I need help to solve part B and give my reasoning in two collum proof.

Answer:

Toni had the highest score.

Step-by-step explanation:

Terri - 45/50 = 90%

Toni - 92%

Tina - 8/9 = 89%

Answer:

13

Step-by-step explanation:

[tex]\frac{91}{7}=\frac{70+21}{7}=10+3=13[/tex]

The solution of 91 divided by 7 in simplest form is,

⇒ 13

We have to given that,

To simplify 91 divided by 7 in simplest form.

It can be written as,

⇒ 91 ÷ (7)

⇒ 91 / 7

⇒ 13

Therefore, The solution of 91 divided by 7 in simplest form is,

⇒ 13

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To determine the number for a unit value the unitary method is used.

The number of quizzes Kathleen will take in 7 weeks is 35.

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

Given that,

Total number of quizzes in 4 weeks = 20

Total number of weeks the school is attended = 7

In order to find total number of quizzes in 7 weeks, apply unitary method to find the number of quizzes per week and then multiply it by 7 as follows,

Since, total number of quizzes in 4 weeks is  20

The number of quizzes in 1 week is 20 / 4 = 5.

Thus, the number of quizzes in 7 weeks is 5 × 7 = 35.

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Given:

13 is the final answer.

The functions have the same x-intercept and the same end behaviour as x approaches infinity.

We are given two functions, f(x) and g(x). A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.

The function f(x) is represented in the graph. The function g(x) is represented by the data in the table. We have to find the correct comparison between the two functions.

The comparison is to be done on the basis of the lengths of the x-intercept and y-intercept and the end behaviour of both functions. From the given values, we conclude that the x-intercepts for both functions are the same, but the y-intercepts are different. The end behaviour of both functions becomes similar as x approaches infinity.

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We are given an inequality proble. Our approach is to test our options.

We begin with the second option.

We'll solve it in parts and compare to our number line

The range of x is therefore: a < x < 10 + a

SECOND OPTION

The value of arccos(-√3/2) is 5π/6.

In the given question,

We have to find the value of [tex]arccos(-\frac{\sqrt{3}}{2})[/tex].

The given term is [tex]arccos(-\frac{\sqrt{3}}{2})[/tex].

We using the quadrant rule.

The value is in negative so we check in which quadrant the value of cos negative.

As we now that in second quadrant only the value of sine and cosine is positive and all value are negative.

The second quadrant of 180 degree or we can also write 180 degree as π.

From the trigonometry table we know that at 30 degree or (π/6) the value of cos is √3/2.

So the value of cos at which -√3/2 is

-√3/2 = cos(π - π/6)

-√3/2 = cos(π×6/6 - π/6)

-√3/2 = cos(6π/6 - π/6)

-√3/2 = cos{(6π- π)/6}

-√3/2 = cos 5π/6

So we can write it as

arccos(-√3/2)=arccos(cos 5π/6)

Since there is a arccos and cos both so only left 5π/6.

arccos(-√3/2)=5π/6

Hence, the value of arccos(-√3/2) is 5π/6.

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Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

The bisector forms peripendicular (90) angles VZW and WZY. It also divides the side in half so you have VZ=ZY. It seems like you wrote everything else for the question

In order to find the number of empty bins, let's calculate how many packs will be made with the given material.

240 markers can be organized in 240/8 = 30 packs

320 crayons can be organized in 320/8 = 40 packs

336 colored pencils can be organized in 336/8 = 42 packs

In total we have 30 + 40 + 42 = 112 packs

Each bin can hold 8 packs, to in order to hold 112 packs, we need 112/8 = 14 bins.

We have 24 bins. Since 14 will be used, we will have 24 - 14 = 10 empty bins.

Answer

-√214 is between -15 and -14.

Explanation

To solve this, we need to first obtain the value of the -√214

-√214 = -14.63

Hence, we can see that this number is between -15 and -14.

Hope this Helps!!!

The number of smaller cube that will fit in the larger cube is 27x¹³ considering their volumes.

The volume of a cube with length l is l × l × l = l³

From the question, we have that the length of the bigger cube is 3x^6 and that of the smaller cube is x² hence;

volume of the larger cube = (3x^6)³

volume of the larger cube = 27x^18

and,

volume of the smaller cube = (x²)³

volume of the smaller cube = x^5

We need to divide the volume of the larger cube by volume of the smaller cube to know what amount of the smaller cube that can fit in to the bigger cube.

So (27x^18)/(x^5) = 27x¹³

Therefore the number of the smaller cube to fit in to the bigger cube is derived as 27x¹³ for any real values of x.

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Answer:

It must be less than 180º.

Step-by-step explanation:

A triangle always adds up to 180º which then means that since two angles have already been stated that means the total of those two angles is 74º which you subtract from 180º to get 106º which is the measure of the third angle.

The second endpoint of ST is B(-1,12).

It is given in the question that:-

Endpoints of line segment EF are (2,-4) and (5,-9).

One of the endpoint of ST is (4,9).

We have to find the second endpoint of ST.

As both of the line segments are congruent hence, the length of each line segment will be same.

We can find the length of the line segment EF using the distance formula.

Length of the line segment EF :-

[tex]\sqrt{(-9-(-4)^2+(5-2)^2}=\sqrt{(-9+4)^2+3^2}=\sqrt{25+9}=\sqrt{34} units[/tex]

Hence, length of the line segment ST should also be the same.

We can check that from the options and get B(-1,12) as the answer.

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Answer:

9.4%

Step-by-step explanation:

To convert any given imporper fraction into a percentage, we multiply it by 100. This way, we can convert the fraction given as following:

The number of fiction books in the library is equal to 16

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given the ratio of fiction to nonfiction books in a classroom, the library is 2 to 3, and then the total ratio of both books will be 2+3 = 5. If there are 24 books non-fiction books in the library, to get the number of fiction books that are there we will follow the following steps.

First, we will calculate the total number of books in the shelf;

3/5  x Total number of books = total non fiction books

3/5 * Total number of books = 24

3*Total number of books = 5*24

3*Total number of books = 120

Total number of books = 120/3

Total number of books = 40

Therefore there are 40 total books on the shelf.

Total number of fiction books = 2/5 * 40

Total number of fiction books = 2* 8

Total number of fiction books = 16 books

Hence there are 16 fiction books on the shelf.

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The quantity of petrol used to travel 160 mile is 17.78 liters

The quantity of petrol used to travel 495 miles = 55 liters

Here we have to use the unitary method

The unitary method is defined as the method that uses to find the unit rate

The quantity of petrol used to travel 1 mile = The quantity of petrol used to travel 495 miles / 495

Substitute the values in the equation

The quantity of petrol used to travel 1 mile = 55 / 495

= 1 /9 liters

The quantity of petrol used to travel 160 mile = The quantity of petrol used to travel 1 mile × 160

Substitute the value in the equation

The quantity of petrol used to travel 160 mile  = (1 / 9) × 160

= 17.78 liters

Hence, the quantity of petrol used to travel 160 mile is 17.78 liters

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The quotient  19 4/8 divided 4 5/8  is about 3

We need to estimate the quotient .. 19 4/8 divided 4 5/8

19 4/8 ÷ 4 5/8

Converting the mixed fraction 19 4/8 into improper fraction

(19x8 + 4)/8 = 154/ 8

Converting the mixed fraction 4 5/8 into improper fraction

(4x8 + 5)/ 8 = 45/8

Dividing 154/ 8 with 45 / 8

(154/8) / (45/8)

Multiplying both numerator and denominator with 8

154 / 45

3.2 = 3 (approx)

Therefore,  the quotient .. 19 4/8 divided 4 5/8  is about 3

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6.8

1) Let's calculate this product by distributing the factor -2 multiplying the number within the parentheses.

-2(-3.4) Equal signs yield positive and remove the parentheses

6.8

2) So 6.8 is the answer for that product.

Okay, here we have this:

Considering the provided equation of the parabola, we are going to find the requested domain and range, so we obtain the following:

Domain: Corresponds to all the values that x can take in the function. Given that in this case no value of x indeterminates the function, and that x can take any value, then its domain will be: (-∞, ∞).

Range: Corresponds to all the values that the dependent variable can take. In this case, since it is a parabola of the form ax^2+bx+c, and that a is less than or greater than 0, its range will be all values greater than or equal to its y-coordinate of the vertex, which for this case is (5, -15). So its range is: [-15, ∞).

Therefore finally we obtain that the correct answer is the fourth option.

The angle between the ropes is 53°.

We are given that a barge is being towed by two tugboats using ropes. The force vectors of the two tugboats are represented by F1 and F2. A vector is an entity that has both a magnitude and a direction. The vectors are F1 = 11000i + 5000j and F2 = 14500i + -8000j. We need to find the angle between the ropes. The best method is to find the dot product. Let the angle between the ropes be θ. We can say that cos(θ) = F1.F2/(|F1|*|F2|) = (11000*14500 + 5000*-8000)/[√[(11000)² + (5000)²] * √[(14500)² + (-8000)²]] = (11*14.5 + 5*-8)/[√[(11)² + (5)²] * √[(14.5)² + (-8)²]] = 119.5/[√146*√274.25] = 119.5/200.1 = 0.597. So, the value of θ is 53°.

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I'll get the slope of the arrow on the graph

P1 = (-1, 1)

P2 = (-4, 3)

slope = m = (3 - 1) / (-4 + 1)

m = 2/-3

slope = m = -2/3

The cost of Goods Sold will be $93.5

What is Addition?

A process of combining two or more numbers is called addition.

Given that;

The Cost of Goods Sold for one Holiday Basket:

1 basket = $24.00 per dozen

2 lbs. Cheddar cheese = $1.50 per pound

1 canned ham = $60.00 per dozen

3 jars of jelly = $1.00 each

6 oranges = $2.00 per dozen

1 box crackers = 2.00 per box

Cellophane wrap = $.50 each

Now,

Since, Each basket has only one of each item in it.

So, The total cost = $24 + $1.50 x 2 + $60 + $1 x 3 + $1 + $2 + $0.50

                           = $93.5

Thus, The cost of Goods Sold will be $93.5

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The proof for the congruence of angles 3 and 4 is given by the image presented at the end of the answer.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, that is, having the same angle measure.

The vertical angles in this problem are listed as follows:

The transitive property of congruence defines that:

If two angles are congruent to a third angle, then the two angles are also congruent between themselves.

Hence the angles that are congruent based on the transitive property of congruence are given as follows:

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First, we need to calculate the volume of the package and the volume of the box

Package

Box

we need to subtract the volume of the package from the volume of the box

159 in^3 of packing peanuts will fill into the box

In order to determine if the ball reaches the 24 ft, replace h = 24 and solve the quadratic equation. If the solutions are real, then, the ball does reach 24ft.

Proceed as follow:

h = 16t² + 36t + 6

24 = 16t² + 36t + 6

16t² + 36t + 6 - 24 = 0

16t² + 36t - 18 = 0

use he quadratic formula, given by:

In this case, a = 16, b = 36 and c = -18

negative times do not have physical meanning, then, the available solution is

t = 0.42

Hence, you can conclude that the ball reaches 24 ft for a time of 0.42 seconds.

t + b = 38

6t + 4b = 188 is the equation to calculate the system of the restaurant .

Restaurants must foster an atmosphere of delicious food, attractive surroundings, and courteous living. In order to maintain the restaurant's financial viability, it is crucial for the owners to choose the seating arrangement, chairs, and sofas with an eye toward projecting a certain image.

The most typical categories of seating arrangement queries. There are intricate row arrangements, double rows, rectangular rows, linear rows, and circular rows.

Theatre. The simplest and most popular seating arrangement for events is the theater style setup.

n distinct things permuted (when repetition is not allowed) Repetition when it is acceptable. When the objects are not distinct, permutation (Permutation of multi sets)

The following formula determines how many permutations of n objects, taken r at a time: (n,r)! P(n,r)=n!

The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.

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Explanation

We will have to find the population density of each of the regions

To get the population density, we will have to divide the population of each region and then divide by the area of the of each region

For part A

The population density of region A is

For region B

The area of region B is

The population density of region B is

For region C

The population density of region C

Thus, we can observe that Region C has a population density lower than 60 animals per square miles

Thus, option C is correct

Part A) The definition of speed can be used to establish the equation of the line that depicts the relationship between distance and time, which is (y = 62x).

Part B) Option c

What is a speed, exactly?

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path.

Given:

In 3 hours and 186 miles, Car X goes.

To find the equation of the line that represents the relationship between distance and time, perform the following steps:

Step 1: Assume that car X traveled a total distance of y miles and traveled that amount in x minutes.

Step 2: The speed is determined by the distance to time ratio.

speed = distance / time

Step 3: Add the distance and time values to the equation above.

Speed = y/x   —— (1) (1)

Step 4 - Based on the provided information, the speed is determined by:

speed = 186/3 = 62

Step 5: Adding the speed value to the equation (1).

y/x = 62

y = 62x

(Y = 62x) is the equation of the line that depicts the relationship between space and time.

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√ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We know that ,

Trigonometric identities

sin²θ+cos²θ=1

so 1-cos²θ= sin²θ

sec²θ+tan²θ=1

1-sec²θ=tan²θ

So √ 1-cos²θ/1-sec²θ

√ 1-cos²θ/1-sec²θ=√sin²θ/tan²θ

The square root will get cancelled

=sinθ/tanθ

=sinθ/sinθ/cosθ  (because tanθ=sinθ/cosθ)

=cosθ

Hence √ 1-cos²θ/1-sec²θ=cosθ, cosθ is the simplified form of √ 1-cos²θ/1-sec²θ

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Answer:Given points are (6, -2) and (12, -2). Find the slope of the line using the formula m = (y2 - y1)/(x2 - x1) Here, y1 = -2, y2 = -2, x1 = 6 and x2 = 12

⇒ m = (-2 - -2)/(12 - 6) = 0/6 = 0

Step-by-step explanation: i hoped i helped a little :)