In the diagram, AB, BC and CD are three sides of a regular polygon F
A
a) Work out the size of angle y.
square polygon P
B
D
square
regular 12-sided polygon
y z
b) Work out the size of angle z.
c) What is the name of polygon P?

The value of the expression "(x²y - 2z)/4", when x = 12 , y = 8 and z = 6, is (c) 285.

An "Expression" is defined as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, which are written using mathematical symbols and follow certain rules.

We have to evaluate the expression : (x²y - 2z)/4, if x = 12 , y = 8 and z = 6,

To evaluate , we substitute x = 12 , y = 8 and z = 6, in the expression,

So, We have,

⇒ (12² × 8 - 2×6)/4,

⇒ (144 × 8 - 12)/4,

⇒ (144 × 8 - 12)/4,

⇒ (1152 - 12)/4,

⇒ 1140/4,

⇒ 285,

Therefore, the value of the given expression, when x=12, y=8, and z=6, is 285, the correct option is (c).

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The length of c in the triangle is 4.2 units.

The side of a triangle can be found using cosine law as follows:

Hence,

c² = a² + b² - 2ab cos C

where

Therefore,

c² = 7² + 8² - 2(7)(8) cos 32°

c² = 49 + 64  - 112 cos 32°

c² = 113 - 112(0.84804809615)

c² = 113 - 94.9813867695

c² = 18.019

square root both sides of the equation

c = √18.019

c  = 4.24487926801

c = 4.2 units

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the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

a) The events are dependent because the selection of the first number affects the probability of selecting a number less than 6 on the second draw.

b) To calculate the probability of selecting a number less than 6 both times, we need to first find the probability of selecting a number less than 6 on the first draw and then the probability of selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw.

The probability of selecting a number less than 6 on the first draw is 5/20, or 1/4, since there are 5 numbers less than 6 (1, 2, 3, 4, and 5) out of 20 total numbers.

Given that a number less than 6 was selected on the first draw, there are only 4 numbers less than 6 left in the box out of a total of 19 remaining numbers. So, the probability of selecting a number less than 6 on the second draw is 4/19.

To find the probability of both events occurring, we multiply the probabilities:

P(selecting a number less than 6 both times) = P(selecting a number less than 6 on the first draw) × P(selecting a number less than 6 on the second draw given that a number less than 6 was selected on the first draw)

P(selecting a number less than 6 both times) = (1/4) × (4/19) = 1/19

Therefore, the probability of selecting a number less than 6 both times is 1/19 or approximately 0.0526.

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The distance from which the sprinkler can spread water is  4.37 feet

To determine the value, we need to know the area of the circle.

The formula for the area of a circle is expressed as;

A = πr²

Given that the parameters are;

Substitute the values, we have;

15 = 3.14r²

Divide both sides by the coefficient, we get;

r² = 4. 77

find the square root of both sides, we get;

r = 2. 19 feet

But note that the formula for diameter is given as;

Diameter = 2radius

Diameter = 2(2.19)

multiply the values

Diameter = 4.37 feet

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The output of the OR gate will be 1.

An important component for electronics and computing, the NOT gate or inverter is a basic digital logic gate. It is designed with one input and output that conduct logical negation.

Essentially, this means it turns the input signal to its opposite. When given an input binary value at "1," the method generates "0" as the output and vice versa.

Two input signals, P=0 and Q=1, are subjected to the following process. The message carried by Q is inverted via a NOT gate using its negation feature, returning Q' = 0 at its output.

The resultant value of Q' (evaluated as zero), is then processed using an OR logic operation along with input P into another gate. Outputs from an OR port may only produce "1" if any of the input signal(s) carry a 1. As one of the inputs from this specific procedure provides "0", the result will inevitably be "1".

Consequently, a final analysis reveals that regardless of what the initial value for P was, the result obtained formulating the two signals through a NOT and OR devices matches an outcome of "1".

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Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.

All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.

So, total months = 9 + 12 + 12 = 33

Now, using the multiplication operation, we get

⇒ Total money saved = 33 * 20

⇒ Total money saved = $660

It is given that she spent 75% of her savings on computer.

So, using the subtraction operation, we get

⇒ Amount left = 660 - 75%

⇒ Amount left = $165

Hence, Anna has $165 left in the jar.

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Answer:

2105, plug it into calculator

Answer:

Positive Association

Complementary Angles

Negative Association

Clusters in Data

Supplementary Angle

Non-linear Association

Step-by-step explanation:

Match the boxes on the left to the answers:

Positive Association

Complementary Angles

Negative Association

Clusters in Data

Supplementary Angle

Non-linear Association

Answer:

Step-by-step explanation: 0+0=0

Answer:

0

Step-by-step explanation:

0+0= nothing that why.

Answer:

Step-by-step explanation:

(a) Lett be the time (in days) since the start of the experiment, and let

y be the amount of the substance at time t.

Write a formula relating y to t.

Use exact expressions to fill in the missing parts of the formula.

Do not use approximations.

y = ei

Answer: (a) The formula relating the amount of substance, y, to time, t, is given by:

y = y₀ * e^(-λ*t)

where y₀ is the initial amount of the substance, λ is the decay constant, and e is the mathematical constant approximately equal to 2.71828.

The half-life, T½, is related to the decay constant as:

T½ = ln(2)/λ

We are given that the half-life of the substance is 16 days, so we can solve for λ:

λ = ln(2)/T½ = ln(2)/16

Substituting this value of λ in the formula for y, we get:

y = 65.7 * e^(-ln(2)*t/16)

(b) To find the amount of substance present after 13 days, we substitute t = 13 in the formula for y:

y = 65.7 * e^(-ln(2)*13/16) ≈ 42.1

Rounding to the nearest tenth, we get y ≈ 42.1 g. Therefore, approximately 42.1 g of the substance will be present after 13 days.

Step-by-step explanation:

Answer:

15, 18, 21, 24, 27, 30 ( +3)

7, 14, 28, 56, 112, 224, 448 ( x 2)

77, 70, 63, 56, 49, 42, 35 ( - 7)

20, 31, 42, 53, 64, 75, 86, 97 (+11)

22, 35, 48, 61, 74, 87 (+13)

Answer:To find sin(π/4), we can use the fact that sin(π/4) = sin(45°). We also know that sin(45°) = 1/√2 or approximately 0.707 (rounded to 3 decimal places). Therefore, sin(π/4) is approximately equal to 0.707.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

First you calculate the area of the rectangle. then you substract the area of the triangle.

The area of a rectangle is equal to the product of its length and breadth. In other words, if the length of a rectangle is ‘l’ and its breadth is ‘b’, then its area ‘A’ can be calculated as A = l x b= 6*8= 48

The area of a triangle can be calculated using the formula A = 0.5 x b x h where ‘b’ is the length of the base of the triangle and ‘h’ is its height. so A =0.5*8*3 = 12

Area of the figure = 48-12=36

a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.

b) The domain of V is [0, 3) in interval notation.

c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.

d) The maximum volume is 160/27 cm³.

(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.

Since the height of the box is x cm, the volume of the box can be expressed as

V = x(20-2x)(6-2x) cm³.

(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.

(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get

dV/dx = 4x³ - 52x² + 120x.

Setting dV/dx = 0, we get

x = 0 or x = 3 or x = 10/3.

Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.

We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get

V(0) = V(3) = 0

and

V(10/3) = 160/27.

(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.

So, the length of the box is

20-2(10/3)

= 40/3 cm,

the width of the box is

6-2(10/3)

= 2/3 cm, and

the height of the box is 10/3 cm.

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Answer:

247

Step-by-step explanation:

p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.

To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:

(141-5) = 22 + (n - 1)3

136 = 22 + 3n - 3

117 = 3n

n = 39

Therefore, there are 39 terms in the arithmetic series.

To find the sum of the first n terms of an arithmetic series, we can use the formula:

Sn = n/2(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:

S39 = 39/2(22 + (141-5))

S39 = 19(136)

S39 = 2584

Therefore, the sum of the first 39 terms of the series is 2584.

Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.

We know that the common difference is 3, so we can write the nth term as:

an = a1 + (n - 1)d

an = 22 + (n - 1)3

an = 3n + 19

Substituting this into the formula for the sum of the first n terms, we get:

Sn = n/2(a1 + an)

Sn = n/2(22 + 3n + 19)

Sn = n/2(3n + 41)

[tex]Sn = 3/2 n^2 + 41/2 n[/tex]

Therefore, p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

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Answer:

[tex] {(x - 1)}^{2} + {(y - 2)}^{2} = 5 [/tex]

The statement that best describes the relationship between the two variables is "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different." (option a).

To understand the relationship between these two variables, we need to analyze the frequencies by row and by column. The rows represent one variable (in this case, gender), and the columns represent the other variable (participation in school sports).

If we look at the relative frequencies by row, we see that the percentage of girls participating in school sports is higher in the fall (63%) than in the spring (43%), while for boys, the opposite is true. This indicates an association between gender and participation in school sports, as the relative frequencies vary by row.

Alternatively, if we look at the relative frequencies by column, we see that the percentage of boys participating in school sports is higher in the spring (57%) than in the fall (37%), while for girls, the opposite is true. This also indicates an association between gender and participation in school sports, as the relative frequencies vary by column.

Therefore, we can conclude that the best statement to describe the relationship between the two variables is option A: "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different."

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Complete Question:

Siloni computed in a two-way table the relative frequencies of boys’ and girls’ participation in school sports at her school.

School Sports Participation by Gender Fall Spring

Boys 37% 57%

Girls 63% 43%

Which statement best describes the relationship between the two variables?

a) There is an association because the relative frequencies by column are different.

b) There is an association because the relative frequencies by row are different.

c) There is no association because the relative frequencies by column are different.

d) There is no association because the relative frequencies by row are different.

Answer:

Step-by-step explanation:

decimal: 0.44444444444

fraction: 4/9

Answer: To calculate the mean weekly earnings for each occupation in 2010, we need to add up the weekly earnings for each occupation and divide by the number of occupations.

For Forestry, logging and support:

Mean weekly earnings = (971) / (1) = $971

For Manufacturing:

Mean weekly earnings = (977) / (1) = $977

For Transportation and warehousing:

Mean weekly earnings = (900) / (1) = $900

For Construction:

Mean weekly earnings = (1071) / (1) = $1071

For Retail trade:

Mean weekly earnings = (501) / (1) = $501

Therefore, the mean weekly earnings for workers in the listed occupations in 2010 are:

Forestry, logging and support: $971

Manufacturing: $977

Transportation and warehousing: $900

Construction: $1071

Retail trade: $501

Step-by-step explanation:

The mean number of processes to be performed before a commercially successful one is 8.

The probability of success in each attempt is 0.125, so the parameter of the geometric distribution is p=0.125.

The mean of a geometric distribution with parameter p is equal to 1/p, so:

Mean = 1/p = 1/0.125 = 8

Therefore, the mean number of processes to be performed before a commercially successful one is 8.

In probability and statistics, the mean (or average) is a measure of the central tendency of a set of numbers. It is calculated by adding up all the numbers in a set and then dividing the sum by the total number of values in the set. The mean is a commonly used measure of the central tendency because it takes into account all the values in the set and provides a single value that represents the "typical" value.

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The measure of ∠ADC is equal to 180 degrees.

The measure of ∠ABC is equal to 90 degrees.

In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.

In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.

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Answer:

2600This is a probability conversion problem.

The individual that will be paying the most for their purchase is: B.edgar paid with a credit card and paid the minimum payment each month

The individual that will pay the most according to the data provided is Edgar. Edgar's payment is spread out to the longest length of time. So, he will have to pay the added dues for extending his payment.

Usually, the person who pays cash pays the least amount while the person who pays in installments is charged for additional time spent in making the payment.

Complete Question:

Each of the following people bought a watch that costs $300. Which of the following people will pay the most for their purchase A.Sarah paid cash B.edgar paid with a credit card and paid the minimum payment each month C.susan paid with a credit card and paid the minimum payment plus 30 each month D. Sean paid with a credit card and paid the full balance the first of the month

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Since MO is parallel to PR, then angle MNQ and angle RQN are alternate interior angles and are congruent. Therefore, angle MNQ = angle RQN = 115 degrees.

When a line that intersects two parallel lines, also known as a transversal, creates an intersection with a pair of other lines, it forms what is referred to as alternate interior angles.

From the diagram we can see that RQN and MQN are similar angles from the diagram

Hence we have that RQN=115 = MNQ

Therefore MNQ = 115 degrees

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measure of Angle PRT = 90 degrees

A circle with center T exists -- Given

Point R is on the the circle. -- THIS IS AN ASSUMPTION BASED ON THE PICTURE (if you have more information that makes this not true, the rest of this logic fails).

Line segment TR is the radius of the circle. -- Definition of radius

Line PR is tangent to the circle. -- PR touches at exactly one point: R

Angle PRT has a vertex as point R. -- definition of angle PRT

Since PR is tangent to the circle, TR is perpendicular to PR -- consequence of lines perpendicular to circles

Perpendicular lines form right angles. -- Consequence of two congruent angles that form a straight angle pair.

The measure of a right angle is 90 degrees. -- definition of right angle

Therefore, the measure of angle PRT is 90 degrees.

Answer: Sure, here's how to solve the system of equations:

1. Start with the first equation: 3x = y - 2

Solve for y by adding 2 to both sides: y = 3x + 2

2. Substitute the value of y from the first equation into the second equation:

6x = 4 - 2y

6x = 4 - 2(3x + 2) (substitute y = 3x + 2)

6x = 4 - 6x - 4

12x = 0

3. Solve for x by dividing both sides by 12: x = 0

4. Substitute the value of x from step 3 into either equation to solve for y:

y = 3x + 2

y = 3(0) + 2

y = 2

Therefore, the solution to the system of equations is (x, y) = (0, 2).

hope this helpsss :D

Step-by-step explanation:

The scale factor for this right triangles is equal to 5/4.

In Mathematics, the scale factor of any geometric figure can be determined by dividing the dimension or side length of the new figure (image) by the dimension or side length of the original figure (pre-image):

Scale factor = Dimension of new figure (image)/Dimension of original figure (pre-image)

By substituting the given dimensions into the formula for scale factor, we have;

Scale factor = image dimension/pre-image dimension

Scale factor = 15/12 = (25/4)/5

Scale factor = 5/4.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

31

Step-by-step explanation:

the next number is 31 in this series