 8/52. This can be reduced to the fraction 2/13.

For the second question: There are four 2s and thirteen clubs in a standard deck of 52 cards. Since one of the 2s is a club, there are three additional 2s that are not clubs. The probability of drawing either a two or a club is the number of successful outcomes (3 additional 2s + 13 clubs) divided by the total number of possible outcomes (52 cards). So, the probability is (3+13)/52 = 16/52. This can be reduced to the fraction 4/13.

Therefore,
1) Probability of drawing either a two or a ten: 2/13
2) Probability of drawing either a two or a club: 4/13

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The equation of the line of best fit relating age (in years) and the median height (in cm) of boys is given.

Answers

the slope of   [tex]6.5[/tex] in this equation indicates that for each additional year of age, the median height of boys increases by approximately 6.5 cm. Thus, option D is correct.

What is median?

The statement that best interprets the slope in the context of the problem is "The slope is 6.5, this means that each year boys grow approximately  [tex]6.5[/tex]  cm."

The slope of a linear equation represents the rate of change, or the amount by which the dependent variable (in this case, median height) changes for each unit increase in the independent variable (in this case, age).

Therefore, the slope of  [tex]6.5[/tex] in this equation indicates that for each additional year of age, the median height of boys increases by approximately [tex]6.5[/tex] cm.

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The student council wants to determine the best date for the end-of-year dance for the 350 students. They survey every 5th student who gets off the bus one morning. Eighteen students voted for May 2, 39 students voted for May 9, and 13 students voted for May 16. Which date is it likely that 105 of the 350 students would choose for the dance?

Answers

There is a probability that 105 of the 350 students would select May 9 for the dance.

What is the sample  about?

To solve the above we need to find the proportion of students in the sample who voted for each date and this can be done by:

May 2:  18/70

  = 0.257

May 9: 39/70

  = 0.557

May 16: 13/70

   = 0.186

if the whole population of 350 students voted, then

May 2: 0.257 x 350

   =  90

May 9: 0.557 x 350

 = 195

May 16: 0.186 x 350

  = 65

From the above calculation, we can see that if 105 students out of 350) were to choose a date, the most likely date that they will select is  May 9, since it is the one that has the highest proportion of votes in the sample.

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Will give brainiest answer
which pair of equations would represent lines that are perpendicular to each other?
i. 3x - 2y = 12
ii. 3x + 2y = -12
iii. 2x - 3y = -12

Answers

Answer:

Step-by-step explanation:

Two lines are perpendicular to each other if their slopes are negative reciprocals of each other. So,  The equations i and ii are perpendicular to each other since their slopes are negative reciprocals of each other.

In other words, if the slope of one line is m, then the slope of the other line is -1/m.

To determine the slope of each equation, we can rewrite each equation in slope-intercept form, y = mx + b, where m is the slope and b is the

y-intercept.

i. 3x - 2y = 12

-2y = -3x + 12

y = (3/2)x - 6

The slope of this line is 3/2.

ii. 3x + 2y = -12

2y = -3x - 12

y = (-3/2)x - 6

The slope of this line is -3/2.

iii. 2x - 3y = -12

-3y = -2x - 12

y = (2/3)x + 4

The slope of this line is 2/3.

Therefore, equations i and ii are perpendicular to each other since their slopes are negative reciprocals of each other. Equation iii is not perpendicular to either of the other two equations.

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