the teacher has a small class with only 7 students. the teacher grades their homework and reports scores of: 10, 7, 8, 12, 9, 11, and 13. what is the median?

Answer:

Following are the response to the given question:

Step-by-step explanation:

Move b a bit further if the angle between cd and ab changes when you move b if you want to make a perpendicular point to cd The angle BEC is 90 ° for making the AB line perpendicular to the line CD to transfer point B to the angle between the two lines.

Answer:

x = 2 and x = +2

Step-by-step explanation:

It's essential that you use parentheses to clarify what's happening here:

h(x)=x-4/x^2-4  =>  h(x)=(x-4) / (x^2-4)

We have vertical asymptotes at x values at which the denominator (x^2 - 4) is zero.  That would be x = 2 and x = +2.

Given:

A scale drawing of a rectangular park is 5 inches wide and 7 inches long.

The actual park is 280 yards long.

To find:

The area of the actual park.

Solution:

Length of drawing = 7 inches

Length of actual park = 280 yards

The scale factor is

7 inches : 280 yards

1 inches : 40 yards

The width of the drawing is 5 inches. So, the width of actual part is

\(40\times 5=200 yards\)

The area of the actual park is

\(Area=Length \times width\)

\(Area=280\times 200\)

\(Area=56000\)

Therefore, the area of the actual park is 56000 sq. yards.

UV = 11 and TV = 41

A line segment has two fixed end points in a line. The length of the line segment is the distance between two fixed points. The length can be measured by units such as centimeters, millimeters, feet or inches

The points on a line are matched one to one with the real numbers in ruler postulate.  Coordinate of the point is the real number that corresponds to a point. The distance between points A and B (AB) is equal to the difference of the coordinates of A and B.

As given,

TU = 16, UV = x+4  and TV = 8x -15

TU + UV = TV

16 + x+4 = 8x -15

16 + 4 +1 5 = 8x - x

35 = 7x

x = 35/5

x= 7

We can find UV = x + 4 by substituting the value of x

= 7 +4

= 11

and TV = 8x - 15

= (8*7) - 15

=56 - 15

=41

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Answer:

6.5

Step-by-step explanation:

26 - 13 = 13

13/2 = 6.5

Answer:

6.5

Step-by-step explanation:

the average would add the 2 together then divide by 2

26 - 13 = 13

13 / 2 = 6.5

We can conclude that they form a right triangle

So GF = FH

OF^2 = GF^2 + OG^2

OF^2 = 8.4^2 + 8^2

OF^2 = 70.56 + 64

OF^2 = 134.56

OF = 11.6

a) The probability space is (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).

b) The probability that the sum of the numbers drawn is 4 is 2/9.

c) The probability that the sum of the numbers is at least 4 is 2/3.

a) The probability of an event is measured between 0 and 1, and the probability space is a collection of all probable results, hence the probability space is:

P= (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)

Hence, the probability space can be written as a set, S = {1,2,3}.

b) If 2 balls are drawn and sum of the numbers is 4, then there could be only one probable way of drawing the balls, which is ball 1 and 3, so probability that the sum of the numbers is 4 is:

P = 2/9

c) If 2 balls are drawn and sum of the numbers is at least 4, then probable ways of drawing the balls are:

(1,3), (2,2), (2,3), (3, 1), (3, 2), and (3, 3)

Hence, the probability that the sum of the numbers is at least 4 = 6/9 = 2/3

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Five times as large= multply by 5

As large as five times

Then

X =5x 3x6 =

X = 90

the answer is A and D

when you differentiate the question you find that the maximum point is (0,0)i.e

\( \frac{dy}{dx} = - 8x\)

when dy/dx is 0 values of x are 0,0

and the function shows that valies of x are real numbers.

The domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

Given function as

f(x) = -4x²

The range is the set of values that correspond with the domain.

Range: (−∞,0], {y|y≤0}

Domain: (−∞,∞), {x|x∈R}

and the function shows that values of x are real numbers.

The maximum point is when differentiating the function, which is (0,0) i.e

dy/dx = -8x

Values of x are 0 when dy/dx is 0.

Hence, the domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

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Answer:

x > -39

Step-by-step explanation:

-0.3x < 6.7 + 5

-0.3x < 11.7

divide by -0.3

Answer is x > -39

Answer:

True

Step-by-step explanation:

Answer:

i would say that A. would be the answer...because 0 is a #number.

The length of Sarah's drawing is given by the following equation:

0.1g = 0.8.

The scale of the drawing is obtained applying the proportions in the context of this problem.

The scale is defined as the division of the drawn length by the actual length.

Sarah's drawing has a scale factor of 1 inch to 0.1 inch, meaning that each inch she draws has an actual length of 0.1 inch.

The rule of three is defined as follows:

1 inch - 0.1 inches

g inches - 0.8 inches

Hence the equation is:

0.1g = 0.8.

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Answer:

4$ for one hotdog

Step-by-step explanation:

60/15 =

4.

One hotdog equal 4$

brainliest?

The rate of one hot dog is $4.

We are given that there are 15 hot dogs which cost $60.We have to calculate the amount of rate for one hot dog.

By the unitary method,

Amount of rate for one hot dog = is $60/15=$4

Hence one hot dog cost $4.

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The answer is

60% rise in quantity demanded of good x.

Explanation:

Percentage change in quantity demanded for good Y:

= (Change in Quantity ÷ Initial Quantity) × 100

= (60 units ÷ 400 units) × 100

= 15%

Percentage change in price of good Y = 10% Rise

Therefore, the price elasticity of demand for Good Y is as follows:

= Percentage change in Quantity demanded ÷ Percentage change in price

= 15 ÷ 10

= 1.5

Hence,

Price elasticity of demand of good x:

= 2 × price elasticity of demand of good y

= 2 × 1.5

= 3

Percentage change in price of good x:

= (Change in price ÷ Initial price) × 100

= (2 ÷ 10) × 100

= 20%

Therefore,

Price elasticity of demand for Good x = Percentage change in Quantity demanded ÷ Percentage change in price

3 = Percentage change in Quantity demanded ÷ 20

3 × 20 = Percentage change in Quantity demanded

60% = Percentage change in Quantity demanded for good x

Hence, 60% rise in quantity demanded of good x.

Answer:

Step-by-step explanation:

Convert fractions to decimals. Then compare the whole part of the decimal numbers. The decimal having the  highest whole part is the greatest number.

If whole part of the decimals are same, compare the tenth place ....

\(68 \frac{1}{2}= \frac{137}{2}=68.5\)

\(\frac{336}{5}=67.2\)

67.59

67.22

Greatest to least:  68.5  , 67.59  , 67.22 , 67.2

                            68 1/2  , 67.59 , 67.22 ,  336/5

Answer:

A. 6/10

Step-by-step explanation:

Answer:

the answer is a 6

                          _

                         10

Step-by-step explanation:

Answer:

3443ye

Step-by-step explanation:

Answer:

y=3x-1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

y=3x-1

have a nice day ! :)

The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.

Amount of water that the bottle can hold = 32 ounces

Bottles of water consumed = 2

A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.

Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -

= w > 2 × 32

Therefore,

Simplifying the right side of the inequality:

w > 64

Complete Question:

Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?

a. w>2

b. 32<w

c. w = 64

d. 64<w

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1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

-5x+(- 15 ) = 20

x=-7

Step by Step

-5x+(-15)= 20 becomes

-5-15=20 add 15 tp (15 and 20)

-5x=35 ( divide by 51

x=-7

Answer:

B

Step-by-step explanation:

Answer:

x = 0 and x = 4/3

Step 1:  First, we must find the derivative of f(x), noted by f'(x)

When you have a polynomial in the form x^n, we take the derivative of each polynomial using the following formula:

\(f'(x)=nx^n^-^1\)

This means that the exponent becomes a coefficient and we subtract from the exponent.

We can do take the derivatives of x^3 and -2x^2 separately and combine them at the end:

x^3:

\(x^3\\3x^3^-^1\\3x^2\)

-2x^2

\(-2x^2\\-2(2x^2^-^1)\\-4x\)

Thus, f'(x) is 3x^2 - 4x

Step 2:  Critical points are found when f'(x) = 0 or when f'(x) = undefined.  There are no values for x which would make 3x^2 - 4x undefined, so we can set the function equal to 0 and solving will give us our critical points

We see that we can factor out x from 3x^2 - 4x to get

x(3x - 4) = 0

Now, we can set the two expressions equal to 0 to solve for x:

Setting x equal to 0:

x = 0

Setting 3x - 4 equal to 0:

3x - 4 = 0

3x = 4

x = 4/3

Therefore, the two critical points of the function are x = 0 and x = 4/3

Answer:

Step-by-step explanation:

a) it is a reflection

b) it is vertex B"

A stem-and-leaf diagram separates each value of a data set into two parts: the stem and the leaf.

The stem is the first part of the number, typically the largest place value, and it is used to group similar values together. The leaves are the last part of the number, typically the smallest place value, and they provide the specific values within each group.

For example, consider a data set with the values 15, 19, 10, 11, 15. In a stem-and-leaf diagram, the stem for these values would be 1 and the leaves would be 5, 9, 0, 1, and 5, respectively.

The stem-and-leaf diagram would then look something like this:

This format allows for a quick visualization of the distribution of the data and can be useful for identifying patterns and relationships within the data set.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

Step-by-step explanation:

Let the previous salary be x

Increase = 5%

New salary = £880

Answer:

Step-by-step explanation:

according to the question

\(x \times \frac{105}{100} = 880\)

\(x = 880 \times \frac{100}{105} \)

\(x = 838.10\)

Answer:

3 cups of flour

Step-by-step explanation:

We know

2 cups of sugar = 1 cup of flour

1 cup of sugar = 0.5 cup of flour

To find how many cup of flour for 6 cups of sugar

We take 6 times 0.5 = 3 cups of flour

So, 3 cups of flour will be needed for 6 cups of sugar.

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The augmented matrix for the system of equations is:

| 1  2 -2  2 -1 | 0 |
| 1  2 -1  3 -2 | 0 |
| 2  4 -7  1  1 | 0 |

A basis for the solution space S is {(-2, 1, 0, 0, 4), (2, 0, 1, 0, -4), (3, 0, 0, 1, -4)}. The dimension of the solution space S is 3, since there are 3 free variables and 3 basis vectors.

To solve the system by Gauss elimination method, we first need to eliminate the x1 term from the second and third equations. To do this, we can subtract the first equation from the second and third equations:

| 1  2 -2  2 -1 | 0 |
| 0  0  1  1 -1 | 0 |
| 0  0 -3 -3  3 | 0 |

Next, we can eliminate the x3 term from the third equation by adding 3 times the second equation to the third equation:

| 1  2 -2  2 -1 | 0 |
| 0  0  1  1 -1 | 0 |
| 0  0  0  0  0 | 0 |

Now, we can see that the third equation is redundant, so we can ignore it. The remaining equations give us:

x1 + 2x2 - 2x3 + 2x4 - x5 = 0
x3 - x4 + x5 = 0

We can solve for x3 and x5 in terms of x1, x2, and x4:

x3 = x4 - x5
x5 = 2x1 + 4x2 - 4x3 - 4x4

Substituting these equations back into the first equation gives us:

x1 + 2x2 - 2(x4 - x5) + 2x4 - (2x1 + 4x2 - 4x3 - 4x4) = 0

Simplifying gives us:

-2x1 - 4x2 + 4x3 + 6x4 = 0

We can solve for x1 in terms of x2, x3, and x4:

x1 = -2x2 + 2x3 + 3x4

Now, we can express the solution space S in terms of the free variables x2, x3, and x4:

S = {(-2x2 + 2x3 + 3x4, x2, x3, x4, 2x1 + 4x2 - 4x3 - 4x4) | x2, x3, x4 ∈ R}

A basis for the solution space S is:

{(-2, 1, 0, 0, 4), (2, 0, 1, 0, -4), (3, 0, 0, 1, -4)}

The dimension of the solution space S is 3, since there are 3 free variables and 3 basis vectors.

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