What is the value of y?

Answer:

Step-by-step explanation:

Solve the System of Equations

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

Point Form:

(−1,7)

Equation Form:

x=−1,y=7

A series of terms is referred to as a geometric progression if each next term is produced by multiplying each previous term by a fixed amount. (GP), whereas the common ratio is the name given to the constant value. In the case of the GP 2, 4, 8, 16, 32, 64, for instance, the common ratio is 2.

The phrase that comes after the previous one in the GP, having a common ratio of r = l/[r(n-1)]. S=a/(1 - r), where 0 r 1, is the sum of infinite, or the sum of a GP with infinite terms.

A number progression is said to as a geometric progression if any two consecutive terms is always same.

Hence we have a=3,n=9,r=2

Now [tex]t=ar^n^-^![/tex]

=[tex]3*2^9^-^1[/tex]

=[tex]3*2^8[/tex]

=3×256

=768

∴ The ninth term of the G.P. is 768.

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The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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The angle θ that is coterminal with angle 14π/3, is 20π/3

Coterminal angles are the angles that have the same initial side and share the terminal sides. These angles occupy the standard position, though their values are different. They are on the same sides, in the same quadrant and their vertices are identical.

Given that, we need to find a coterminal angle of 14π/3,

The formula to find the coterminal angles is, θ ± 2πn where, n is an integer and it denotes the number of rotations around the coordinate plane.

For finding one coterminal angle: n = 1 (anticlockwise)

Then the corresponding coterminal angle is,

= 14π/3 + 2πn

= 14π/3 + 2π(1)

= 14π/3 + 2π

= 20π/3

Hence, the angle θ that is coterminal with angle 14π/3, is 20π/3

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The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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The average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] is 1.

A function is a process or set of instructions that takes inputs, performs a specific task, and produces an output. Functions are key components of programming languages, allowing the coder to create complex commands with simple instructions. For example, a function can be used to add two numbers together or to generate a random number. Functions can also be combined to create more complex sequences of instructions.

The average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] can be determined by taking the difference of the output values of the function at the endpoints of the interval, and then dividing it by the difference of the input values of the interval.

The output of the function at x=3 is f(3)=9/-3*3 +4 = -5,
and the output of the function at x=5 is f(5)=9/-3*5 +4 = -3.

Therefore, the difference of the output values is f(5)-f(3) = -3 - (-5) = 2

The difference of the input values is 5-3 = 2

Therefore, the average rate of change of the function on the interval [3,5] is f(5)-f(3) / (5-3) = 2/2 = 1.

Hence, the average rate of change of the function f(x)=9/-3x+4, on the interval [3,5] is 1.

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The congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

For the given triangles ABC and triangle LMN we can see that:

Line segment AB = LM

Segment AC= LN

and, CB = MN

Hence, the congruence statement for the triangle is: The triangles ABC and LMN are congruent using the SSS criteria.

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The United States' decision to remain neutral was motivated by its over $1 billion in annual trade with Europe.

Early 20th-century American trade with Europe helped the US remain neutral by enabling it to maintain business ties with both the Allied and Central Powers.

The US was able to avoid taking a political stance and maintain its neutral status by supplying goods to both sides of the conflict. Additionally, trade helped the US maintain its economic stability because it would have been detrimental to the nation's economy to break off trade with one party.

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"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

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Step-by-step explanation:

The probability of selecting a defective watch is 400/10,000 = 2/50.

The probability of selecting 50 defective watches out of 100 selected is given by the binomial distribution:

(100 choose 50) * (2/50)^50 * (1/2)^(100-50) = 0.072.

So the probability that exactly 50 out of 100 selected watches are defective is approximately 0.072.

a) The sample and the population are given as follows:

b) The numbers are classified as follows:

Population: Collection or set of individuals or objects or events whose properties will be studied.

Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.

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Step-by-step explanation:

To find the probability of getting an even number, we need to count the number of even numbers and divide it by the total number of sides of the die:

Number of even numbers = 10 (2, 4, 6, 8, 10, 12, 14, 16, 18, 19)

Total number of sides = 19

P(even number) = Number of even numbers / Total number of sides = 10/19 = 0.526 (or 52.6%)

The algebraic representation of the sentence the sum of 3x and 70 exceeds 13x is: 3x + 70 > 13x.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given that the sum of 3x and 70 exceeds 13x, this is represented as:

3x + 70 >13x

Hence, the algebraic representation of the sentence the sum of 3x and 70 exceeds 13x is: 3x + 70 > 13x.

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The given function

F(x)  = √(8 - x²)/ (2x² - 5)

is continuous at  x = -2,

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  = √(8 - x²)/ (2x² - 5)

To check whether it is continuous at x = -2

First taking LHL,

[tex]\lim_{h \to \00}[/tex] √[8 - ( -2 -0)²]/ [2(-2-0)² - 5]

⇒ √4/(8-5)

⇒   2/3

Now, taking RHL

[tex]\lim_{h \to \00}[/tex]  √[8 - ( -2 +0)²]/ [2(-2+0)² - 5]

⇒ √4/(8-5)

⇒   2/3

The value at x = -2

F(3)  = √[8 - ( -2 +0)²]/ [2(-2+0)² - 5]

⇒ √4/(8-5)

⇒   2/3

RHL = LHL =  F(-2)

Hence Proved,  the function is continuous at x = -2

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The time required to paint the cone when the base area is doubled is determined as 5.0 minutes.

The amount of time requires to paint the entire cone when the area of the base of the cone is doubled is calculated using simple proportion as shown below;

                                                               time

Area of base of  cone = 49π in². ----------------------->   2.5 minutes

Area of base of  cone = 2 (49π in² ) ------------------->   ?

49 x = ( 2 x 49 x 2.5 )

x = 2 x 2.5 min

x = 5.0 minutes

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Answer:

∠YPV = 50°

∠XPV = 130°

∠WPZ = 85°

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc.

6. Arc ZVW is a major arc.

7. Arc YWZ is a major arc.

8. Arc ZXW is a major arc.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc.  

Step-by-step explanation:

As WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.

As VW is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPX + ∠XPV = 180°

⇒ 50° + ∠XPV = 180°

⇒ ∠XPV = 130°

As XY is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°

⇒ ∠WPZ + 45° + 50° = 180°

⇒ ∠WPZ + 95° = 180°

⇒ ∠WPZ = 85°

Add the central angles to the given circle diagram (see attachment).

Note that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.

Note that three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.

As WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle.

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 50° + 45° = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.

6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.

7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.

8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.  

The answers to the respective arcs are given as follows:

The arcs are defined as follows:

It is to be noted that two-letter arcs might not necessarily be minor arcs if their measure is more than 180°. Therefore, use circle P to double-check each two-letter arc.

Also, three-letter arcs might not necessarily be major arcs if their measure is less than 180°. Therefore, use circle P to double-check each three-letter arc.

To solve for the arcs:

Given that WV and XY are diameters, and ∠WPX = 50° then according to the vertical angles theorem, ∠YPV = 50°.

As VW is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPX + ∠XPV = 180°

⇒ 50° + ∠XPV = 180°

⇒ ∠XPV = 130°

Since XY is a diameter of circle P, and angles on a straight line sum to 180°:

⇒ ∠WPZ + ∠ZPY + ∠YPV = 180°

⇒ ∠WPZ + 45° + 50° = 180°

⇒ ∠WPZ + 95° = 180°

⇒ ∠WPZ = 85°

Given that WV and XY are diameters of circle P, when the endpoints of a three-letter arc are the endpoints of one diameter, the arc will be a semicircle. Thus,

1. Arc YZ is a minor arc.

2. Arc WX is a minor arc.

3. ∠VPZ = 50° + 45° = 95°

4. Arc VZ is a minor arc.

5. Arc VWX is a major arc: Start at endpoint V, move counterclockwise around the circle through point W through to endpoint X.

6. Arc ZVW is a major arc: Start at endpoint Z, move clockwise around the circle through point V through to endpoint W.

7. Arc YWZ is a major arc: Start at endpoint Y, move clockwise around the circle through point W through to endpoint Z.

8. Arc ZXW is a major arc: Start at endpoint Z, move clockwise around the circle through point X through to endpoint W.

9. ∠VPX = 130°

10. Arc XVY is a semicircle.

11. Arc XWY is a semicircle.

12. Arc WZX is a major arc: Start at endpoint W, move clockwise around the circle through point Z through to endpoint X.  

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Answer: t=-5

Step-by-step explanation:

Multiply by -6 on both sides to get rid of the -1/6

Subtract 12 on both sides
Divide 18 by -90 on the other side

[tex](-1/6(12+18t))(-6)=13(-6)\\12+18t=-78\\18t=-90\\\\t=-5[/tex]

Answer:

5

Step-by-step explanation:

The greatest common factor between all 3 fruits is 5. There would be 3 apple slices, 4 oranges, and 12 grapes per cup.

Object A moves with variable speed and Object B moves with constant speed.

The correct option is D.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

A graph titles Distance vs time.

A curved line is drawn through point 10 on y-axis and this line is labeled Object A.

The graph of the object A is shown as a curved line.

The graph for Object B is a straight slanting line passing through the origin.

The graph for Object B is a linear proportional relationship.

So, Object A moves with variable speed and Object B moves with constant speed.

Therefore, object A moves with variable speed and Object B moves with constant speed.

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Answer:

28 different selections

Step-by-step explanation:

The number of ways in which k items can be drawn from a larger sample of n items is given by:

[tex]nC_k\;[/tex] pronounced as "n choose k" relates to a class of problems known as combinatorics

[tex]nC_k\;[/tex] is given by the formula
[tex]nC_k\; =\dfrac{n!}{k!(n-k)!}[/tex]

where ! stands for the factorial of a number

n! = n x (n-1) x ...... x 3 x 2 x 1

Plugging values of n and k into the equation we get

[tex]8C_2\; =\dfrac{8!}{2!(8-2)!} = \dfrac{8!}{2!\;6!}[/tex]

We can rewrite 8! as 8 x 7 x 6!

So
[tex]8C_2\; =\dfrac{8\cdot 7 \cdot 6!}{2!\; 6!} = \dfrac{8 \cdot 7}{2 \cdot 1} = \dfrac{56}{2} = 28[/tex]

Answer:lmkmonmklmlkmlkn

Step-by-step explanation:;lmklmlkmlkm

Answer: [tex]11a+16[/tex] feet

Step-by-step explanation:

The perimeter is equal to the sum of the lengths of the sides.

[tex]2a+2a+2a+8+5a+8=11a+16[/tex]

The result is the same, $2.7048. This result is not surprising because as the number of compounding periods increases, the difference between the amount after each compounding period becomes smaller and smaller. Eventually, the amount after compounding reaches a limit, which is $2.7048 in this case.

a. To calculate the value of the investment compounded monthly, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (12 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 12)^(12 * 1)

A = $1.00 * (1 + 100% / 12)^12

A = $1.00 * (1.0083)^12

A = $1.0083^12

A = $2.682

b. To calculate the value of the investment compounded weekly, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (52 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 52)^(52 * 1)

A = $1.00 * (1 + 100% / 52)^52

A = $1.00 * (1.00192)^52

A = $1.00192^52

A = $2.7005

c. To calculate the value of the investment compounded daily, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (365 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 365)^(365 * 1)

A = $1.00 * (1 + 100% / 365)^365

A = $1.00 * (1.00027)^365

A = $1.00027^365

A = $2.7048

d. To calculate the value of the investment compounded 1000 times in a year, the formula to use is:

A = P * (1 + r/m)^(mt)

where P is the principal, r is the annual interest rate (100% in this case), t is the time in years (1 in this case), m is the number of times compounded in a year (1000 in this case), and A is the amount after compounding.

A = $1.00 * (1 + 100% / 1000)^(1000 * 1)

A = $1.00 * (1 + 100% / 1000)^1000

A = $1.00 * (1.001)^1000

A = $1.001^1000

A = $2.7048

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Answer:

The solution is Option C.

The annual percentage rate of Penny is 22.4 %

Step-by-step explanation:

The value of the given number after division is 10c² + 5c - 9.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

Given to divide  (40c³ +20c² −36c) ÷ (4c)

dividing each term separately,

40c³/4c + 20c²/4c - 36c/4c

dividing constant by constant and variables by variable,

10c² + 5c - 9

Hence the division is 10c² + 5c - 9.

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The solution to the integral ∫ [csc x · (cot x + csc x)] dx is - (csc x + cot x) + C. (Correct choice: A)

In this problem we find the case of an integral involving trigonometric functions, this can be solved quickly by means of algebra properties and integral tables. Integral tables are an useful resource to find the result of integrals that require a lot of time to be solved.

First, write the function within the integration operator and simplify by algebra properties:

csc x · (cot x + csc x)

csc x · cot x + csc² x

Second, rewrite the integral by integral properties:

∫ [csc x · (cot x + csc x)] dx = ∫ csc x · cot x dx + ∫ csc² x dx

Third, use integral tables to find the solution to the integral:

∫ [csc x · (cot x + csc x)] dx = - csc x - cot x + C

∫ [csc x · (cot x + csc x)] dx = - (csc x + cot x) + C

Where is C is the integration constant.

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if Fred has 40 balls in his room then there are 7 pits in his room.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that there are 12 balls to every 2 pits

Fred has 40 balls in his room

We have to find the number of pits for 40 balls

Let x be the number of pits for 40 balls.

Form an proportional equation

12/2=40/x

6=40/x

x=40/6=20/3

x=6.667=7

Hence, if Fred has 40 balls in his room then there are 7 pits in his room.

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Answer:

X = 50

Z = 50

W = 130

Y = 130

Sum of Interior Angles: 360 degrees

Step-by-step explanation:

We can infer from the diagram, X = 50, therefore Z must be as well. W is congruent to Y, so 260 / 2 = 130. Quadrilateral is equal to 360 degrees.

If the economy is producing 12 units of guns and 4 units of butter, the opportunity cost of increasing the production of butter from 4 units to 11 units is 4 units of guns.

In Economics, an opportunity cost is sometimes referred to as alternative forgone and it can be defined as the value, profit or benefits that are given up and forfeited by an individual or business organization, in order to choose or acquire something that is deemed most significant at a particular point in time.

This ultimately implies that, the opportunity cost of owning or earning a thing is the alternative that is foregone in the attainment or earning of another value, profit or benefits.

Cost increase = 11 units - 4 units = 7 units of butter.

In this context, we can reasonably infer and logically deduce that the opportunity cost of 7 more units of butter would be 4 units of guns.

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Answer:

slope:m=5m=5

Step-by-step explanation:

Step-by-step explanation:

y-y1=m (x-x1)

y-4=5 (x-3)

y-4=5x-15

5x-y=11