Which of the following statements is false?
A. The parallel sides of an isosceles trapezoid are congruent.
B. Opposite sides of a parallelogram are congruent.
C. The diagonals of a rhombus are perpendicular and bisect each other.
D. The base angles of an isosceles trapezoid are congruent.

The line is:

y = 400*x + 2000

And the statements are:

The original purchase price of the computer is given by the y-intercept, which is $2,000

The change in the price of the computer is the slope, which is 400.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

Using the graph we can identify two points like:

(1, 1600) and (5, 0)

Then the slope is:

a = (0 - 1,600)/(5 - 1) = 400

And the y-intercept is 2,000, as we can see on the graph.

Then the line is:

y = 400*x + 2,000

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Relations in the options (a), (b) and (e) are the Equivalence relations as, the relations are reflexive, symmetric and transitive all.

Given, five relations as,

a) {(a, b) | a and b are the same age}

b) {(a, b) | a and b have the same parents}

c) {(a, b) | a and b share a common parent}

d) {(a, b) | a and b have met}

e) {(a, b) | a and b speak a common language}

we have to find which of them are equivalence relations

a) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.

So, R = {(a, b) | a and b are the same age} is an equivalence relation.

b) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.

So, R = {(a, b) | a and b have the same parents} is an equivalence relation.

c) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.

So, R = {(a, b) | a and b share a common parent} is not an equivalence relation.

d) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.

So, R = {(a, b) | a and b have met} is not an equivalence relation.

e) as, (a , a) ∈ R ∀ a hence, Reflexive.

also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.

and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.

So, R = {(a, b) | a and b speak a common language} is an equivalence relation.

Hence, the relations in options (a) , (b) and (e) are the equivalence relations.

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Answer:

C: 1/2

Step-by-step explanation:

Use the slope formula

Answer:1/2

Step-by-step explanation:

1__1/_2__6

The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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Answer:

you multiply through parenthesis

Step-by-step explanation:

ex.

3(3x+4)=48

9x+12=48

-12. -12

9x=36

9x/9. 36/9

x=4

I think this is what you are asking but I'm not for sure

Answer:

yes

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

1/2=.5 and .5x10=5, 5+3=8 so that proves it is correct.

Answer:

P = 56.562

Step-by-step explanation:

Perimeter of a semicircle:

P = πr + 2r

Given:

r = 11

Work:

P = πr + 2r

P = 3.142(11) + 2(11)

P = 34.562 + 22

P = 56.562

Answer:

1.429 lbs per dollar of sugar

Step-by-step explanation:

multiply by 5 get 10 lbs of sugar for 7 dollars divide by 7 get 1.4285 round up

Based on the cost of two pounds of sugar, we can calculate the quantity of sugar to a dollar to be 0.7 pounds.

You can find out the quantity of sugar you get per dollar using the formula:

= Price of sugar / Number of pounds

Solving gives

= 1.40 / 2

= 0.7 pounds

In conclusion, you get 0.7 pounds.

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Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

\(x_1 = -4, x_2 = 5, x_3 = 12\)

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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The value of y' by implicit differentiation, the value of y is \(y = \sqrt{5x +c}\)

We differentiate each side of an equation with two variables by taking one as a variable and the rest are constant.

Given

The function is \(y^2 + 5 = 5x\)

where x and y are variables..

On differentiating the equation, we have;

\(2yy' + 0 = 5\)

on simplifying, we have

2yy' = 5

Now solve the equation explicitly for y and differentiate to get y' in terms of x.

2yy' = 5

Separate the variables

\(y^2 = 5x + c\)

Taking square root on both the side

\(y = \sqrt{5x +c}\)

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Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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Given that

The cost of 1 m ribbon = Rs.75

The cost of 7/5 m ribbon

→ (7/5)×75

→ (7×75)/5

→7×15

→₹ 105

The cost of 7/5 m ribbon is ₹105.

Answer:

33.33%

Step-by-step explanation:

Decrease in price= Original price -- New price

= $6 - $4

= $2

Percentage decrease= $2÷$6 × 100

= 33.33%

The volume of the cone is 314cm³

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.

The volume of the cone is 1/3πr²h

h²= 13²-5²

h = √169 - 25

h = √144

h = 12 cm

V = 1/3πr²h

V = 1/3 ×3.14 × 5² × 12

V = 942/3

V = 314 cm³

therefore the volume of the cone is 314cm³

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The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Explanation

Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or normal distribution, in a set of data.

There are two main things that make a distribution skewed left: The mean is to the left of the peak. This is the main definition behind “skewness”, which is technically a measure of the distribution of values around the mean. The tail is longer on the left.

A "skewed right" distribution is one in which the tail is on the right side. A "skewed left" distribution is one in which the tail is on the left side. The above histogram is for a distribution that is skewed right.

From the given question

Part B

Since the answer to part A is option C

We can infer from the definition above that the tail is on the right-hand side

Therefore, It is Right-Skewed.

The area of​ RSTU is 144 cm² which is equal to the area of JKLM.

The area of the square is defined as the product of the length and width.

Given square JKLM and t(-6,4) t (1,5)

We have to determine the area of​ RSTU.

The given translation doesn't change the shape or dimensions, therefore the area will remain the same.

Here Side of (JKLM)​ = Side of RSTU

So the area of​ RSTU = the area of​ JKLM

The area of​ RSTU = (length of JM)²

The area of​ RSTU = (12cm)²

The area of​ RSTU = 144 cm²

Thus, the area of​ RSTU is 144 cm² which is equal to the area of JKLM.

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The question seems to be incomplete the correct question has been attached in file

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Answer:

12i

Step-by-step explanation:

sqrt(-1) = i, sqrt(144) = 12

Answer: C or

41*67/2=1373.5

Step-by-step explanation:

Hi

(i) The exponential growth model to predict the number of rabbits after 'x' years is \(A = 2e^{6.21460809842x}\).

(ii) The number of rabbits at the end of 3 years will be 250000000.

A continuous exponential growth function is of the form \(A = Pe^{rt}\), where A is the final amount, which was initially P, growing continuously at the rate of r, after a time of t years.

In the question, we are asked to construct an exponential model to predict the number of rabbits after 'x' years.

We assume the exponential growth model to be a continuous model, of the form \(A = Pe^{rt}\), where A is the final amount of rabbits, which was initially P, growing continuously at the rate of r, after a time of t years.

The initial quantity of rabbits, P = 2.

Time, t = x years.

Substituting the values, we get:

\(A = 2e^{rx}\) ... (i)

We have been told that after 1 year, the number of rabbits was 1000.

Thus, substituting A = 1000, and x = 1, we get:

\(1000 = 2e^{r*1}\\\Rightarrow 1000 = 2e^r\\\Rightarrow e^r = 1000/2 = 500\)

Taking log on both sides, we get:

\(log_ee^r = log_e500\\\Rightarrow rlog_ee = log_e500\\\Rightarrow r = 6.21460809842\)

Thus, the rate of growth, r = 6.21460809842.

Substituting r = 6.21460809842 in (i), we get:

\(A = 2e^{6.21460809842x}\), which is the required model.

To find the number of rabbits at the end of 3 years, we put x = 3, in the above equation to get:

\(A = 2e^{6.21460809842*3}\\\Rightarrow A = 2e^{18.6438242953}\\\Rightarrow A = 2*125000000\\\Rightarrow A =250000000\)

Thus, there would be 250000000 rabbits at the end of 3 years.

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12m³ is your answer

Answer:

Given:

length[l]=2m

breadth or width [b]=6m

height [h]=1/2 l=1/2×2=1m

it seems that it is a cuboid

we have

volume of cuboid =l×b×h=2×1×6=12m³

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

What is banquet?

A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.

To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.

Let's define the variables:

Let x be the number of adult guests.

Let y be the number of student guests.

Now, let's write the system of inequalities representing the constraints of the situation:

The total number of guests cannot exceed 125: x + y ≤ 125

The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375

To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.

The boundary lines of each inequality are:

x + y = 125 (the line that connects the points (0, 125) and (125, 0))

45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))

To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.

The resulting graph should look like this:

The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

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Answer:

40

Step-by-step explanation:

-5 * (-8) = 40

Answer:

40

Step-by-step explanation:

Because multiplication of subtract will be added

A significant number of accidents are caused by vehicle equipment failure such as the following except Operative lights.

Operative lights are also called Surgical lights which are medical equipment devices used to illuminate the operating field during surgery.

Surgical lights are referred to by many names: Operating lights, OR lights, operating room lights, surgical lamps, and surgical light heads.

The primary function of surgical lighting is to illuminate the operative site on and/or within a patient for ideal visualization by OR staff during a surgical procedure.

With proper lighting, operating room staff can achieve a higher level of efficacy during surgery and reduce the risk of complications.

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The ways to pack are

This is further explained below.

Generally, The science, art, and technology of packaging involves confining or safeguarding goods for distribution, storage, sale, and usage. The process of creating, analyzing, and designing packages is sometimes referred to as packaging.

In conclusion,

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The tree grew about 3.83 inches between the first and third week.

An equation is an expression that shows the relationship between two or more numbers and variables.

On the first week, the tree was 27 1/2 inches (27.5) tall. On the second week, it was 29 1/4 inches (29.25) tall. On the third week, it was 31 1/3 inches (31.33) tall.

The length grown = 31.33 - 17.5 = 3.83 inches

The tree grew about 3.83 inches between the first and third week.

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Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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