The pie below is cut into 8 equal slices. Shade 1/2 of this pie.

answer

(z+2)(z-2)

steps

its a rule

a²-b²= (a+b) (a-b)

vedantu

Using the law of sines, the value of a in the given triangle, to the nearest tenth, is calculated as: 19.9.

The law of sines that we would apply is given as:

sin A/a = sin B/b = sin C/c.

Given the following:

a = ?

A = 64 degrees

b = 17

B = 50 degrees

Plug in the values into the equation, sin A/a = sin B/b:

sin 64/a = sin 50/17

Cross multiply:

a * sin 50 = sin 64 * 17

Divide both sides by sin 50

a * sin 50 / sin 50 = sin 64 * 17 / sin 50

a ≈ 19.9 [nearest tenth]

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The value of a to the nearest tenth is 20.0

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Using sine rule to solve for a;

The side opposite to angle 64 is a and the side opposite to angle 50 is 17

a/sinA = b/sinB

a/sin64 = 17/sin50

asin50 = 17sin64

0.766a = 17 × 0.899

0.766a = 15.283

a= 15.283/0.766

a = 20.0( nearest tenth)

Therefore the value of a is 20.0

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Part A: The table that displays a complete list of possible outcomes would be = Table B, that is option B.

Part B: The probability that the chosen events will take place = 0.3.

To calculate the probability of the given event the formula that should be used is given below. That is;

Probability = possible outcome/sample space

The total number of blues balls = 1

The total number of red balls = 2

The total number of yellow balls = 2

The total number of balls = 5, while total number of colour = 3

For part A: the possible sample outcomes = (H,B), (HR), (HY), (TB), (TR), (TY).

For part B:

Using the formula the possible outcome = 2

Sample space = 7

Probability = 2/7 = 0.3

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This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex Algebraic equations and expressions.

The algebraic expression ÷ 8 can be written in a variety of ways depending on the context and the specific operation being performed. However, in general, the phrase "divided by 8" or "the quotient of x and 8" can be used to represent this expression.

For example, if we have an algebraic expression such as 24 ÷ 8, we can write it as

24 divided by 8

the quotient of 24 and 8

24/8

In each case, the idea is the same: we are dividing 24 into 8 equal parts, or finding how many groups of 8 are contained in 24.

In the context of an algebraic equation or expression, the phrase "divided by 8" is often used to indicate that the variable or expression preceding it is being divided by 8. For example:

3x ÷ 8

(2y + 5) ÷ 8

In these cases, we are dividing the value of 3x or the sum of 2y and 5 by 8. The quotient of these expressions will depend on the specific values of x and y."divided by 8" is a commonly used phrase to represent the algebraic expression ÷ 8. This phrase can be used in a variety of contexts, from simple arithmetic problems to more complex algebraic equations and expressions.

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The total deer population for year 8 will be D. about 2081 deer.

To calculate the total deer population, we use the mark-recapture formula where: N = M * C/R

M = Total number of deer population captured and marked

C = Total number of deer population that had or did not have a mark

R = Total deer population recaptured and marked

So, for the given problem, the figures are as follows:

M = 1608

C = 110

R = 85

N = 1608 * 85 = 176,880/85 = 2080.94

So, the estimated deer population is about 2081 deer.

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The correct option number that is NOT a good method for solving the problem is: Option C: 20.48.[c-0.08.6-c0] (45000. ((0.08)(6)=0.08. t)at 45000-(00:48) Il 6 -0.08- 1) at -562500- 20.48.[c-0.08.6-c0]

The problem requires finding the Accumulated Total Value of the income stream generated by Hank's Auto Wash over six years, assuming the income is reinvested at an interest rate of 8% per year, compounded continuously. To solve the problem, we need to use the formula for continuous compounding:

A = P[tex]e^{(rt)[/tex]

Where A is the accumulated total value, P is the initial principal (in this case, the annual revenue of $45,000), e is the mathematical constant e (approximately 2.71828), r is the interest rate (0.08), and t is the time period (6 years).

Plugging in the values, we get:

A = 45000[tex]e^{(0.086)[/tex]

A = 45000[tex]e^{0.48[/tex]

A = 450001.6186

A = $72,838.50

Therefore, the accumulated total value of the income stream at the end of 6 years is $72,838.50.

The method that is NOT a good method for solving the problem is "45000.20.48.[c-0.08.6-c0]." This is not a valid formula for calculating the accumulated total value of an income stream under continuous compounding.

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The distance between point A (2, 4) and point B (-2, 1) is equal to 5 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(-2 - 2)² + (1 - 4)²]

Distance = √[(-4)² + (-3)²]

Distance = √[16 + 9]

Distance = √25

Distance = 5 units.

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Complete Question:

3. Find the distance from point A to B.

A (2, 4) B (-2, 1) C(2, -1)​ D (0, 0)

Using the laws of exponents, the equivalent expression would be 1 / 64.

To find the equivalent expression of ( 4 / 7 ) ⁻ ³  . 7 ⁻³, we can use the law of exponents.

Using this law, we get:

( 4 / 7 ) ⁻ ³  =  ( 1 / ( 4 / 7 )) ³

( 1 / ( 4 / 7 )) ³ = ( 7 / 4 ) ³

( 7 / 4) ³ x 7 ⁻³

( 7 / 4) ³ x ( 1 /7 ³ )

(( 7 ³ ) /( 4 ³ ) ) x ( 1/ 7 ³ )

( ( 7 ³ ) / ( 4 ³ ) )  x ( 1 / 7 ³ ) = 1 / (4 ³ )

1 / (4 ³ ) = 1 / 64

In conclusion, the equivalent expression is 1 / 64.

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The given scenario, where a sample of teen drivers at a high school is surveyed about their engagement in the illegal activity of texting while driving, is an example of Selection bias. Option C

Selection bias occurs when the process of selecting participants for a study or survey is not random or representative of the entire population.

In this case, the sample consists only of teen drivers at a high school, which may not accurately represent all teen drivers in the broader population. The sample is limited to a specific group, which can introduce bias and affect the generalizability of the results to the wider population of teen drivers.

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Answer:

By substituting the values of A, C, and D the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

Step-by-step explanation:

From the given information, we have;The vertical stretch of the sine function = 3 × The parent function∴ A = 3Given that the horizontal shift left = π/2 units, (from an online source with similar question)The vertical shift down = 4 unitsThe given function, g is g(x) = A·sin(x + C) + DWhere;A = The amplitude = The maximum displacement from the rest or equilibrium position = 3C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)Therefore, the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4

The measures of the marked angles in the figure are:

x = 0.8°

6x + 8° = 12.8°

x + 12° = 12.8°

We have that:

x + 12° and 6x + 8°.

We equate the expression: 6x + 8° = x + 12°

We then  solve for x:

6x - x = 12° - 8°

5x = 4°

We then divide  both sides by 5:

x = 4° / 5

x = 0.8°

We get the  measure of the marked angle for

6x + 8°:

6(0.8°) + 8° = 4.8° + 8° = 12.8°

We also get the measure of the marked angle as:

x + 12°:

0.8° + 12° = 12.8°

In conclusion, an  angle is formed when two straight lines or rays meet at a common endpoint.

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Rational square roots: √225, √81, √576, √36, √441, √324

Irrational square roots: √300, √120, √12, √50, √200

Let's determine whether each square root is rational or irrational:

√225 = 15. This is a rational number since it can be expressed as a fraction of two integers (15 = 15/1).

√300 ≈ 17.32050808. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√120 ≈ 10.95445115. This is also an irrational number for the same reasons as above.

√81 = 9. This is a rational number since it can be expressed as a fraction of two integers (9 = 9/1).

√576 = 24. This is a rational number since it can be expressed as a fraction of two integers (24 = 24/1).

√36 = 6. This is a rational number since it can be expressed as a fraction of two integers (6 = 6/1).

√12 ≈ 3.464101615. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

√441 = 21. This is a rational number since it can be expressed as a fraction of two integers (21 = 21/1).

√50 ≈ 7.071067812. This is an irrational number for the same reasons as above.

√324 = 18. This is a rational number since it can be expressed as a fraction of two integers (18 = 18/1).

√200 ≈ 14.14213562. This is an irrational number because it cannot be expressed as a fraction of two integers and it has non-repeating, non-terminating decimal digits.

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Answer: 2(x − 6)(x − 3) is the answer

Step-by-step explanation:

Answer: Obtuse triangle? The line marked with O and E is more than 90 degrees

Step-by-step explanation:

The cost of 13 yards of material sold at #1000 per yard would be:

13 x #1000 = #13,000

The sentence given in the question does not include a participial phrase. Hence, correct option is False

The sentence "The picture frame held a picture of our family on vacation" does not include a participial phrase.

A participial phrase is a phrase that acts as an adjective. In this sentence, the phrase "on vacation" is an adjective phrase that describes the noun "family." However, it is not a participial phrase because it is not formed from a verb.

A participle is a verb form that can be used as an adjective. In this sentence, the verb "hold" is not used as an adjective.

Therefore, the phrase "on vacation" is not a participial phrase.

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The appropriate inference procedure is the t test for μdiff.

We know that,

The mean is a basic mathematical average of two or more values.

There are several methods for computing the mean for a given collection of numbers, including the arithmetic mean approach, which utilizes the sum of the numbers in the series, and the geometric mean method, which is the average of a set of products.

The t test is used to compare the means of two groups.

We also know that,

Inferential statistics is a field of statistics that employs a variety of analytical procedures to draw conclusions about population data from sample data. Aside from inferential statistics, descriptive statistics are a subset of statistics. Inferential statistics aid in drawing inferences about the population, whereas descriptive statistics summarize the data set's features.

It is a very important tool that can be used in inferential statistics.

Since it shows whether the means of two groups are significantly different, we can say that, the appropriate inference procedure is the t test for μdiff.

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After considering all the given data we come to the conclusion that the gross income of the given individual is = $2640.

The individual's gross income per month can be evaluated as follows
Gross Income = Hourly rate × Hours worked per week × Weeks per month
Staging the values given in the problem statement:
Gross Income = 16.50 × 40 × 4 = $2640
The FICA tax is a mixture of Social Security and Medicare taxes, here it involves the total 15.3% of earnings. The individual is  responsible for half of the total bill (7.65%), which involves a 6.2% Social Security tax and 1.45% Medicare tax on the individual's earnings.
The Federal Tax withholding is 10% of the individual's gross income per month.
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Answer:

(-1,1)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

equation form:
x=-1, y=1

have a great day and thx for your inquiry :)

By substituting each of the provided options into the given system of linear equations, it is revealed that the ordered pair (-1, 1) is a valid solution for both the equations.

The correct answer is (-1, 1)

In mathematics, a system of linear equations consists of multiple linear equations with the same variables. These equations describe various relationships among these variables, typically representing lines in a multi-dimensional space. Solving such systems involves finding values for the variables that satisfy all equations simultaneously. Methods like substitution, elimination, or matrix algebra can be used to solve these systems. These systems are fundamental in fields like physics, engineering, economics, and computer science for modeling and solving real-world problems involving multiple interconnected variables.

We can solve this problem by substituting values from the given options into the equations and checking for which option both equations are valid. The system of linear equations is: x + 4y = 3 and y = -4x - 3.

Therefore, the ordered pair that is a solution to the system of linear equations is (-1, 1).

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A cylinder has two types of edges: the curved edges and the top and bottom edges.

A cylinder is a three-dimensional geometric shape that consists of two circular bases and a curved surface connecting the bases. The circular bases have a certain number of edges, depending on the number of sides each base has.

Since a circle has no straight edges, the circular bases of a cylinder do not contribute any edges.

The curved surface of a cylinder has no straight edges either, as it consists of a smooth, continuous surface.

Therefore, the curved surface does not contribute any edges to the cylinder.

The only remaining edges are the top and bottom edges of the cylinder. Each base of the cylinder has a single edge that runs along the circumference of the circular base.

Hence, the cylinder has two edges from its top and bottom bases.

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Part A: After 15 days will have 32,768 magical beans.

Part B: As the value of the magical beans is less than the value of the car the trade does not make sense at least not from a financial perspective. B NO.

Part C: We would need at least 17 days for the number of magical beans to exceed the value of the car. C MAYBE?.

Based on the given information can observe that the number of beans doubles every day.

So, after 15 days will have 2¹⁵ = 32,768 magical beans.

The value of the 32,768 magical beans would be:

32,768 beans × $0.50/bean

= $16,384

Part C:

Let us assume that after 'n' days, the number of beans would be equal to or greater than the value of the car.

Value of the car in terms of magical beans = $65,000/$0.5 per bean

= 130,000 beans

Now, we can set up an equation based on the doubling of beans:

2ⁿ >= 130,000

Taking the logarithm base 2 on both sides, we get:

n × log2(2) >= log2(130,000)

n >= log2(130,000)

n >= 16.98

We would need at least 17 days for the number of magical beans to exceed the value of the car.

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The blue rectangular prism have a greater volume of 36 cubic units which makes the option C correct.

The volume of a rectangular prism is calculated by multiplication of its three dimensions which are the length, width, and height . That is Length × Width × Height in the same units.

volume of red rectangular prism = 4 units × 3 units × 2 units

volume of red rectangular prism = 24 cubic units

volume of blue rectangular prism = 4 units × 3 units × 3 units

volume of blue rectangular prism = 36 cubic units

Therefore, the blue rectangular prism have a greater volume of 36 cubic units

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Answer:

14/33

Step-by-step explanation:

1/3

= 1/3 x 11/11

= (1 x 11)/(3 x 11)

= 11/33

2/11

= 2/11 x 3/3

= (2 x 3)/(11 x 3)

= 6/33

1/3 - 2/11 + 9/33

= 11/33 - 6/33 + 9/33

= (11 - 6 + 9)/33

= (5 + 9)/33

= 14/33

Hello!

m     dm    cm    mm

5   ,   0        0

500cm = 5m

The standard deviation of the data set is 11.75.

To calculate the standard deviation of the data set, we first need to find the variance, which is the average of the sum of squares of the differences between each data value and the mean. We already calculated the sum of squares of the differences in Part (c), which is 828.

The formula for variance is:

variance = sum of squares of differences / number of data values

Since we have six data values, the variance is:

variance = 828 / 6

variance = 138

Now we can calculate the standard deviation, which is the square root of the variance:

standard deviation = sqrt(variance)

standard deviation = sqrt(138)

standard deviation = 11.75 (rounded to two decimal places)

Therefore, the standard deviation of the data set is 11.75.

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Answer:

  302 m²

Step-by-step explanation:

You want the area of the figure composed of a triangle and rectangle.

The formulas for the areas of the parts are given in the problem statement.

The base length of the triangle is (18 m - 5m - 5 m) = 8 m. Then its area is ...

  A = 1/2bh

  A = 1/2(8 m)(8 m) = 32 m²

The area of the rectangle is ...

  A = LW

  A = (18 m)(15 m) = 270 m²

The area of the figure is the sum of the areas of its parts:

  A = (triangle area) + (rectangle area)

  A = 32 m² +270 m² = 302 m²

The area of the figure is 302 m².

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This is the equation of a hyperbola, since it has a constant difference between the distances from any point on the curve to two fixed points (known as the foci). In this case, the foci are located at (-2, 0) and (2, 0).

To convert the given polar equation, r(1+3sinθ) = 4, to a rectangular equation, we can use the following equations:

x = rcos(θ)

y = rsin(θ)

Substituting r(1+3sinθ) = 4, we get:

x = r*cos(θ) = (4/(1+3sinθ))cos(θ)

y = rsin(θ) = (4/(1+3sinθ))*sin(θ)

Simplifying further, we can use the identity sin^2(θ) + cos^2(θ) = 1 to get:

x = 4cos(θ)/(1+3sinθ)

y = 4sin(θ)/(1+3sinθ)

Therefore, the rectangular equation of the conic section in terms of x and y is:

x = 4cos(θ)/(1+3sinθ)

y = 4sin(θ)/(1+3sinθ).

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Answer:

Step-by-step explanation:

The sum of three angles in a triangle is equal to 180°.

(1) 40°, 90°, 60°

40 + 90 + 60 = 190. Therefore, it could not be the measures of the three angles if a triangle.

(3) 120°, 30°, 20°

120 + 30 + 20 = 170. Therefore, it could not be the measures of the three angles if a triangle.

(2) 50°, 100°, 30°

50 + 100 + 30 = 180. Therefore, it could be the measures of the three angles if a triangle.

(4) 70°, 70°, 60°

70 + 70 + 60 = 200. Therefore, it could not be the measures of the three angles if a triangle.

The probability that a person's favorite pastime is cooking is 0.125 (or 12.5%).

To find the probability that a person's favorite pastime is cooking, we need to divide the number of people whose favorite pastime is cooking by the total number of people.

Given the following pastimes,

Reading = 25

Sports = 40

Crafts = 20

Cooking = 15

Others = 20

Since 15 people listed cooking as their favorite pastime. To find the total number of people, we can add up the number of people who listed each pastime:

Total = Reading + Sports + Crafts + Cooking + Others

Total = 25 + 40 + 20 + 15 + 20 = 120

Therefore, the probability that a person's favorite pastime is cooking is:

P(cooking) = Cooking  / Total

           = 15 / 120

           = 0.125 or 12.5%

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