complete the following table , what’s C, AC, BC

The surface area of the prism for the given dimensions is equal to option B. 180 square centimeters.

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

In a Triangle ,

Base = 12cm

height = 5cm

Area of the triangle = ( 1/2 ) × base × height

                                 = (1/2)× 12 × 5

                                 = 30 cm²

Length of rectangle 1 = 12cm

Width of rectangle 1 = 4cm

Area of rectangle 1 = 12 × 4

                                = 48 cm²

Length of rectangle2= 13cm

Width of rectangle 2 = 4cm

Area of rectangle 2= 13 × 4

                                = 52 cm²

Length of rectangle 3 = 5cm

Width of rectangle 3 = 4cm

Area of rectangle 3 = 5 × 4

                                = 20 cm²

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

Substitute the values of the area we have,

⇒ Surface area of the prism  = 2(30 ) + 48 + 52 + 20

⇒ Surface area of the prism  =  180 square centimeters

Therefore, the surface area of the prism is equal to option B. 180 square centimeters.

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Answer:

The series ∑6n=1 3n is a sum of the first 6 terms of the sequence 3n, which starts with n = 1 and increases by 3 for each successive term. Therefore, the first 6 terms of the sequence are:

3(1), 3(2), 3(3), 3(4), 3(5), 3(6)

which simplify to:

3, 6, 9, 12, 15, 18

The sum of these terms is:

∑6n=1 3n = 3 + 6 + 9 + 12 + 15 + 18 = 63

Therefore, S6, the sum of the first 6 terms of the series, is 63.

Answer:

The given sequence is decreasing by a factor of 2 each time, so each term is half of the previous term.

We can write the nth term of the sequence as:

a_n = a_1 * (1/2)^(n-1)

where a_1 is the first term of the sequence (12 in this case) and n is the position of the term we want to find.

For example, to find the 4th term of the sequence, we would have:

a_4 = 12 * (1/2)^(4-1)

= 12 * (1/2)^3

= 12 * 1/8

= 1.5

Therefore, the formula for the nth term of the sequence 12, 6, 3, ... is:

a_n = 12 * (1/2)^(n-1)

The question about a particular animal that could NOT be answered using only the data collected from the tracking collars would be do the movement patterns of the animal vary according to the weather? That is option C.

A tracking collars is a neck device that usually has a GPS device attached to it which is used by biologists to track the movement of animals that are under study.

The functions of the tracking collars include the following:

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Complete question:

Biologists often attach tracking collars to wild animals. For each animal, the following geolocation data is collected at frequent intervals.

The time

The date

The location of the animal

Which of the following questions about a particular animal could NOT be answered using only the data collected from the tracking collars?

A. Approximately how many miles did the animal travel in one week?

B. Does the animal travel in groups with other tracked animals?

C. Do the movement patterns of the animal vary according to the weather?

D. In what geographic locations does the animal typically travel?

C. Do the movement patterns of the animal vary according to the weather?

If Group of students conducted an investigation to learn about "pea-plants", then the "independent-variable" is  "Water-per-day (mL)".

The "Independent-Variable" is defined as a variable which is controlled by the researcher.

In the investigation of the "pea-plants", the amount of water per day (mL) given to the plants is the independent variable because it is the variable that is intentionally varied by the students.

The students are manipulating the amount of water given to each plant to observe the effect it has on the height of the plant after two weeks.

By controlling the amount of water given to each plant, the students can determine whether there is a relationship between water intake and plant growth.

Therefore, water given to plants per-day will be the "independent-variable".

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The given question is incomplete, the complete question is

Group of students conduct an investigation to learn more about pea plants. Their data are summarized below.

Plant      Water per day (mL)        Height after 2 weeks (cm)

  1                     20                                          11

 2                     50                                          18

 3                    100                                         24

 4                     20                                          16

Which is the independent variable in the investigation?

Using Tia's box method, the multiplication of the polynomials (x + 2)(x² -3x + 5) in the standard form is  x³ - x² - x + 10

Here, we need to multiply the polynomials (x + 2)(x² -3x + 5)

Tia's stargergy for multiplying polynomials is to make a box that fits the two factors.

Using Tia's box method,

          x²          -3x            +5

x         x³           -3x²          +5x

+2     +2x²         -6x           +10

Consider (x + 2)(x² -3x + 5)

= (x . x²) - (x . 3x) + (x . 5) + (2x²) -(2 × 3x) + (2 × 5)

= x³ - 3x² + 5x + 2x² - 6x + 10

= x³ - 3x² + 2x² + 5x - 6x + 10

= x³ - x² - x + 10

This is the required polynomial.

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Find the complete question below.

The coordinates best represent the vertex of the graph is given by (1, -2).

Hence the correct option is (D).

Graph is a pictorial representation of a curve or a function or a relation.

From the given graph we can see that the curve is an upward parabola which has vertex at a point other than origin.

We can see that where the vertex is formed the value along X axis is 1 and the value along Y axis is -2 (towards down).

So the vertex of the given graph is at (1, -2).  

Hence the correct option will be (D).

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Answer:

69

Step-by-step explanation:

(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)

x - 28 = 41

x = 69

(i)  [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

[tex]\lim_{x \to 0}[/tex] h(x) = h(0)

[tex]\lim_{x \to 0}[/tex] x cos x/sin λx = 1/7

[tex]\lim_{x \to 0}[/tex] cos x.[tex]\lim_{x \to 0}[/tex] 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

Step-by-step explanation:

To answer this question, we need to know the dimensions of the rectangle and the triangle. Assuming that the triangle is right-angled and has one side coinciding with one side of the rectangle, we can use the formula for the area of a triangle: \ ( \frac {1} {2} \) × base × height1. The base and height of the triangle are the same as the length and width of the rectangle. The area of the rectangle is length × width. The probability that a point chosen randomly inside the rectangle is in the triangle is then the ratio of the area of the triangle to that of the rectangle, which is: \ ( \frac {\frac {1} {2} \times length \times width} {length \times width} \) = \ ( \frac {1} {2} \). So, the probability is 0.5 or 50% to the nearest hundredth2.

Answer:    C  .08

Step-by-step explanation:

Probability is the part out of the whole.  you first need to find the part, which is the triangle

In other words find out how much of the triangle is taking up the rectangle, which is done through area

A(triangle)=1/2 b h      where b=6   h=9

A(triangle)=1/2 (6)(9) = 27

A(rectangle)= Lw      where L=24    h=15

A(rectangle)= (24)(15) = 360

P(triangle in rectangle)= 27/360

=.075   rounded = .08

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:1/4, 25%

Step-by-step explanation:

even number: 2,4,6

odd umber 1,3,5

even number probability when 1 dice is rolled: 3/6 = 1/2

2 dice is rolled: 1/2*1.2 = 1/4 = 25%

The average rate of decrease of the area as the length goes from 13 cm to 16 cm is given as follows:

D) 11 and 1/3 cm² per cm.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

From the graph, the parameters are given as follows:

Hence the rate is approximated as follows:

r = (24 - 60)/(16 - 13)

r = -12 cm² per cm.

Which is closest to option D.

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I answered this on Khan Academy and my lawyer above me has the papers for the work.

See u in court...

Answer:

Here is a Venn diagram that illustrates the information:

```

           ___________

          |           |

          |    N      |

          |_____  ____|

          |\    ||    /|

          | \   ||   / |

          |  \  ||  /  |

          |   \ || /   |

          |  C \||/ T  |

          |_____\v/____|

              A

```

In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.

Using the Venn diagram, we can find the number of students who read:

a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.

b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.

c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.

Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.

Based on the graph, there is no association because the distribution of preferred transportation differs among the age groups. The Option C is correct.

The significant factors is accessibility and convenience because younger individuals may be more likely to use public transportation such as buses or trains because it is more affordable and convenient than owning a car.

But the older individuals may prefer to use personal cars because it provides more flexibility and control over their transportation needs. Another factor that influences is the cost of ownership, maintenance, and fuel.

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The values for the cosine and cotangent functions for the angle x is

O cos0 = -√2/2, cot0 =-1

Let the angle be x

given that the point [ -√2/2, √2/2] is on the terminal ray of angle x

the x-coordinate of the point is -√2/2 and this is the cos hence

cos x = -√2/2.

To find the cotangent

the y coordinate is the sin therefore sin x = √2/2

tan x = sin x / cosx = (√2/2) / (-√2/2) = -1

and cotangent is the reciprocal of the tangent

cot x = 1 / tan x = -1/1 = -1.

cos x = -√2/2 and cot x = -1.

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The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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The solutions to the function y = -x^2 - 8x + 8 are (-8.9, 0) and (0.9, 0)

From the question, we have the following parameters that can be used in our computation:

y = -x^2 - 8x + 8

To solve using a graphing calculator, we enter the equation in a graph and write out the solution

Having said that we have

When y = -x^2 - 8x + 8 is plotted, the soluton is (-8.9, 0) and (0.9, 0)

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Answer:

The artist used 1680 colored squares of glass.

The simplification of the fractions given above through multiplication would be;

1.) 9 11/12

2.) 11 19/40

For question 1.)

2 5/6 × 3 2/4

Change the mixed fraction to single fraction;

= 17/6 × 14/4

= 17/6 × 7/2

= 119/12

= 9 11/12

For question 2.)

5 2/5 × 2 1/8

= 27/5 × 17/8

= 459/40

= 11 19/40

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Answer:

To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:

miles per gallon = distance traveled / amount of gas used

distance traveled = 456 miles

amount of gas used = 12 gallons

miles per gallon = 456 miles / 12 gallons

miles per gallon = 38 miles/gallon

Therefore, Jodi's car traveled 38 miles per gallon of gas.

Answer:

38 miles

Step-by-step explanation:

Set up your division: 456 / 12

456 divided by 12 is 38

So, Jodi's car travels at 38 miles per gallon of gas.

The length of cable in the coil that weighs 5 1/2 kilograms is 1/2 meter.

Let x be the length of cable in meters that weighs 5 1/2 kilograms.

Then, we can write:

1 meter / (75/1000) kilograms = x meters / 5.5 kilograms

Simplifying the left side, we get:

1 meter / (75/1000) kilograms = 1000 / 75 meters/kilogram

= 40/3 meters/kilogram

Substituting this into our proportion, we get:

40/3 meters/kilogram * x meters = 5.5 kilograms

Multiplying both sides by 3/40, we get:

x meters = (5.5 kilograms) * (3/40) * (40/3 meters/kilogram)

               = 1/2 meter

The length is 1/2 meter

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Answer:

a

Step-by-step explanation:

Answer:

she can divide the amount of cookies to friends

Step-by-step explanation:

120/5= 24

Answer:

The probability that the number chosen is not even = 4/8

Answer:

Pre-algebra is a fundamental branch of mathematics that deals with basic arithmetic operations, such as addition, subtraction, multiplication, and division, and introduces concepts like variables, equations, and inequalities. Here are some general steps to solve pre-algebra problems:

1. Identify the problem: Read the problem carefully and identify what it is asking you to do. Identify the key information and any variables that are given.

2. Translate the problem: Translate the problem into an equation or inequality, using variables to represent unknown quantities.

3. Solve the equation or inequality: Use algebraic manipulation to solve for the variable. Follow the order of operations and simplify the expression as much as possible.

4. Check your answer: Verify that your solution is correct by plugging it back into the original equation or inequality and making sure that it satisfies the conditions of the problem.

It's important to practice pre-algebra problems regularly to develop your problem-solving skills. You can find practice problems and tutorials online or in textbooks, and you can work with a tutor or teacher to get additional help. Remember to stay patient, focused, and positive, and don't be afraid to ask for help if you need it.

The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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Answer:

AB = (20/√2)(√2/√2) = 10√2