The point P(x, y) is on the terminal ray of angle Theta. If Theta is between Pi radians and StartFraction 3 pi Over 2 EndFraction radians and = Negative five-halves, what are the coordinates of P(x, y)?
P(Negative StartRoot 21 EndRoot, –2)
P (StartRoot 21 EndRoot, –2)
P(–2, StartRoot 21 EndRoot)
P(–2, Negative StartRoot 21 EndRoot)

Answer:

Y=2x

Step-by-step explanation:

I did the iready quiz already:)

The equation of the proportional relationship represented by the table and the graph is: y = 2x.

If m is the slope or unit rate, a proportional relationship between two variables, x and y, can be represented with an equation as, y = mx.

Let's find the equation that represents the relationship represented by the graph and the table. Let's use the graph.

m = y/x

Using the point, (2, 4),

m = 4/2 = 2

Substitute m = 2 into y = mx

y = 2x

Therefore, the equation of the proportional relationship represented by the table and the graph is: y = 2x.

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Answer:

1.

avg time = total time/ 3

for big car :-

= 4.46/ 3

= 1.48

for small car :-

= 5.14/ 3

= 1.71

2.

avg speed = total distance/ total time

for big car:-

= 2/ 4.46

= 0.45

for small car :-

= 2/ 5.14

= 0.4

Answer:

The name of the solid with 20 faces that are congruent equilateral triangles is icosahedron.

The solid you are referring to is called an icosahedron. An icosahedron is a specific type of convex polyhedron that has 20 faces. In this case, all 20 faces are congruent equilateral triangles. Option d is correct answer.

To understand why this solid is called an icosahedron, let's break down the term. "Icosa-" comes from the Greek word for twenty, while "-hedron" means face. Therefore, an icosahedron is a polyhedron with twenty faces.

Each face of an icosahedron is an equilateral triangle, meaning that all three sides of the triangle are equal in length, and all three angles are equal to 60 degrees. Since all 20 faces are congruent, they have the same side lengths and angles.

The icosahedron has a total of 12 vertices and 30 edges. The vertices are the points where three edges meet, and the edges are the line segments connecting the vertices. The icosahedron has a symmetrical and regular structure, making it one of the five Platonic solids.

An icosahedron is a convex polyhedron with 20 congruent equilateral triangle faces, 12 vertices, and 30 edges.

Option d is correct answer.

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The algebraic expression for the given statement is k-13.

The given statement is "15 less than the sum of k and 2".

We need to form the algebraic expression for the given statement.

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.

Now, the sum of k and 2=k+2

15 less than the sum of k and 2=(k+2)-15

=k+2-15

=k-13

Therefore, the algebraic expression for the given statement is k-13.

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Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

Answer:

The volume of the wood used is \(1,116\ cm^3\)

Step-by-step explanation:

The Volume of a Rectangular Cuboid

In a rectangular cuboid, all angles are right, and the opposite faces are equal.

The volume of a cuboid of dimensions a,b,c is:

V=a.b.c

The rectangular box is made of wood with externals dimensions of 25 cm by 20 cm by 15 cm.

The external volume of the box is:

\(V_e=(25)*(20)*(15)=7,500\ cm^3\)

The walls of the box are 0.5 thick each, this means that the internal dimensions are 1 cm less than the external dimensions, including the lid.

Thus the internal volume is:

\(V_i=(24)*(19)*(14)=6,384\ cm^3\)

The volume of the wood used is the difference between the external and the internal volumes:

\(V_w=7,500\ cm^3-6,384\ cm^3=1,116\ cm^3\)

The volume of the wood used is \(\mathbf{1,116\ cm^3}\)

Answer:

The cost of r rides = 2r + 10

The cost of 15 rides = $40

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

Assume that the cost of r rides is c

∵ The number of the ride is r

∴ x = r

∵ The cost of r rides is c

∴ y = c

∵ The price of admission into the park is $10 ⇒ initial amount

∴ b = 10

∵ She will have to pay $2 for every ride ⇒ rate of change

∴ m = 2

→ Substitute them in the form of the equation above

∴ c = 2r + 10

∴ The cost of r rides = 2r + 10

∵ She goes on 15 rides

∴ r = 15

→ Substitute it in the form of the equation

∵ c = 2(15) + 10

∴ c = 30 + 10

∴ c = 40

∴ The cost of 15 rides = $40

The number of bacteria after 5 hours with initial numbers 3500 increased double in each hour is equal to 112,000.

Initially number of bacteria in a culture =  3500

Total hours the number of bacteria double = Each hour

Then the growth rate is equal to  2

As the number of bacteria after each hour is twice the previous numbers.

Formula used for the number of bacteria after t hours ,

N = N₀ x 2^t

where N₀ is the initial number of bacteria.

Time in hours = t hours

And N is the number of bacteria after t hours.

After 5 hours, the number of bacteria present is equal to,

⇒N = 3500 x 2^5

⇒N = 3500 x 32

⇒N = 112,000

Therefore, number of bacteria present after 5 hours is equal to 112,000.

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A) The resulting hash table with separate chaining is as follows:

[0: (12, e) -> (9, e) -> (12, f)]

[1: (1, a) -> (4, b) -> (17, d) -> (4, g)]

[2: (2, c) -> (19, f) -> (8, c)]

B) The number of collisions that occurred is 4.

A) To construct the hash table using separate chaining with a table size of 10 and the hash function h(x) = (x + 3) % 3, we will insert the key-value pairs in the given order and handle collisions by appending new elements to the end of the linked list in each bucket.

1. (1, a):

  - Hash value: h(1) = (1 + 3) % 3 = 1

  - Insert (1, a) into bucket 1: [1: (1, a)]

2. (4, b):

  - Hash value: h(4) = (4 + 3) % 3 = 1

  - Collision occurs in bucket 1

  - Append (4, b) to the linked list in bucket 1: [1: (1, a) -> (4, b)]

3. (2, c):

  - Hash value: h(2) = (2 + 3) % 3 = 2

  - Insert (2, c) into bucket 2: [1: (1, a) -> (4, b)], [2: (2, c)]

4. (17, d):

  - Hash value: h(17) = (17 + 3) % 3 = 1

  - Collision occurs in bucket 1

  - Append (17, d) to the linked list in bucket 1: [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c)]

5. (12, e):

  - Hash value: h(12) = (12 + 3) % 3 = 0

  - Insert (12, e) into bucket 0: [0: (12, e)], [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c)]

6. (9, e):

  - Hash value: h(9) = (9 + 3) % 3 = 0

  - Collision occurs in bucket 0

  - Append (9, e) to the linked list in bucket 0: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c)]

7. (19, f):

  - Hash value: h(19) = (19 + 3) % 3 = 2

  - Insert (19, f) into bucket 2: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d)], [2: (2, c) -> (19, f)]

8. (4, g):

  - Hash value: h(4) = (4 + 3) % 3 = 1

  - Collision occurs in bucket 1

  - Append (4, g) to the linked list in bucket 1: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d) -> (4, g)], [2: (2, c) -> (19, f)]

9. (8, c):

  - Hash value: h(8) = (8 + 3) % 3 = 2

  - Collision occurs in bucket 2

  - Append (8, c) to the linked list in bucket 2: [0: (12, e) -> (9, e)], [1: (1, a) -> (4, b) -> (17, d) -> (4, g)], [2: (2, c) -> (19, f) -> (8, c)]

10. (12, f):

   - Hash value: h(12) = (12 + 3) % 3 = 0

   - Collision occurs in bucket 0

   - Append (12, f) to the linked list in bucket 0: [0: (12, e) -> (9, e) -> (12, f)], [1: (1, a) -> (4, b) -> (17, d) -> (4, g)], [2: (2, c) -> (19, f) -> (8, c)]

The resulting hash table with separate chaining is as follows:

[0: (12, e) -> (9, e) -> (12, f)]

[1: (1, a) -> (4, b) -> (17, d) -> (4, g)]

[2: (2, c) -> (19, f) -> (8, c)]

B) The number of collisions that occurred is 4.

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Answer:

1/6

Step-by-step explanation:

There are 6 faces on a die, and you can only roll one face only. So, the denominator will be 6 because there are 6 faces, and 1 as the numerator because that's the equal proportion for each face (unless you use two dice)

Answer:

78.75 or 78 3/4

Step-by-step explanation:

The correct option that indicates how Christa sliced the rectangular pyramid is the second option.

Christa sliced the pyramid perpendicular to its base through two edges.

A rectangular pyramid is a pyramid with a rectangular base and four triangular faces.

The height of the cross section indicates that the location where Christa sliced the shape is lower than the apex of the pyramid.

The trapezoid shape of the cross section of the pyramid indicates that the top and base of the cross section are parallel, indicating that Christa sliced the pyramid parallel to a side of the base of the pyramid, such that it intersects two of the edges of the pyramid

The correct option is therefore the second option;

Christa sliced the pyramid perpendicular to its base through two edges

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The answer of the given question based on perimeter of trapezoid the ratio will be  x:y is 8:5.

A trapezoid is quadrilateral with at least one pair of the parallel sides. The parallel sides are called  bases of  trapezoid, and  non-parallel sides are called legs.

Let's denote the lengths of the four sides of Trapezoid 1 as a, b, c, and d, and the lengths of the corresponding sides of Trapezoid 2 as m, n, p, and q, respectively. Then we have:

a + b + c + d = 240 (perimeter of Trapezoid 1)

m + n + p + q = 150 (perimeter of Trapezoid 2)

Since Trapezoid 1 and Trapezoid 2 are similar, we can write:

m = ax

n = bx

p = cy

q = dy

where x and y are the ratios of the longer and shorter bases of Trapezoid 1 to Trapezoid 2, respectively.

Substituting these expressions into the equations for the perimeters of the trapezoids, we get:

a(x+y) + b(x+y) + c(x+y) + d(x+y) = 240

(ax+bx+cy+dy) = 150

Simplifying these equations, we get:

(a+b+c+d)(x+y) = 240

(a+b+c+d)(x+y)(x/y) = 150

by Dividing  second equation by  first, we will get:

x/y = 240/150 = 8/5

Therefore, the ratio x:y is 8:5.

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Answer:

Step-by-step explanation:

As per the question we have:

This can be a function with the slope of m = 1 or m = - 1 as these lines must be perpendicular to each other and make 90°/2 = 45° or 45° + 90° = 135° angle with the x- or y- axis.

So the lines could be:

Lines must be perpendicular to each other as they are cutting at y intercept -1

Slope intercept form of line

for slope -1

For slope 1

y=x-1

Step 1. Identify the variables.

Step 2. Find the first constraint using the condition for the total number of books in each box.

The problem states "Christina needs to pack the boxes so there are at least 20 books in each box" This means that the sum of x and y must be at least 20, this is represented in the following inequality:

That is the first constraint.

Step 3. Find the second constraint using the condition for the weight of each box.

The problem states: "the boxes cannot weigh more than 30 pounds" and since the paperback books weigh 0.8 pounds and the hardcover books weigh 1.3 pounds each, the sum of their weights is:

This sum cannot be more than 30, which is represented by the following inequality:

Answer:

The set of constraints is

Answer:

60%

Step-by-step explanation:

For an integral value of \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ \) and

\(I_2 = \int_{ 1}^{-2} f(x)dx = -10 \\ \), the computed value of integral \(\int_{ 1}^{3} f(x)dx\) is equals to the -6. So, option(c) is right one.

In mathematics, an integral is the continuous process of a sum, which is used to calculate areas, volumes, and their properties. Integration is a way to sum up parts to the whole.

We have an integral say \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ \)

\(I_2 = \int_{ 1}^{-2} f(x)dx = 10 \\ \)

We have to determine value of \(\int_{ 1}^{3} f(x)dx\).

Using the properties of integral, consider integral \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18\\ \)

from distribution property, \(I_1 = \int_{ -2}^{3} 2f(x) dx + \int_{ -2}^{3} 2 dx = 18 \\ \)

\(2 \int_{ -2}^{3} f(x) dx + [ 2x]_{ -2}^{3} = 18\)

\(2 \int_{ -2}^{3} f(x) dx + 10 = 18\)

\(2 \int_{ -2}^{3} f(x) dx = 8\)

\(\int_{ -2}^{3} f(x) dx = 4\)

Now, consider the required integral and rewrite, \(\int_{ 1}^{3} f(x)dx = \int_{ 1}^{-2} f(x)dx + \int_{ -2}^{3} f(x)dx \\ \)

Substitute all known values of integrals

\(\int_{ 1}^{3} f(x)dx = 10 + 4 = 14 \)

Hence, required value is 14.

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Answer: 1,200 and 1,800

Step-by-step explanation: saw it some where

There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.

To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.

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Answer:

Bank A will exchange it

Step-by-step example

Step-by-step explanation:

6x - 8 = 4x

6x- 4x = 8

2x = 8

x = 8/2

x = 4

\(...\)

Answer:    x=4

Step-by-step explanation:

6x-8=4x   subtract 4x from both sides

-4x   -4x

2x-8=0     isolate x by adding 8 on both sides

+8    +8

2x=8     divide by 2 on both sides

/2    /2

x=4

The length of third side is 4 cm. This can be solved using the concept of right angled triangle.

Three straight sides and three angles make up a triangle, a two-dimensional form. Three vertices, three angles, and three sides define a triangle. In a triangle, the lengths of its two longest sides are always bigger than its third side's length.

A triangle seems to be a three-sided polygon with three vertices. There is a 180-degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.

Triangles can be categorized into one of three groups, namely Scalene, Isosceles, or Equilateral, depending on how long their sides are.

the triangle given is Right Angled Triangle because to find a third side provided two sides are given is only possible in a right angled triangle.

We know that the right-angled triangle follows Pythagoras Theorem

According to Pythagoras Theorem, the sum of squares of two sides is equal to the square of the third side:

(Perpendicular)² + (Base)² = (Hypotenuse)²

or, (2√3)² + (2)² = (Hypotenuse)²

or, 12 + 4 = (Hypotenuse)²

or, (Hypotenuse)² = 16

or, Hypotenuse = √16

or, Hypotenuse = 4 cm

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The researcher needs to select a sample of at least 12 days to estimate the true mean of the water temperature within 4° with 99% confidence.

In order to estimate the true mean of the water temperature in a lake within a certain range with 99% confidence, the researcher needs to select a sample of at least a certain number of days.

To determine the number of days the researcher should select to measure the temperature, we can use the formula for sample size calculation in estimating the population mean. The formula is given by:

n = (Z^2 * σ^2) / E^2

where n is the required sample size, Z is the Z-score corresponding to the desired confidence level (in this case, 99% confidence corresponds to a Z-score of approximately 2.57), σ^2 is the variance of the population (given as 29°), and E is the desired margin of error (4° in this case)

Substituting the values into the formula, we get:

n = (2.57^2 * 29) / 4^2

n = (6.6049 * 29) / 16

n = 191.2961 / 16

n ≈ 11.96

Since the sample size must be a whole number, we round up to the next whole number. Therefore, the researcher needs to select a sample of at least 12 days to estimate the true mean of the water temperature within 4° with 99% confidence.

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..................false

From the given table, the annual premium rate as a percentage of value insured a person at age 35 has to pay is 0.14%.

Reasons:

The data in the table are presented as follows;

\(\begin{tabular}{|c|c|c|}Age&Annual Insurance Premiums (per \$1,000 of face value)&\\&10-Year Term &\\&Male&Female\\35&1.40&1.36\\40&1.64&1.59\\45&2.07&2.01\end{array}\right]\)

From the above table, we have that the amount a 35 year old without health issues will pay per $1,000 is $1.40

Therefore, the amount to be paid for $115,000 is 115 × $1.4 = $161

The amount Bernard pays = 15% more = 1.15 × $161 = $185.15

Therefore;

The amount more Bernard has to pay = $185.15 - $161 = $24.15 ≈ $24

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Answer:

$24 or D, Hope this helps :D

Step-by-step explanation: