Ella has a collection of vintage action figures that is worth $430. If the collection
appreciates at a rate of 4% per year, which equation represents the value of the
collection after 7 years?

Answer:

Step-by-step explanation:

The domain is the set of x-values, and the range is the set of y-values.

Answer:

x < -1

Step-by-step explanation:

Draw a parabola (the graph) passing trough two x-intercepts -1 and 3 and open up.

Answer:

12

Step-by-step explanation:

Direct Variation. I think it's gonna be like this.

SInce Z is not inversely to y , its varies directly to both.

Then it's,

Z=kxy, where k is constant.

subst. Z=6,x=2 and y=6.

6=k×2×6

6=k×12=12k

6=12k=½

the formula connecting them is

Z=½xy

Z=½×3×8

Z= 1×3×8÷2

Z=24÷2

Z=12.

That's my solution.

Answer:

Part A: The appropriate design for the study includes;

Treatment used; Chamomile oil treatment

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the symptoms can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

Step-by-step explanation:

The length of BC as shown in the diagram is 6.32units

The formula for calculating the distance between two points is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the following coordinate points (3, 6) and (5, 0)

Substitute

BC = √(0-6)²+(5-3)²

BC = √(36+4)

BC = √40

BC = 6.32 units

Hence the length of BC as shown in the diagram is 6.32units

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Answer:

Given - an equilateral triangle

An equilateral triangle means all sides equal and all angle equal to 60°

In triangle BOA

sin 60° = OB/ AB

√3/2. = 80/AB

AB = 160√3/3

X = 160√3/3

Answer:

6

Step-by-step explanation:

21 - 15 = 6

Answer:

115.2 in^2

Step-by-step explanation:

total surface area Stot = 113.2 in2

lateral surface area Slat = 103.2 in2

top surface area Stop = 6 in2

bottom surface area Sbot = 6 in2

Answer:

D. [tex] \frac{2}{6} [/tex]

Step-by-step explanation:

2÷ 6 = 0.33333

As you can see 3 is repeating.

Therefore [tex] \frac{2}{6} [/tex] as repeating decimal form.

Answer:

n = 8

Step-by-step explanation:

13n-6 = 98

Solution:

Hence the value of n is 8.

13n - 6 = 98

13n = 98 + 6

13n = 104

n = 104/13

n = 8

The vertex-form of the quadratic equation is given by y = (x + 4)² - 13, and the minimum value of y is of -13.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient. If a > 0, k is the minimum value of y, and if a < 0, it is the maximum value.

In this problem, the equation is:

y = x² + 8x + 3.

Completing the squares, the function is:

y = (x + 4)² - 13

13 is subtracted as (x + 4)² = x² + 8x + 16, hence for the equations to be equal 13 has to be subtracted. k = -13 is also the minimum value of y.

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The minimum y-value of the function for the parabolic equation is -13.

The vertex for an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v= -\dfrac{b}{2a}}[/tex]

From the given equation:

y = x² + 8x + 3

The parameters for the parabola are:

a = 1, b = 8, c = 3

[tex]\mathbf{x_v= -\dfrac{8}{2\times 1}}[/tex]

[tex]\mathbf{x_v= -4}[/tex]

If we replace the value of [tex]\mathbf{x_v= -4}[/tex] to find the minimum value of [tex]\mathbf{y_v}[/tex] value, we have:

[tex]\mathbf{y_v = -13}[/tex]

Thus, the parabola vertex is (-4,-13). If a< 0, the vertex is a maximum value and If a>0, the vertex is a minimum value.

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Answer:

(3(3) × 3(4) ) ÷ 3(2)

(9 × 12) ÷ 6

108 ÷ 6

18

The correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

The total sample will have 9 numbers

S = { 1,2,3,4,5,6,7,8,9} = 9

Even Number = { 2,4,6,8} = 4

Odd Number  = { 1,3,5,7,9} = 5

P ( A ) = ( 4 / 9 )

P ( B ) = ( 5 / 9 )

The probability will be calculated as:-

P( A:B ) = [tex]\dfrac{P(A)\times P(B)}{P(B)}[/tex]

P( A:B ) =[tex]\dfrac{( 5/9 ) ( 4/9 )}{5 / 9 }[/tex]

P( A:B ) = 4 / 9

Therefore the correct answer is option B which is P ( A|B) will be ( 4 / 9 ).

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Answer:

24

Step-by-step explanation:

The question is saying, how many three digit numbers can be made from the digits 3, 4, 6, and 7 but there can't be two of the same digit in them. For example 346 fits the requirements, but 776 doesn't, because it has two 7s.

Okay, on to the problem:

We can do one digit at a time.

First digit:

There are 4 digits that we can choose from. (3, 4, 6, and 7)

Second digit:

No matter which digit we chose for the first digit, there is only going to be 3 of them left, because we already chose one, and you can't repeat that same digit. So there are 3 options.

Third digit:

Using the same logic, there are only 2 options left.

We have 4 choices for the first digit, 3 choices for the second, and 2 for the third.

Hence, this is 4 * 3 * 2 = 24 three-digit numbers that can be made.

Answer:

Vertex

Vertex are the end points of parabola where it opens up

locus are the group of points

latus rectum is the line parallel to it .

Answer:

It's very simple: divide the 40 m² area by area of 1 one sphere

[tex] \frac{40 \: m {}^{2} }{3.41 \times 15m {}^{2} } = 565[/tex]

The relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases. Then the correct option is D.

A statement, principle, or policy that creates the link between two variables is known as a function.

The table gives the average monthly precipitation, in inches, in Seattle, Washington, from January through July, where January is month 1 and July is month 7.

Month                                                     1       2       3       4       5       6       7

Average monthly precipitation          5.2    3.9    3.3    2.0    1.6     1.4    0.6

Then the relationship between the variables in the data will be as the number of months increases, the average monthly precipitation, in inches, decreases.

Then the correct option is D.

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Answer:

Step-by-step explanation:

Comment

There is only 1 number under probability that is greater than or equal to 5. That number is 15

There are 4 possible answers. Only 1 is successful.

Answer: P(y≥5) = 1/4 or 0.25

Answer:

-4 and -6 are the answers

The number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with

Since the number of pennies after n days equals N = 2ⁿ

Let

So, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L

Making n subject of the formula, we have

n = ㏒(D/L)/㏒2

Substituting the values of the variables into the equation, we have

n = ㏒(D/L)/㏒2

n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2

n = ㏒(3/1.5 × 10¹⁹)/㏒2

n = ㏒(2 × 10¹⁹)/㏒2

n = ㏒2 + ㏒10¹⁹/㏒2

n = (19㏒10 + ㏒2)/㏒2

n = (19 + 0.3010)/0.3010

n = 19.3010/0.3010

n = 64.1

n ≅ 64 days

So, the number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

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The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)

The equation can be split as follows:

y = 1 - cos(x)

y = 2 - 2sin²(x)

Next, we plot the graph of the above equations (see graph 1)

Under the domain interval (-π, π), the curves of the equations intersect at:

(-π/3, 0.5) and (π/3, 0.5)

Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)

The equation can be split as follows:

y = 4cos⁴(x) - 5cos²(x) + 1

y = o

Next, we plot the graph of the above equations (see graph 2)

Under the domain interval [0, 2π), the curves of the equations intersect at:

(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

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The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2

The coordinates are given as:

Parallelogram 1: (0, 2), (2, 6), (6, 4), and (4, 0).

Parallelogram 2: (2, 0), (4, -6), (2, -8), and (0, -2)

Next, calculate the base and the height

For parallelogram 1, we have:

Base = (0, 2) and (2, 6)

Height = (6, 4), and (4, 0).

So, we have:

[tex]Base = \sqrt{(0 - 2)^2 + (2 -6)^2} = \sqrt{20}[/tex]

[tex]Height = \sqrt{(6 - 4)^2 + (4 -0)^2} = \sqrt{20}[/tex]

The area is:

Area = Base * Height

Area = √20 * √20

Area = 20

For parallelogram 2, we have:

Base = (0, -2) and (4, -6)

Height = (4, -6) and (2, -8)

So, we have:

[tex]Base = \sqrt{(0 -4)^2 + (-2 +6)^2} = \sqrt{32}[/tex]

[tex]Height = \sqrt{(4 - 2)^2 + (-6 +8)^2} = \sqrt{8}[/tex]

The area is:

Area = Base * Height

Area = √32 * √8

Area = 16

By comparing both areas, we have:

20 is greater than 16 by 4

This means that the area of parallelogram 1 is greater by 4 units

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Answer:

g(f(x)) = 9x² + 12x + 5

Step-by-step explanation:

g(f(x))

= g(3x + 2) ← substitute x = 3x + 2 into g(x)

= (3x + 2)² + 1

to expand (3x + 2)² = (3x + 2)(3x + 2)

each term in the second factor is multiplied by each term in the first factor

3x(3x + 2) + 2(3x + 2) ← distribute both parenthesis

= 9x² + 6x + 6x + 4 ← collect like terms

= 9x² + 12x + 4

then

g(f(x)) = (3x + 2)² + 1 = 9x² + 12x + 4 + 1 = 9x² + 12x + 5

Answer: B

Step-by-step explanation:

A quadratic equation has degree 2.

Answer:

The amount of money you saved by receiving a discount of 25% is $5.5

Step-by-step explanation:

Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. Selling price is the actual price at which an article is sold after any reduction or discounts in the cost price.

discount is always calculated on the cost price of the article

formula to calculate the discount and discount %

Discount = List Price - Selling Price

Discount (%) = (Discount/cost price) × 100

here, in the question discount % is given = 25%

cost price of the item = $22

therefore using the above mentioned discount percentage formula:

25 = (Discount/22)×100

25/100 = Discount/ 22

0.25 × 22 = Discount

$5.5     = Discount

thus ,  

the amount of many you saved by receiving a discount of 25% is $5.5

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Answer:

Both the numerator and denominator should be multiplied by the same number to arrive at the equivalent fraction.

Step-by-step explanation:

Equivalent fractions =  two or more than two fractions are said to be equal if both results the same fraction after simplification.

For example, consider the fraction 1/3

Multiplying numerator and denominator with 2, we get 1/3 × 2/2 = 2/6

Multiplying numerator and denominator with 3, we get 1/3 × 3/3 = 3/9

Multiplying numerator and denominator with 4, we get 1/3 × 4/4 = 4/12

Therefore, we can conclude that,

1/3 = 2/6 = 3/9 = 4/12 these are equivalent fractions.

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Answer: 2 and 6/8

Step-by-step explanation:

The number of traders that sell oranges and mangoes only are 17.

Since there are three sets, use the formula

n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)

A represents apple traders = 40

O represents orange traders = 46

M represents mangoes traders = 50

A∪O∪M = total traders = 100

A∩O = 14

O∩M = ?

A∩M = 15

A∩O∩M = 10

Substitute values into the formula

100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10

100 = 146 - 29 - O∩M

100 = 117 - O∩M

Make O∩M subject of formula

- O∩M = 100 -117

O∩M = 17 traders

Therefore, the number of traders that sell oranges and mangoes only are 17.

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