8.2 end of unit assessment Triangle ABC and DEF are similar

Answer:

t/7

Step-by-step explanation:

Since the ratio between the amount of water and the time should be the same, 84/12 = 7.

Hence, the ratio is t/7.

Hope this helped!

Answer:

x > 6

Step-by-step explanation:

\(x + 3 - 5 > 4 \\ \\ x - 2 > 4 \\ \\ x > 4 + 2 \\ \\ x > 6 \\ \)

At least 5 expected observations in each cell in order to apply the chi-square test of independence, we prefer to have at least 5 expected observations in each cell. The correct answer is c.

The chi-square test of independence is a statistical method used to determine whether two categorical variables are independent or associated with each other.

To apply this test, it is preferred to have at least 5 expected observations in each cell of the contingency table. The expected frequency is calculated based on the assumption of independence between the two variables.

If the expected frequency is less than 5 in any cell, the chi-square test may not be valid and alternative methods, such as Fisher's exact test, should be considered. Having a sufficient sample size can also improve the accuracy and reliability of the test results.

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Answer:

15) 30°

16) 49.5°

Step-by-step explanation:

15) We solve using the Trigonometric function of Sine

sin θ = Opposite/Hypotenuse

Opposite = 12

Hypotenuse = 24

sinθ = 12/24

θ = arc sin(12/24)

= 30°

Approximately = 30°

16)We solve using the Trigonometric function of Cosine

cos θ = Adjacent/Hypotenuse

Adjacent = 13

Hypotenuse = 20

cos θ = 13/20

θ = arc cos (13/20)

= 49.458398126°

Approximately = 49.5°

The sum of the multiplicities of the roots in a polynomial equation is equal to the degree of the polynomial (the highest power of the variable in the equation).

This is known as the Fundamental Theorem of Algebra. The multiplicity of a root is the number of times a root appears in a polynomial equation, and it can be a whole number, a fraction, or even an irrational number.

For example, if the polynomial equation is x³ + 2x² + 4x - 8 = 0, then the degree of the polynomial is 3 and the multiplicities of the roots are 1, 2, and 1, respectively.

Therefore, the sum of the multiplicities of the roots in this equation is 3. This is true for any polynomial equation: the sum of the multiplicities of the roots will always be equal to the degree of the polynomial.

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Hello!

We have the equation 2x² +5x -63 = 0

First, let's find the coefficients a, b and c as ax² +bx +c = 0:

• a = 2

• b = 5

• c = -63

Now, we will use the formula below to solve this equation:

Let's replace the coefficients with the values that we already found:

Now, let's divide it into two solutions, look:

Right answer: C) -7 is a solution.

To find the market equilibrium price and quantity, we need to set the supply and demand equations equal to each other.

The supply equation is Ps = 3Qs + 3, where Ps represents the price for suppliers and Qs represents the quantity supplied.

The demand equation is Pd = -6Qd + 30, where Pd represents the price for consumers and Qd represents the quantity demanded.

After the subsidy of $9 is given to rubber band consumers, the new demand equation becomes Pd = -6Qd + 21, as the subsidy decreases the price for consumers by $9.

a. To find the market equilibrium price, we set Ps equal to Pd:
3Qs + 3 = -6Qd + 21

b. To find the market equilibrium quantity, we solve for Qs or Qd:
3Qs + 3 = -6(3Qs + 21) + 21
Simplifying, we get 3Qs + 3 = -18Qs - 123
Combining like terms, we have 21Qs = -120
Dividing by 21, we find Qs = -120/21
Qs ≈ -5.71

Since the quantity cannot be negative, we round Qs down to zero.
Qs = 0

c. To find the consumer surplus, we need to find the area below the demand curve and above the equilibrium price. Since the equilibrium price is the same as the price with the subsidy, we can calculate the consumer surplus by finding the area of a triangle:
Consumer Surplus = (1/2) * (Equilibrium Quantity) * (Subsidy)
Consumer Surplus = (1/2) * (Qd) * (9)
Plugging in Qd = 0 (from part b), we get Consumer Surplus = 0.

d. To find the producer surplus, we need to find the area above the supply curve and below the equilibrium price. Since the equilibrium price is the same as the price with the subsidy, we can calculate the producer surplus by finding the area of a triangle:
Producer Surplus = (1/2) * (Equilibrium Quantity) * (Subsidy)
Producer Surplus = (1/2) * (Qs) * (9)
Plugging in Qs = 0 (from part b), we get Producer Surplus = 0.

e. The deadweight loss represents the loss of economic efficiency due to the subsidy. It can be calculated as the difference between the total surplus without the subsidy and the total surplus with the subsidy. In this case, since both the consumer surplus and producer surplus are zero, the deadweight loss is also zero.

f. The government expenditure is the total amount of money the government spends on the subsidy. In this case, the subsidy is $9, and since the quantity supplied is zero, the government expenditure is also zero.

g. The total surplus is the sum of the consumer surplus and the producer surplus. In this case, since both the consumer surplus and producer surplus are zero, the total surplus is also zero.

h. To draw and label a graph for this market, we need to plot the supply and demand curves. The supply curve is Ps = 3Qs + 3, and the demand curve is Pd = -6Qd + 21. The equilibrium price is the point where the supply and demand curves intersect. In this case, the equilibrium price is $3 and the equilibrium quantity is zero.

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Answer:

We can use algebra to find the two consecutive even integers whose product is 168.

Let's call the first even integer x. Since it is consecutive to another even integer, the next one will be x+2. The product of these two integers is:

x * (x+2) = 168

We can solve for x by simplifying the equation:

x^2 + 2x = 168

x^2 + 2x - 168 = 0

We can factor the left side of the equation:

(x-14)(x+12) = 0

So the two solutions for x are -12 and 14.

The negative integers are -12 and -14.

The two integers that multiply to give 168 are -12 and -14, but keep in mind that they are not consecutive integers.

Answer:

t+12

Step-by-step explanation:

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Answer:

t+12

Step-by-step explanation:

12 meters longer means that you're adding meters onto the throw. Hope that helps :)

Answer:

b

Step-by-step explanation:

Answer:

1) 25deg. Angle EGF

2) 25deg. Angle BGC

3) Angle 2 and BGC or Angle 1 and EGF

Answer:

Step-by-step explanation:

when  1/2 inch equals 4 feet the room is  2.25 inches, then

2 1/4 = 8/4 + 1/4  = 9/4

9/4 inches is the scale distance of the room

each 1/2 inch is 4 feet so divide  9/4 by 1/2 then multiply that by 4 to find the distance of the room

9/4 ÷ 1/2  = 9/4

9/4 * 2/1 = 18/4

18/4 = 9/2

9/2 * 4 feet = 9/2 * 4/1

9/2 * 4/1 = 36/2

36/2=18

the room is 18 feet across

then if the scale is 2/3 of an inch is  4 feet , then

2/3 * 9/4 = 18/12

18/12 = 3 inches  is the scale size of Quinto's room

From the information, the correct value that expresses the division will be 300 ÷ 75 = R

From the information given, the thing to do is simply to use the number in the box to divide the number beside it and get the information.

This will be:

= 3000 ÷ 75 = 40

= 300 ÷ 75 = 4

Therefore, the expression is 300 ÷ 75 = R.

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Answer:

f(x)=x²-2

x=0 y=-2

x=1 y=-1

x=1.414 y=-0.000604

x=2 y=2

x=3 y=7

Step-by-step explanation:

The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

I hope you have your answer now I'm glad to help

Answer:

The answer is Bottom Left

The area of the union, denoted as U, formed by all the disks in the plane that touch the line segment AB, where AB has a length of 1, is equal to π/4.

To find the area of the union of all disks in the plane that touch AB, we can consider the extreme cases where the disks are tangent to AB.

Let's assume a disk is centered at a point C on AB. The radius of this disk will be denoted by r.

Case 1: The disk touches AB externally

In this case, the distance from the center of the disk to AB is r. Therefore, the diameter of the disk (2r) is equal to the length of AB, which is 1. Hence, r = 1/2.

Case 2: The disk touches AB internally

In this case, the distance from the center of the disk to AB is 0. The radius (r) of the disk will be equal to the distance between the center of the disk and one of the endpoints of AB (A or B). Therefore, r = 0.

Now, let's consider all possible positions for the centers of these disks.

If the center of the disk is located outside the line segment AB, it will fall into Case 1. If the center is located on AB itself, it will fall into Case 2.

The set U, which represents the union of all such disks, will consist of two disks:

1. The disk with radius 1/2 and centered at the midpoint of AB.

2. The disk with radius 0 and centered at any point on AB.

The area of the disk with radius 1/2 is given by π(1/2)^2 = π/4.

The area of the disk with radius 0 is 0, as it degenerates into a single point. Therefore, the total area of U is π/4.

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The complete question is:

A plane contains points A and B with AB=1. Let U be the union of all disks of radius in the plane that touch AB. What is the area of U?

The total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.20.

To calculate the total cost, we need to determine the cost of each type of binder clip separately and then sum them up.

The cost of medium binder clips is $5 per pound, and Kayla purchased 0.1 pounds. Therefore, the cost of medium binder clips is 0.1 pounds * $5 per pound = $0.50.

The cost of jumbo binder clips is $6 per pound, and Kayla purchased 0.2 pounds. Thus, the cost of jumbo binder clips is 0.2 pounds * $6 per pound = $1.20.

Finally, to find the total cost, we add the individual costs together: $0.50 + $1.20 = $1.70.

Therefore, the total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.70.

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(a) The surface area of the paraboloid z = x² + y², cut by z = 2, is 4π square units.

(b) The surface area of the football-shaped surface obtained by rotating the curve y = cos x, - π/2 ≤ x ≤ π/2, around the x-axis is 4π square units.

(a) To find the surface area of the paraboloid z = x² + y² cut by z = 2, we need to determine the intersection curve between the paraboloid and the plane z = 2. Substituting z = 2 into the equation of the paraboloid, we obtain x² + y² = 2. This represents a circle in the xy-plane with radius √2. The surface area of the paraboloid within this circle can be found by integrating the circumference of the circle multiplied by the height of the paraboloid. The circumference of the circle is 2π√2, and the height of the paraboloid is the difference between the maximum z-value (2) and the minimum z-value (0) within the circle, which is 2. Therefore, the surface area is given by 2π√2 * 2 = 4π square units.

(b) For the football-shaped surface obtained by rotating the curve y = cos x, - π/2 ≤ x ≤ π/2, around the x-axis, we can use the formula for the surface area of a surface of revolution. This formula states that the surface area is equal to the integral of 2πy multiplied by the arc length of the curve. The curve y = cos x within the given range represents the upper and lower halves of the football shape. The arc length of the curve can be calculated using the arc length formula. After performing the necessary calculations, the result is a surface area of 4π square units.

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please see photo attached

Answer:

20

Step-by-step explanation:

Make 12 into a fraction : 12/1

Then , using division with fractions , flip the 3/5 and multiply 12/1 and 5/3 .

The equation will look like this :

12/1 x 5/3

So 12 x 5 = 60 and 1 x 3 = 3 , making the fraction 60/3

That then simplifies to 20

:)

Dependent variable: mood rating;

independent variable: dog petting or couch sitting.

In the given experiment, there are two variables being observed: the independent variable and the dependent variable. The independent variable is the act of petting a live dog or sitting quietly on a couch for 15 minutes.

This variable is experimentally controlled and altered to test its impact on the dependent variable. The researcher changes or controls the independent variable to see how it affects the dependent variable in the experiment. On the other hand, the dependent variable is the participants' rating of their mood on a 10-point scale. It is often referred to as the outcome variable and is the variable being measured in an experiment. The dependent variable is affected by the independent variable, and in this scenario, the mood of the 50 people is the dependent variable. The clinical psychologist measures the outcome or result, which is the mood of the participants, making it the dependent variable.

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Explanation:

We need to divide both sides by -2 to fully isolate x.

Dividing both sides by a negative number will flip the inequality sign

We go from -6 < -2x to 3 > x

Then we flip 3 > x to x < 3 which is choice C

-----------------

A slightly longer approach:

-6 < -2x

-6+2x < 0 .... add 2x to both sides

2x < 6 .... add 6 to both sides

2x/2 < 6/2 .... divide both sides by 2

x < 3

We get the same answer as the previous section. It helps show why the sign flip happened when dividing both sides by a negative number.

Answer:

28x

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Hope it helps!

the advantages of being paid salary is u get it even if u work 1 hour and the disadvantage of getting paid hourly is u have to work for along time

Answer:

The answer is below

Step-by-step explanation:

Speed is the time rate of change of velocity, it is the ratio of distance to time.

Mr. Fowles runs at a steady 4.2 miles per hour. The time taken to cover 26 miles is:

speed = distance / time

time = distance / speed = 26 / 4.2 = 6.19 hour

I run at 3 miles per hour. I was given 3 mile lead, so the remaining distance is 23 miles (26 - 3). The time needed to complete the 23 miles is:

time = distance / speed = 23 / 3 = 7.67 hour

a) Let d be the distance Mr Fowles catches me. Hence:

time = (d + 3)/4.2; also time = d/3

(d + 3)/4.2 = d/3

3d + 9 = 4.2d

1.2d = 9

d = 7.5 miles

He would catch me at 10.5 (7.5 + 3) miles from the starting point.

b) Mr. fowles finishes after 6.19 hour. At that time, the distance is have covered is:

distance = 6.19 * 3 mi/hr = 18.57 mile

Distance behind = 23 mile - 18.57 = 4.43 mile

c) time longer = 7.67 hour - 6.19 hour = 1.48 hour