Ten sixth-grade students reported the hours of sleep they get on nights


before a school day. Their responses are recorded in the dot plot. Looking


at the dot plot, Lin estimated the mean number of hours of sleep to be 8. 5


hours. Noah's estimate was 7. 5 hours. Diego's estimate was 6. 5


hours. Which estimate do you think is best? Solve for the mean to figure out


who was closer. *


Lin


ООО


Noah


Diego

Answer:

90

Step-by-step explanation:

The probability of choosing a person at random who is a junior and plays video games is of:

0.32 = 32%.

These are non-independent events.

A probability in the context of a problem is given by the division of the number of desired outcomes by the number of total outcomes.

For the probability in the context of this problem, the outcomes are given as follows:

Hence the probability is of:

p = 48/150 = 0.32 = 32%.

The probability of being a junior is of:

60/150 = 6/15.

The probability of playing videogames is of:

99/150

The multiplication of these probabilities is of:

6/15 x 99/150 = 0.264.

Different than 0.32, hence these two events are not independent.

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Answer:

6:9

Step-by-step explanation:

there are six circle and nine triangle

so the ratio is

6:9

Answer:

a) 9.135

b) 392.79

Step-by-step explanation:

Hope my answers are helpful

Step-by-step explanation:

Use distributive property to rewrite 6m(3n+1) in its equivalent form

Answer:

Sate why the measure of angle d is 120 degrees

The expression in terms of x, for the perimeter of the quadrilateral is:

22x + 12

The perimeter of an object is the sum of the sides of the the object. Thus, the perimeter of the quadrilateral can be found by adding all the four sides of the quadrilateral. That is:

Perimeter = (3x-5) + (2x+7) + (15x-2) + (2x-3)

Perimeter =  3x-5 + 2x+7 + 15x-2 + 2x-3

Perimeter =  22x + 12

Therefore,  the expression in terms of x, for the perimeter is 22x + 12.

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Complete question

Check the image

The  values of x is (4,-8) he two vectors will be orthogonal.

Let u=(x+4) i-4 j

x=x i+8 j

Now, U and v are orthogonal.

A number of vectors that are mutually perpendicular to each other, meaning they form an angle of 90° with a magnitude of one unit with each other, are called orthogonal unit vectors.

Therefore, u.v=0

⇒\(((x+4) i-4 j) \cdot(x i+8 j)=0 \\\)

⇒\(x(x+4)-32=0 \\\)

⇒\(x^2+4 x-32=0 \\\)

⇒\(x^2+8 x-4 x-32=0 \\\)

⇒\(x(x+8)-4(x+8)=0 \\\)

⇒x=4, x=-8

Therefore, the value of x=4 and x=-8 the two vectors will be orthogonal.

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a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Answer:

The correct option is;

A. The total points Shelly earned

Step-by-step explanation:

The given details are;

The number of tasks completed by Shelly and Terrence in the game = x

The total points scored by Terrence = 20 less than the total point scored by Shelly

The expression for Terrence's total point is 90·x - 20

Let the total points Shelly earned = Y

Therefore since the total points scored by Terrence = 20 less than the total point scored by Shelly, we have;

The total points scored by Terrence = Y - 20

Comparing the two expressions for the total points scored by Terrence which are;

90·x - 20 and Y - 20 we have;

90·x - 20 = Y - 20

Adding 20 to both sides of the equation gives;

90·x - 20 + 20= Y - 20 + 20

Which gives;

90·x = Y

Therefore, the first term of the expression 90·x - 20, which is 90·x is equal to Y, which is the total points Shelly earned

The correct option is therefore the total points Shelly earned.

Answer:

A. The total points Shelly earned

Step-by-step explanation:

Hope this helps!

Have a great day! :)

Any vector v in R2 can be expressed as a linear combination of x1 and x2, so x1 and x2 span R2. If x1, x2, and x3 were linearly independent, then the matrix with x1, x2, and x3 as its rows would have a non-zero determinant, which would contradict this fact.

(a) To show that x1 and x2 form a basis for R2, we need to show that they are linearly independent and span R2.
First, we show that they are linearly independent. Suppose we have scalars a and b such that ax1 + bx2 = 0. This gives us the system of equations:
2a + 4b = 0
a + 3b = 0
Solving this system, we get a = -2b. Substituting this into the second equation, we get b = 0, and then a = 0. Thus, the only solution to ax1 + bx2 = 0 is a = b = 0, which shows that x1 and x2 are linearly independent.
Next, we show that they span R2. Any vector in R2 can be written as a linear combination of x1 and x2. Suppose we have a vector v = (x,y) in R2. Then, we can solve for a and b in equation v = ax1 + bx2 to get:
x = 2a + 4b
y = a + 3b
Solving for a and b, we get a = (3x - 2y)/2 and b = (x - a)/4. Thus, any vector v in R2 can be expressed as a linear combination of x1 and x2, so x1 and x2 span R2.

(b) x1, x2, and x3 must be linearly dependent because there are more vectors than dimensions in R2. In other words, it is not possible for three linearly independent vectors to exist in R2.
One way to see this is to use the fact that the determinant of a matrix with three rows and two columns (i.e. a 3x2 matrix) is always zero. If x1, x2, and x3 were linearly independent, then the matrix with x1, x2, and x3 as its rows would have a non-zero determinant, which would contradict this fact.

(c) Since x1 and x2 form a basis for R2 and x3 is in R2, we know that Span(x1, x2, x3) is a subspace of R2. To find its dimension, we must determine how many vectors are needed to form a basis for Span(x1, x2, x3).
Since x1 and x2 are already a basis for R2, we know that any vector in Span(x1, x2, x3) can be written as a linear combination of x1, x2, and x3. Thus, we only need to consider whether x3 can be written as a linear combination of x1 and x2.
Suppose there exist scalars a and b such that x3 = ax1 + bx2. This gives us the system of equations:
2a + 4b = 7
a + 3b = -3
Solving this system, we get a = -4 and b = 3. Thus, x3 can be written as -4x1 + 3x2.
Since x3 is a linear combination of x1 and x2, we don't need all three vectors to form a basis for Span(x1, x2, x3). In fact, we can remove x3 and still have a basis for Span(x1, x2, x3), which means that Span(x1, x2, x3) is a subspace of R2 with dimension 2.

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Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

Answer:

Statistic

Step-by-step explanation:

Statistic: numbers that summarize data from a sample

Parameter: numbers that summarize data for an entire population

Answer:

0...

Step-by-step explanation:

what kind of question...- no matter how manny times you multiply 13 you cant make it into 16

Answer:

19/22

Step-by-step explanation:

cc = 9

sand = 10

pb = 3

total = 22

P(not pb) = 19/22

Answer:

1 year at 8 percent

Step-by-step explanation:

i took the test

Answer:

1) x/2 + 1
2) x/2 + 1
3) x/2 + 1

Step-by-step explanation:

1) (2x * 1/4) = (2 * 1/4 * x) = (1/2 * x) = (x/2)
(4 * 1/4) = (4/4) = (1)
(x/2) + (1) = (x/2 + 1)

2) (1/6 * 3 * x) = (3/6 * x) = (1/2 * x) = (x/2)
(1/6 * 6) = (6/6) = (1)

(x/2) + (1) = (x/2 + 1)

3) (1/4 * x) = (3/12 * x) = (3x/12)
(3x/12) + (3x/12) = (6x/12) = (1/2 * x) = (x/2)
(9 - 8) = 1
(x/2) + (1) = (x/2 + 1)

The expanded form of the expressions is 2x + 1 and x/2 + 1

Given the expression 1/4(2x + 4)

Expand the expression

1/4(2x + 4) = 1/4(2x) + 1/4(4)

1/4(2x + 4) = 2x + 1

For the expression 1/6(3x + 6)

1/6(3x + 6) = 1/6(3x) + 1/6(6)

1/6(3x + 6) = x/2 + 1

For the expression 1/4 x + 9 + 3/12 x - 8

Simplify the expression

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

2/4 x  + 1

1/2 x + 1

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Answer:

i believe it would be the first and third option RSandTU   and    RTandSU

Step-by-step explanation:

none of the lines can be  parallel in this prisim so we are just looking for lines that have no intersectionswith each other. the lines i chose do not intersect.

Answer:

1/3

Step-by-step explanation:

1. When we divide any x-input by the y-input, we get 3. This is the same as multiplying the x-input by 1/3 to get the y-input. Let's see if it works!

2. Great! All our x-inputs and y-inputs match up, meaning the constant of proportionality, k, is 1/3.

Answer:

Solution given:

ratio of boys to the girls=5:3

let ratio be 5x and 3x

we have

5x+3x=40

8x=40

x=40/8

x=5

5x=5*5=25

3x=3*5=15

\(\)

No of boys=25

No of girls=15

The points that are 4 units apart are B and D

Which points are 4 units apart? On a coordinate plane, point A is at (-2, 4), point B is at (3, -6), point C is at (-1, 0), point D is at (3, -2).

B and C

C and D

A and C

B and D

To do this, we simply calculate the distance using the following equation

\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2\)

Using the given points, we have:

\(BC = \sqrt{(3+ 1)^2 + (-6 -0)^2} = 7.2\)

\(CD = \sqrt{(-1 - 3)^2 + (0 +2)^2} = 4.5\)

\(AC = \sqrt{(-2 + 1)^2 + (4 -0)^2} = 4.1\)

\(BD = \sqrt{(3 - 3)^2 + (-6 +2)^2} = 4\)

Hence, the points that are 4 units apart are B and D

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At this rate, Paula will use 35 oz of sauce and 28 oz of cheese to make 7 pizzas.

To determine how much sauce and cheese Paula's Pizza Parlor will use to make 7 pizzas, we need to first find the rate at which the ingredients are used. From the given information, we can see that 3 pizzas require 15 oz of sauce and 12 oz of cheese. This means that each pizza requires 5 oz of sauce and 4 oz of cheese.

To find the total amount of sauce and cheese needed for 7 pizzas, we can simply multiply the amount needed for one pizza by 7. This gives us a total of 35 oz of sauce and 28 oz of cheese needed to make 7 pizzas.

It is important to accurately calculate the amount of ingredients needed for a given amount of pizzas to ensure that there is enough to satisfy demand without wasting excess ingredients. This can help businesses like Paula's Pizza Parlor manage their inventory and expenses efficiently.

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In response to the stated question, we may state that As a result, the prism value of x is around 6.432 cm.

A prism is a polyhedron with either an n-sided polygonal basis, a second base that is a shifted copy of the original base, and n extra faces (essentially all parallelograms), with two connecting the corresponding sides of the base. Any cross sections those are parallel to the base are translations of it. A prism is a three separate, solid, three-dimensional object with two faces. It has the same merge, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with out any bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by planes that are obliquely oriented to one another. A typical prism has two triangular faces and parallel square faces. They are made of either glass or metal.

Two congruent triangles and three rectangular faces make up the right triangular prism.

L is the length of the rectangular faces.

W is the width of the rectangular faces.

H is the height of the rectangular faces and the prism.

B is the triangle's base.

x is the height of the triangles.

SA = 2B + PH

B = 1/2 * base * height

B = 1/2 * 13 cm * x = 6.5x cm²

P = 13 cm + 5 cm + x = 18 cm + x

SA = 2B + PH

376.8 cm² = 2(6.5x cm²) + (18 cm + x)(12 cm)

376.8 cm² = 13x cm² + (18 cm)(12 cm) + 12x cm²

376.8 cm² = 25x cm² + 216 cm²

25x cm² = 376.8 cm² - 216 cm²

25x cm² = 160.8 cm²

x = 6.432 cm

As a result, the value of x is around 6.432 cm.

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The only cardinal number whose letters are in alphabetical order in English is "forty". This word meets the criteria because its letters appear in alphabetical order: "f", "o", "r", "t", "y".
To find the cardinal number with letters in alphabetical order, we need to examine each number individually. Starting from zero, we can see that "zero" does not have letters in alphabetical order. Similarly, "one" and "two" do not meet the criteria. The word "three" has letters in alphabetical order, but it is not a cardinal number. Continuing our search, we find that "forty" is the first and only cardinal number where the letters are arranged in alphabetical order.
In English, the only cardinal number whose letters are in alphabetical order is "forty".

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Answer:

60 compounding periods

Step-by-step explanation:

The proper formula for compound interest is A = P(1 + r/n)^(nt), where r is the interest rate as a decimal fraction, n is the number of times that interest is compounded in 1 year, and t is the number of years.

In this problem, we don't need to calculate the Amount, but only the number of compounding periods.  That is nt, which here is 12*5, or 60.

Answer:

i believe its hurricane

Step-by-step explanation:

This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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Answer:

A 16.8 is 168 tenths not 168 hundredths.