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A total of $316.67 has to be saved per month for the vacation at Disney.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that your parents are saving up for a fun vacation at Disney. They have figured out it will cost them a total of $3,400. They have already saved $1,500 and plan on saving for the next 6 months,

Assume that they will have to save $x every month. So we can write the inequality as -

6x ≥ (3400 - 1500)

6x ≥ 1900

x ≥ (1900/6)

x ≥ 316.67

Therefore, your parents will have to save a total of $316.67 per month for the vacation.

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Solution for the equation x² + 81 = 0 is x =  ± 9i.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

x² + 81 = 0

To find the solution of the given equation,

Simplify the equation,

x² = -81

x = √-81

x = ±9√-1

Since, i = √-1

x = ± 9i

The solution for the given equation is x =  ± 9i.

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Answer:

-6

Step-by-step explanation:

-6

The value of measure m∠ABC will be 24°.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

As per the given m∠ABD is a straight angle.

m∠ABD = 180°

m∠ABC  + m∠CBD = m∠ABD

6x - 60 + 8x + 16 = 180°

14x - 44 = 180

14x = 224

x = 14

Thus, m∠ABC = 6(14) - 60 = 24°

Hence "Measure ∠ABC will equal 24° in value".

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The correct question below,

Answer:

Step-by-step explanation:

answer is b

The study of probability is a field of mathematics that focuses on determining the possibility that an event will occur.

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The triangle pair that is similar from the given pair is "Triangle Pair 2" .

In the question ,

four triangle pairs are given ,

we have to select the triangle pair that is similar ,

In triangle Pair 2 ,

In triangle BAD and triangle BCD ,

angle A = angle C     ....given ,

side BD = side BD   ......because common side

side AD = side BC     ....because opposite side of parallelogram are equal.

So , the triangle BAD is congruent to triangle BCD ,

So , the triangle pair 2 is congruent .

Therefore , the correct option is (b) Triangle Pair 2   .

The given question is incomplete , the complete question is

Similar Triangles Sorting Activity , Which triangle pair shows similar triangles ?

(a) Triangle Pair 1

(b) Triangle Pair 2

(c) Triangle Pair 3

(d) Triangle Pair 4

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Answer: True

Step-by-step explanation:

The slope is the rate of change, to find it, you can get rise/run or use the equation y2 - y1 / x2 - x1

So it is true!

The slope of the line that passes through the given points (-5, 6) and (-2, 4) as required in the task content is; -2 / 3.

It follows from the task content that the slope of the line that passes through the given points; (-5,6) and (-2,4) be determined as required.

On this note, since the slope, otherwise termed the average rate of change is given by the formula;

Slope, m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Therefore, given the points; (-5, 6) and (-2, 4), the required slope of the line is;

m = ( 4 - 6 ) / ( -2 - (-5) )

m = -2 / (-2 + 5)

m = -2 / 3

Therefore, the required slope of the line which passes through the given points is; -2 / 3.

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Answer:

321.2 * 10^6

Step-by-step explanation:

First at all:

4.4 x  10^6 = 4.400.000

Then 73 * (4,4 x 10^6) = 73* 4.400.000

(73)*(4.400.000) = 321.200.000

In scientific notation:

321.2 * 10^6

For the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.

Box and whiskers plot is the way of representation of data which gives the graphical image of the data set to understand better. In this the data is represented with the help of quartile.

The minimum and the maximum values in the box plot is plotted at the end points.

The following set of data which i s given in the problem.

3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17

Min: 3

The minimum value in the given data is 3. Thus, the min is 3.

Q1:6

First quartile appears at 6. Thus, the value of Q1 is 6.

Med:12

The middle value of the given data is 12 which appears at the center of all the values. Thus the med is 12.

Q3:14.5

Second quartile appears at 14.5. Thus, the value of  second quartile Q2 is 6.

Max: 17

The minimum value in the given data is 17 as shown in the image attached below. Thus, the min is 17.

Hence, for the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.

The complete question is : Answer the statistical measures and create a box and whiskers plot for the following set of data. You may optionally click and drag the numbers into numerical order.

3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17

3,4,5,6,6,7,7,12,13,14,14,15,15,16,17

Min:

Q1:

Med:

Q3:

Max:

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Answer: use a graf

Step-by-step explanation:

find the negative numbers and positive number

He spent $200 on 0 tickets for children, 10 tickets for adults, and 20 tickets for seniors.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Total number of tickets brought=30

Total amount paid=$200

Cost of kid ticket=$3.5

Cost of adult ticket=$8

Cost of senior ticket=$6

Let x, y, z be the number of tickets brought for kid, adult, senior.

x+y+z=30

3.5x+8y+6z=200

2y=x+z

x+y+z=30

3y=30

y=10

x+z=20

z=20-x

3.5x+80+6(20-x)=200

3.5x+80+120-6x=200

2.5x=0

x=0

z=20

He bought 0 tickets for kid, 10 tickets for adult and 20 tickets for senior with an amount of $200.

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The range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)

What is a normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

Here, we have

Given:

Horn lengths of texas longhorn cattle are normally distributed

The mean horn spread:  μ = 60 inches

With a standard deviation:  σ = 4.5 inches

According to the normal distribution, the range for the middle 95% of the values is: (μ  - 2σ,  μ + 2σ)

Replacing the given values:

(60 inches  - 2(4.5 inches), 60 inches + 2(4.5 inches))

(60 inches  - 9 inches, 60 inches + 9 inches)

(51 inches, 69 inches)

Hence, the range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)

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In 24-hour period there will be 94143178827 virus in system.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given:

A virus reproduces by tripling every half hour.

In start the virus is 1.

After half an hour, virus= 3

After one hour= 9 virus

After 1 1/2 hour= 27

We get a geometric Sequence

1, 3, 9, 27, 81, ....

Using

[tex]a_n = a_1 (r)^{n-1[/tex]

[tex]a_{24} = 1 ( 3/1)^ {23[/tex]

[tex]a_{24[/tex] = 94143178827

Hence, In 24-hour period there will be 94143178827 virus in system.

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Answer: sqrt 10

Step-by-step explanation:

3.16227...

Subtraction property will satisfy given inequality option D.

Let's understand what is the Subtraction property

By balancing an equation with the same mathematical operation on both sides, the term "subtraction property of equality" is used.

Given inequality m< A + M <B = M<C. if we subtract both side equal value then we will get M<A = M<C - M<B. then we will get this result

or we can do cross-verify all other option

Transitive-According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."

Symmetric-Actually quite straightforward, equality has the symmetric property. According to this property, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the.

Reflexive - It is said that a number is always equal to itself because of the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a. a=a.

So here we can see option D is most probable solution for given inequality.

Given Question is incomplete complete Question here

Name the Property of Equality that justifies the statement:

If m< A + M <B = M<C.

Then, M<A = M<C - M<B

Transitive Property

Symmetric Property

Reflexive Property

Subtraction Property

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Answer: √-18 = 3√2 i

Because i is √-1 so think like √18 x √-1 which means √18 i so answer is 3√2 i

Simplest Radical Form of the given question is [tex]216\sqrt{10}[/tex].

An phrase that has a root, typically a square or cube root, is referred to as a radical.

The radical consists of three separate parts:

Radicand :This is the one whose root you are discovering.

A radical equation is one that contains the square root, or at least one other variable expression, inside a radical.

Degree: It expresses the degree of radicand multiplication. If a number appears on the root symbol but is absent, it is taken to be 2. (square root).

Symbol: Usually √

Given

[tex]9,8\sqrt{90}\\ 9*8\sqrt{90}=9*8\sqrt{9*10}=9*8*3\sqrt{10} \\=216\sqrt{10}[/tex]

Simplest Radical Form of the given question is [tex]216\sqrt{10}[/tex].

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The measure of angle n is 73°, the measure of angle m is 51° and the line p measures 24 cm.

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.

From the given figure, n is the midpoint of one side of the quadrilateral and m is the midpoint of other side of the quadrilateral.

Pair of opposite sides are parallel

Since, m and n are midpoints on two sides of quadrilateral, so the line passes through the midpoints is parallel to other two sides

Then, ∠n =73° and ∠m =51°

p = 1/2 ×48

⇒ p =24 cm

Therefore, the length of line p is 24 cm.

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Answer: c=9                                                            

Step-by-step explanation:

Using the formula of compound interest, the amount accumulated over 4 years is $15,849.46

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. In Mathematics, compound interest is usually denoted by C.I.

The formula is often given as;

C.I = P(1 + r/n)^nt

Substituting the values into the formula

C.I = 200(1 + 0.0105/12)^12*4

However, over the period of 4 years, the Principal becomes

Principal = 200 * 4 * 12 = 9600

Rate = 1.05 * 12 = 12.6

C.I = 9600(1 + 12.6/12)^12 * 4

C.I = $15,849.46

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Answer:

ED

Step-by-step explanation:

They both have side ED in their triangles!

[tex]A = 20,000 (1-0.12)^x[/tex] this equation shows the value of Marisa's car over a period of x years. Using the concept of depreciation we get this -

Depreciation is an accounting technique for spreading out the expense of a tangible item over the course of its useful life. Depreciation is a measure of how much an asset has been utilized for. It enables businesses to purchase assets over a predetermined length of time and generate income from those assets.

Given that,

Marisa buys a car for $20,000 = P

depreciates at a rate of 12% per year = r

and t is the for the time period.

As we know,

[tex]A = P (1-r)^t[/tex]

Where, A is the value of object after x period of time.

The value of Terrence's car after x years is:

[tex]A = 20,000 (1-0.12)^x[/tex]

Hence, the value of Marisa's car after x years is: [tex]A = 20,000 (1-0.12)^x[/tex]

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Answer:f(x)=20,000(.12)^x

Step-by-step explanation:

took test

Answer: If 4/9 of the fish have a red stripe, we can determine the total number of fish in the tank by dividing the number of fish with red stripes by the fraction of fish with red stripes. This gives us 12 / (4/9) = 12 * (9/4) = 27 fish. So, there are 27 fish in the tank.

[tex] \frac{4}{9} x = 12[/tex]

[tex]x = 12 \times \frac{9}{4} [/tex]

[tex]12 \times 9 = 108[/tex]

[tex]4 \times 1 = 4[/tex]

[tex]x = \frac{108}{4} [/tex]

[tex]x = 27[/tex]

There are 27 fish in the tank. Hope this helps.

Answer:

8

Step-by-step explanation:

The first step would be to determine if both the numerator and the denominator have a highest common factor. If they do, then the number can be simplified into a smaller fraction. Here, the denominator can be fully divided out by 64 to make the whole number 8

Answer:

see explanation

Step-by-step explanation:

After solving a system of equations.

the solution is

36 = 32 ← not possible

the fact that we have 36 = 32, an impossible equation, means that the system has no solution.

Answer:

y+3x=-16

Step-by-step explanation:

y=mx+c

y=-3x+c

-3x is the gradient

-5 is the x value and -1 is the y value

-1=-3x-5+c

-1=15+c

-16=c

y=-3x-16

y+3x=-16