Chegg you are a guidance counselor and want to schedule 4 students for sessions over the coming month. You have eight time slots availabel and want ot schedule each student exactly twice

According to the question, the sum of the numerator and denominator is 5.

Let's represent the length of time in minutes that Anna, Bertram, Carli, and David can hold their breath as A, B, C, and D, respectively.

According to the given information, we have the following equations:

B + C + D = 3A          (Equation 1)

A + C + D = 4B          (Equation 2)

A + B + D = 2C          (Equation 3)

8A + 10B + 6C = \((\frac{2}{5})\) * 60   (Equation 4)

We can solve this system of equations to find the values of A, B, C, and D.

Let's start by simplifying Equation 4:

8A + 10B + 6C = 24

Next, we can use Equation 3 to express D in terms of A, B, and C:

D = 2C - A - B

Substituting this expression for D in Equations 1 and 2, we can rewrite them as:

B + C + (2C - A - B) = 3A

A + C + (2C - A - B) = 4B

Simplifying these equations, we get:

3C - A = 3A

3C - B = 3B

From these equations, we can deduce that A = C and B = 2C.

Substituting these values in Equation 4, we have:

8A + 10B + 6A = 24

14A + 10B = 24

Since B = 2C and A = C, we can rewrite the equation as:

14C + 20C = 24

34C = 24

C = \(\frac{24}{34}\)

= \(\frac{12}{17}\)

Now, substituting C = \(\frac{12}{17}\) in equations A = C and B = 2C, we find:

A = \(\frac{12}{17}\)

B = \(\frac{24}{17}\)

Finally, the length of time that David can hold his breath is D = 2C - A - B:

\(D = 2(\frac{12}{17}) - \frac{12}{17} - \frac{24}{17}\)

\(D = \frac{24}{17} - \frac{12}{17} - \frac{24}{17}\)

\(D=-\frac{12}{17}\)

The length of time that David can hold his breath is \(-\frac{12}{17}\) minutes.

The sum of the numerator and denominator of this fraction is \(-12 + 17 = 5\).

Therefore, the sum of the numerator and denominator is 5.

Please note that it is unusual to have a negative value for the length of time, so you may want to double-check the problem statement or verify the calculations to ensure accuracy.

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A bar graph is the most popular visual representation of quantitative data.

Another name for them is bar charts. One tool used in statistics for data processing is the bar graph. Using a bar diagram, it is simple and quick to compare sets of data among several groupings. On one axis of the graph are discrete numbers, while on the other are categories. The purpose is to illustrate how the two axes are related. Bar charts can also show significant alterations in data over time.

Given,

A bar graph is the most popular visual representation of quantitative data.

b) Bar graph

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Option B: 4x²-x+3

(4x³ + 11x² + 0x + 9) + (x+3) [here, we will include 0x to do long division]

Divide 4x³ by x to get first term of the quotient, 4x³

Then, take 4x² and multiply it with 3 and you will get 4x² + 12

Subtract 4x² + 12 from 4x³ + 11x².

Then, you will get the remainder as -x² + 0x

Now you have to repeat the same same process, divide -x² by x to get second term of quotient, -x

Then take -x and multiply with 3 and you will get -x²- 3x

You will get the remainder as 3x+ 9

Divide 3x by x to get the third term of quotient, 3

Then, take 3 and multiply with 3 and you will get 3x + 9

Subtract and you will get the remainder as 0.

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Answer:

26

Step-by-step explanation:

Answer:

1. there were 24 chocolates in the box at first.

2. the boy with the smallest share received 6 chocolates.

Explanation:

let's represent the number of chocolates in the box with 8x.

the first boy got ⅜ × 8x  = 3x chocolates. now, there are 8x - 3x = 5x chocolates remaining.

the second boy got ⅖ × 5x = 2x chocolates. now, there are 5x - 2x = 3x chocolates remaining.

3x = 9 chocolates

x = 3 chocolates

since the original number of chocolates was represented by 8x, we now know that there were 8 × 3 = 24 chocolates in the box at first.

the first boy got 9 chocolates, the second boy got 6 chocolates and the last boy got 9 chocolates. thus, the boy with the smallest share got 6 chocolates.

i hope this helps! :D

90 feet is the lengths of the sides of the rectangular field .

What do you mean by rectangular?

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 5400, hence:

Area = length * width = x * y

5400 = xy

y = 5400/x

A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:

Amount of fencing needed (P) = x + x + y + y  + y = 2x + 3y

Amount of fencing needed (P) = 2x + 3(5400/x) = 2x + 16200/xTo minimize

the amount of fencing needed, dP/dx = 0, hence:

dP/dx = 2 - 16200/x²

2 - 16200/x² = 0

2 = 16200/x²

2x² = 16200

x² = 8100

x = 90 feet

y = 5400/x =  5400/90 = 90 feet

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Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

The equation of the line perpendicular to the given line and passing through (-3, 7) is; y = (-2/3)x + 5

We are given the equation of a line as; y = (3/2)x - 1

Now, the general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, for our given equation we have;

Slope; m = 3/2

y-intercept; c = -1

Now, for a line perpendicular to this, will have a slope of -1/(3/2) = -2/3

Thus, equation of the line perpendicular to the given line and passing through (-3, 7) is;

y - 7 = (-2/3)(x - (-3))

y - 7 = (-2/3)(x + 3)

y = 7 - 2 - (2/3)x

y = (-2/3)x + 5

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Answer:

16 the answer is 1, 4, 5, 6, yeah good answer

Answer:

1.66 cans or 1.6 rounded.

Step-by-step explanation:

1 can = 240ft

2 cans = 480ft

480 divided by 240 = 1.66666666667.

Rounded number = 1.66 and or 1.6

Answer:

I Think D.

Step-by-step explanation:

To make the given statements true, $967.72 should be invested in the account today, with no additional deposits or withdrawals being made.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:

B = P(1 + r/n)^t

where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded annually, and t is the time in number of year

Based on the given information, P is the unknown and

B = $2174. 30

t = 18

r = 4. 6% = 0.046

n = 1

Plug in the values and solve for P or the amount that should be invested today.

B = P(1 + r/n)^t

$2174. 30 = P(1 + (0.046/1))^18

$2174. 30 = P(1.046)^18

P = $2174. 30 / (1.046)^18

P = $967.72

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If the calculated chi-square test statistic is greater than 4.605, we would reject the null hypothesis of equal proportions at the 10% significance level.

To find the critical value for a chi-square test at the 10% significance level, we need to use a chi-square distribution table with degrees of freedom (df) equal to the number of categories minus 1.

Suppose the instructor is testing for the equality of proportions among k categories, then the degrees of freedom will be k-1.

The critical value for a chi-square test at the 10% significance level with k-1 degrees of freedom is given by the chi-square distribution table.

For example, suppose we have k=3 categories, then the degrees of freedom will be k-1 = 2. Using a chi-square distribution table with 2 degrees of freedom and a 10% significance level, we find the critical value to be 4.605.

Therefore, if the calculated chi-square test statistic is greater than 4.605, we would reject the null hypothesis of equal proportions at the 10% significance level.

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Answer:

  (f·g)(x) = x³ -8x² +20x -16

Step-by-step explanation:

The distributive property is useful for this.

  (f·g)(x) = f(x)·g(x) = (x² -6x +8)(x -2)

  = x(x² -6x +8) -2(x² -6x +8)

  = x³ -6x² +8x -2x² +12x -16

  (f·g)(x) = x³ -8x² +20x -16

_____

Additional comment

I find it convenient to separate the terms of the shortest polynomial. That way, the distributive property doesn't need to be used quite so many times. Of course, any outside minus sign applies to all terms inside parentheses.

Answer:

B, C

Step-by-step explanation:

Seeing as you said ASAP I thought I wouldn't spend time writing an explanation, but let me know if you do want one.

Answer:  B

Step-by-step explanation:each of the pairs of opposite angles made by two intersecting lines.

We can see that the statement is not always true for any vectors u and v in V3.

The statement is not always true.

The cross product of vectors u and v in V3 is a vector that is orthogonal to both u and v. That is,

u x v ⊥ u and u x v ⊥ v

However, this does not necessarily mean that (u x v) * u = 0 for all u and v in V3.

For example, let u = <1, 0, 0> and v = <0, 1, 0>. Then,

u x v = <0, 0, 1>

(u x v) * u = <0, 0, 1> * <1, 0, 0> = 0

So in this case, the statement is true. However, consider the vectors u = <1, 1, 0> and v = <0, 1, 1>. Then,

u x v = <1, -1, 1>

(u x v) * u = <1, -1, 1> * <1, 1, 0> = 0

So in this case, the statement is also true. However, if we take the vector u = <1, 0, 0> and v = <0, 0, 1>, then

u x v = <0, 1, 0>

(u x v) * u = <0, 1, 0> * <1, 0, 0> = 0

So in this case, the statement is true as well.

However, if we take the vector u = <1, 1, 1> and v = <0, 1, 0>, then

u x v = <1, 0, 1>

(u x v) * u = <1, 0, 1> * <1, 1, 1> = 2

So in this case, the statement is not true.

Therefore, we can see that the statement is not always true for any vectors u and v in V3.

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ΔABC was dilated by a scale factor of 2, reflected across the x-axis, and moved through the translation vector (-2, -2).

To find the scale factor of a triangle when comparing it to a similar triangle, follow these steps: Identify corresponding sides, Measure the lengths of corresponding sides and Calculate the ratio of corresponding side lengths.

Calculate the ratio of the corresponding side lengths:

Scale factor = DE/AB = 4/2 = 2

Reflection: The y-coordinates of points A and B in ΔABC are positive, while the y-coordinates of points D and E in ΔDEF are negative. This suggests a reflection across the x-axis.

Translation: To map point A (1, 3) to point D (-1, 1), we can see that the x-coordinate needs to be translated by -2 units (1 + (-2) = -1) and the y-coordinate needs to be translated by -2 units (3 + (-2) = 1). Similarly, for other points in the triangles, the translations are consistent. Thus, the translation vector is (-2, -2).

The above answer is in response to the full question below;

In the similarity transformation of ΔABC, to Δ DEF, Δ ABC was dilated by a scale factor of [?], reflected across the [ ], and moved through the translation [ ].

A  2

B. 1/2

C 1/3

D. 3

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Answer:

     A

Step-by-step explanation:

got it right on edg 2020

Answer: x = 2.16

Step-by-step explanation:

The solution of the expression is, x = 2.16

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3.5x/9 = 4.2/5

Now, We can simplify for x as;

⇒ 3.5x/9 = 4.2/5

⇒ 3.5x = 4.2 × 9 / 5

⇒ 3.5x = 7.56

⇒ x = 2.16

Thus, The solution is, x = 2.16

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Correct Answers:

1) Ordering tiles to replace the roof of a house.

Tiles of a roof cover the top side of a three dimensional house

2) Estimating how long it will take to clean the windows of a greenhouse.

To find this you would divide the surface area of the windows by the rate someone could clean them, giving you a time

3) Buying fabric to sew a couch cover.

Similar to the roof, you are covering a portion of one side of a 3-dimentional object

Incorrect Answers:

1) Deciding whether leftover soup will fit in a container.

Liquid containers are measured in volume

2) Estimating how long it will take to fill a swimming pool with a garden hose.

Liquid containers are measured in volume

3) Deciding whether one muffin pan is enough to bake a muffin recipe.

Muffin batter is liquid, and the size/volume of muffins vary

Answer:

Step-by-step explanation:

\(P_{ABCD}=P_{ACD}+P_{ABD}\)

We can use Heron's formula to calculate area of triangles:

\(P_\triangle=\sqrt{s(s-a)(s-b)(s-c)}\)   where:

a, b, c  - sides of triangle

s  - semi-perimetr of triangle  {(a+b+c):2}

ΔACD:

a = 4.39 ,   b = 3.42  ,  c = 4.57

s = (4.39 + 3.42 + 4.57)÷2 = 12.38÷2 = 6.19

\(P_{ACD}=\sqrt{6.19(6.19-4.39)(6.19-3.42)(6.19-4.57)}\\\\P_{ACD}=\sqrt{6.19\cdot1.8\cdot2.77\cdot1.62}=\sqrt{49.9986108}=7.070969579...\\\\P_{ACD}\approx7.071\)

ΔACD:

a = 5.44 ,   b = 7.84 ,   c = 3.42

s = (5.44 + 7.84 + 3.42)÷2 = 16.7÷2 = \(P_{ACD}=\sqrt{8.35(8.35-5.44)(8.35-7.84)(8.35-3.42)}\\\\P_{ACD}=\sqrt{8.35\cdot2.91\cdot0.51\cdot4,93}=\sqrt{61.09371855}=7.81624708...\\\\P_{ACD}\approx7.816\)

\(P_{ABCD}=P_{ACD}+P_{ABD}\\\\P_{ABCD}\approx7.071+7.816 = 14.887\\\\P_{ABCD}\approx 14.89\)

second one is correct

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The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False.

The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

This is a recursive problem where each player plays optimally. There are two players in the game. The child will pick the balls first and then the game owner takes turns. Both will pick the balls optimally in order to win.

In each turn, k balls can be picked from the box. The winner is the one who picks the last ball. If the child picks the last ball, they win otherwise the game owner wins.

The algorithm is as follows:

Algorithm - Pick Balls

1. Define a recursive function called PickBalls(n). The function takes one parameter as input, which is the number of balls remaining in the box.

2. Check if the number of balls remaining is less than or equal to k. If yes, then return True as the game has ended and the child has won.

3. If the number of balls is greater than k, then pick k balls from the box.

4. If the child picks the last ball, then return True.

5. If the child does not pick the last ball, then the game owner picks the balls recursively.

6. If the game owner picks the last ball, then return False. Otherwise, return True.

Explanation: We are designing a recursive algorithm to find out whether the child will win or lose in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. We are assuming that both players play optimally. The algorithm works as follows:

If the number of balls remaining in the box is less than or equal to k, then the child can pick all the balls and win the game. Therefore, the function returns True.

If the number of balls remaining in the box is greater than k, then the child picks k balls from the box. If the child picks the last ball, then they win the game. Therefore, the function returns True.

If the child does not pick the last ball, then the game owner picks the balls recursively. If the game owner picks the last ball, then they win the game. Therefore, the function returns False. If the game owner does not pick the last ball, then the child picks again and the process repeats itself. If the child eventually picks the last ball, then they win the game. Therefore, the function returns True.

Conclusion: The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

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Answer:

2,10

Step-by-step explanation:

we can see where the line touches the x-axis but right at the line making the points have a 0 as the y, (2,0) and (10,0) the others have don´t have 0 in the y place. To make it short there are 2 points touching the x-axis, not above or below but on the line.  

(a)The probability that all four adults are very confident is approximately 0.0056.

(b) The probability that none of the adults are very confident  is approximately 0.522.

(c) The probability that at least one adult is very confident is   approximately 0.478.  

What is the probability of selecting four adults at random without replacement from a sample of 1000 U.S. adults, given the proportion of very confident individuals?

The probability of selecting four adults at random without replacement from a sample of 1000 U.S. adults depends on the proportion of very confident individuals. By calculating the probability of all four adults being very confident (a), none of the four adults being very confident (b), and at least one of the four adults being very confident (c), we can determine the likelihood of these scenarios occurring based on the given information.

To solve this problem, we can use the concept of probability and combinations.

(a)Given that there are 150 out of 1000 U.S. adults who are very confident, the probability of selecting one adult who is very confident is:

P(very confident) = 150/1000

= 0.15

Since the sampling is done without replacement, after each selection, the sample size decreases by 1. Therefore, for the second selection, the probability becomes 149/999, for the third selection, it becomes 148/998, and for the fourth selection, it becomes 147/997.

To find the probability that all four adults are very confident, we multiply these probabilities together:

P(all four adults are very confident) = (0.15) * (149/999) * (148/998) * (147/997)

≈ 0.0056

(b) The probability of selecting one adult who is not very confident (opposite of very confident) is:

P(not very confident) = 1 - P(very confident)

= 1 - 0.15

= 0.85

Since we are selecting four adults at random without replacement, the probability of none of them being very confident can be calculated as:

P(none very confident) = P(not very confident) * P(not very confident) * P(not very confident) * P(not very confident)

= (0.85)* (0.85) * (0.85) * (0.85)

≈ 0.522

(c) The probability of at least one adult being very confident is the complement of none of them being very confident:

P(at least one very confident) = 1 - P(none very confident)

= 1 - 0.522

= 0.478

Therefore,

(a) The probability that all four adults are very confident is approximately 0.0056.

(b) The probability that none of the adults are very confident is approximately 0.522.

(c) The probability that at least one adult is very confident is approximately 0.478.  

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Answer:

Y = 31.9° (rounded to 3 significant figures)

Answer:

Yes.

Step-by-step explanation:

To find if a triangle is a right triangle or not, we use the Pythagorean theorem. The Pythagorean theorem states that \(a^{2} + b^{2} = c^{2}\).

a and b are the triangle legs. The c is the hypotenuse of the triangle.

Now, to find if a triangle is a right triangle, we plug in 9 for a and b and 9root2 for c.

\(9^{2} + 9^{2} = (9\sqrt{2})^{2}\)

81 + 81 = 81 * 2

162 = 162

So the given triangle, is indeed a right triangle.

Answer:

slope=-1/5

Step-by-step explanation:

the slope is -1/5 because it falls 1 unit from one point before crossing 5 units and hitting another point.