Arithmetic Sequence - Identify the first term and common difference

Answer:

Slope = -4/3 or -1.33 in decimal form

Step-by-step explanation:

To find the slope divide the rise by the run. The rise would be the difference between the 2 y points (y2-y1) divided by the run (x2-1x)

Here the rise is (-9-3 = -12) and the run is (8-(-1) = 9) So -12/9 is -4/3 in fraction form and -1.33 in decimal form.

Purchase consideration less fair value of net assets is goodwill (Purchase Consideration-Fair Value of Net Assets) $690,000,000

What does "goodwill" mean?

Goodwill cannot be purchased or sold on its own; rather, it is a premium over fair value that is paid during a transaction. Other intangible assets include things like licenses or patents that are independent purchases or sales. While most intangibles have a set useful life, goodwill has an unlimited lifespan.

Estimating goodwill

The extra payment made as purchase consideration over the acquiree's net assets' fair market value is referred to as goodwill.

The calculation looks like this:

(Millions of Dollars)

Cost of the purchase: $ 900,000,000

Fair value of net assets is less.

True Cost of the Assets

$15,000,000 in supplies

$200,000,000 in intangible assets

$20,000,000 for property, plant, and equipment

Total $235,000,000

True Cost of Liabilities

$5,000,000 in current liabilities

$20,000,000 in Notes Payable

Total $25,000,000

Goodwill (Purchase Consideration-Fair Value of Net Assets) (Purchase Consideration-Fair Value of Net Assets) $690,000,000

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Answer:   y<1

Step-by-step explanation:

Answer:

43.33%

Step-by-step explanation:

x : 100 = 520 : 1200

x = (520 * 100)/1200

x = 520/12

x = 43.333333%

There will be no change in volume reducing the radius by 10%.

What is Direct Proportion?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. Since the other variable is reversed in this case, the inversely proportional relationship is really represented by the same symbol.

For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant. In contrast, x and y are represented as x 1/y or xy = C in the case of inverse proportion.
Let the radius be r then
The volume of every sphere is,
[tex]\mathrm{V}=4 \pi \frac{\mathrm{r}^3}{3}[/tex]
In the given question, It is given:
The volume V of a sphere varies in direct proportion to the cube of its radius.

That means:[tex]\mathrm{V}[/tex] ∝ [tex]r^{3}[/tex]
That means:[tex]4 \pi \frac{\mathrm{r}^3}{3} = kr^{3}[/tex]⇒[tex]4 \pi \frac{\mathrm{1}}{3} = k[/tex]
So, The equation is independent of radius.
Hence, There will be no change in volume reducing the radius by 10%.

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The probability that a standard normal random variable will be between. 3 and 3. 2 is 0.99932.

What is standard normal random?

We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.

Z∼N(0,1)

P(Z<3)=.99865

P(Z>3.2)=.99931

P(3<Z<3.2)=2(0.99931-0.99865)−1=0.99932

Hence the standard normal random variable will be 0.99932.

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In the given expression 7^(9/4) the values are found to be

Information given in the problem

the expression 7^(9/4)

This equation represents exponents in fraction form and the basics for the calculation is from

a^(b/c) = [tex]\sqrt[c]{a^{b} }[/tex]

Rewriting the expression is done as below

7^(9/4)

= [tex]\sqrt[4]{7^{9} }[/tex]

[tex]\sqrt[4]{7^{9} }[/tex] comparing with [tex]\sqrt[c]{a^{b} }[/tex] gives the following values

a will be equal to 7

b will be equal to 9

c will be equal to 4

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Answer:

Answer: 9 hours. If austin prepared 20 kg of dough in 5 hours, this means he can prepare 4kg of dough an hour. This is because 20/5=4.

Answer:

B.  6 units

Step-by-step explanation:

Given equations:

[tex]y = -2x^2 + 8x[/tex]

[tex]x-2.23y + 10.34 = 0[/tex]

The points at which the rod is attached to the archway are the points of intersection of the two equations.

Rearrange the second equation to make x the subject:

[tex]\implies x=2.23y-10.34[/tex]

Substitute this into the first equation to create a quadratic:

[tex]y = -2(2.23y-10.34)^2 + 8(2.23y-10.34)[/tex]

[tex]y = -2(4.9729y^2-46.1164y+106.9156) + 17.84y-82.72[/tex]

[tex]y=-9.9458y^2+92.2328y-213.8312+17.84y-82.72[/tex]

[tex]y=-9.9458y^2+110.0728y-296.5512[/tex]

[tex]-9.9458y^2+109.0728y-296.5512=0[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Solve the quadratic using the quadratic formula:

[tex]\implies y=\dfrac{-(109.0728) \pm \sqrt{(109.0728)^2-4(-9.9458)(-296.5512)}}{2(-9.9458)}[/tex]

[tex]\implies y=\dfrac{-109.0728 \pm \sqrt{99.12}}{-19.8916}[/tex]

[tex]\implies y=\dfrac{109.0728 \pm \sqrt{99.12}}{19.8916}[/tex]

[tex]\implies y=5.983867702, \quad y=4.982851918[/tex]

As point B is at a higher level than point A, the y-value of point B is approximately 6 units.  

Therefore, point B is 6 units from ground level.

The best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.

It is given that the mean monthly electric bill for 43 residents of the local apartment complex is $69.

That means the sample mean X for 43 residents is $69.

And we know that the sample mean, X is the best point estimate of the population mean, μ.

Therefore the best point estimate for the mean monthly electric bill for all residents of the local apartment complex is $69.

The point estimate for the population mean is the sample mean. Point estimate is the one value that is used to estimate the population parameter. It is also known as the unbiased estimate of the population mean is the sample mean.

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Answer:

Step-by-step explanation:

I believe the tax would be $ 12,150

Answer:

y = -7x + 10

Step-by-step explanation:

As the y's are decreasing by 7, the x are increasing by 1.  This gives us a slope of -7.  When x is 0, y is 10 that is our y intercept.

The new circle be made with double radius of the given circle.

Also,  the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.

Given, a circle

If the radius of the given circle is 'r'

then, the radius of the new circle '2r'

Now, the Circumference of the new circle be,

C' = 2π(2r)

As, the Circumference of the given circle be,

C = 2πr

On dividing, we get

C'/C = 2

C' = 2C

So, the circumference of the new circle is double of the given circle.

Now, the Area of the new circle be,

A' = π(2r)²

As, the Area of the given circle be,

A = πr²

On dividing, we get

A'/A = 4

A' = 4A

So, the Area of the new circle is Four times of the given circle.

Hence, the new circle be made with double radius of the given circle.

Also,  the circumference of the new circle is double of the given circle and the Area of the new circle is Four times of the given circle.

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If a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units

If a, b and c are the sides of the triangle

Then it will be

a + b > c

b + c > a

c + a > b

Given that the side length of the measures are consecutive integer

Smallest consecutive integer is 1, 2 and 3

But

1 +2 > 3

3 = 3

Therefore it will not be the sides of the triangle

Next smallest consecutive integers are 2, 3 and 4

Then,

2+3 > 4

5 > 4

3+4 > 2

7 > 2

2+4 > 3

6 > 3

This will be the sides of the triangle

The perimeter of the triangle is the sum of sides of the triangle

The perimeter = 2 + 3 + 4

= 9 units

Hence, if a triangle whose sides length measures are consecutive integers, then the smallest possible perimeter is 9 units

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As per the substitution method, the value of (x , y) is (-15/2, 11/2)

Substitution method:

Substitution method is the process of solve one equation for one of the variables. And substitute (plug-in) this expression into the other equation and solve. Then resubstitute the value into the original equation to find the corresponding variable.

Given,

Here we have the following expression.

3x + 5y = 5

Y = -x -2

Now, we need to find the value of x and y.

According to the substitution method, let us consider

3x + 5y = 5 -------------------(1)

Y = -x -2 ---------------------(2)

Now, we have to apply the value of y as -x - 2 in equation (1), then we get,

=> 3x + 5(-x - 2) = 5

When we expand it then we get,

=> 3x - 5x - 10 = 5

Simplify the expression,

=> -2x - 10 = 5

=> -2x = 5 + 10

=> -2x = 15

Then the value of x is,

=> x = -15/2

If the value of x is -15/2. then the value of y is calculated by using the equation (2),

=> y = -(-15/2) - 2

=> y = 15/2 - 2

=> y = (15 - 4)/2

=> y = 11/2

Therefore, the value of (x, y) is (-15/2, 11/2).

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Answer:

If the plot point was dilated by a scale factor, it would be multiplying the scale factor with each X and Y. Therefore it would be (-5,-5)

The image of (-1, -1) after the dilation by a scale factor of 5 centered at the origin is (-5, -5).

To find the image of (-1, -1) after a dilation by a scale factor of 5 centered at the origin, we can apply the formula for dilation in the coordinate plane.

The formula for dilation with a scale factor of k centered at the origin is (k * x, k * y), where (x, y) is the original point.

In this case, the original point is (-1, -1), and the scale factor is 5. Applying the dilation formula, we have:

Image = (5 * (-1), 5 * (-1))

= (-5, -5)

This means that the point (-1, -1) is dilated by a factor of 5, and its position is shifted five times farther from the origin in both the x and y directions.

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Answer: 72 in

Step-by-step explanation:

The shortest side length of the original triangle was 3in, and the newer one is now 12in. From 3in to 12in, you use a scale factor of 4. Hence, we multiply each side length of the original triangle by 4. And to find the perimeter of the new triangle, you add all the sides up.

3(4) + 6(4) + 9(4) = 72 in

The value of PN is 20 in.

What are congruent triangles?

Congruent triangles are triangles in which all the sides and all the angles are congruent.

These triangles can appear identical when moved, rotated, flipped, and turned. They coincide if moved in a different direction.

In the diagram, two congruent triangles are given ΔPMN ≅ ΔQSR.

So by CPCTC (corresponding parts of congruent triangles are congruent)

In ΔPMN and ΔQSR

PN=QR=20 in.

PM=SQ=24 in.

MN=RS= 7 in.

If two triangles are said to be congruent then all corresponding parts must be equal.

So, the value of PN is 20 in.

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Answer:

C. 20 in

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

A   Both are the same line

****   B  If that is 4x + 6 y = 8    the lines are parallel ===> no solution***

C   Intersecting lines

D   same line

The balloon is  above 17.7180 the ground

What is the trigonometry ?

A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical studies led to the development of the field in the Hellenistic world during the third century BC.

Given

The angle Ф  is 32°

The hypotenuse becomes 24 feet

Let AB be the opposite side

Using trigonometric function of sinФ

ie sinФ = Opposite / hypotenuse

  sin Ф = AB / 24

   AB = sin Ф * 24

  AB =  sin 32° * 24

   AB = 12.7180

As that person is 5 feet tall we have to add 5 to the value

ie

12.7180 + 5

= 17.7180

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Answer:

312 m^2

Step-by-step explanation:

Start by separating the shapes.

you will get:

2 triangles with the dimensions 6m x 8m

1 rectangle with the dimensions: 9m x 8m

1 rectangle with the dimensions: 6m x 9m

1 rectangle with the dimensions: 10m x 9m

1) find the area of every shape

2 triangles with the dimensions 6m x 8m -----> 48m^2 and 48 m^2

1 rectangle with the dimensions: 9m x 8m ----> 72m^2

1 rectangle with the dimensions: 6m x 9m ----> 54 m^2

1 rectangle with the dimensions: 10m x 9m ---> 90m^2

2) add everything up

48m^2 + 48 m^2 + 72m^2 + 54 m^2 + 90m^2 =

312m^2

Carrie will be paid $390 if she puts in 40 hours of work in a week.

The total amount of time of work = 40 hours.

As we are stated that the earnings for 1 hour is $9.75, so, we will perform multiplication to find the earnings for the time she worked. We are performing multiplication because the amount will increase as the number of hours increases.

Performing calculation now.

Amount earned in a week = 9.75 × 40

Performing multiplication on Right Hand Side of the equation to find the amount earned in a week

Amount earned in a week = $390

Thus, the amount paid to Carrie in a week is $390.

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The amount of money left with Alizay after shopping is Rs 17700 .

Alizay sold shirts for Rs. 2800.

She sold 14 shirts.

Cost earned from selling 14 shirts = 14 × 2800 = Rs. 39200

Spent on shopping =Rs. 14000

Spent on Grocery = Rs. 7500

Total amount spent = Rs.(14000+7500) = Rs. 21500

Amount of money left = Rs 39200 - Rs 21500 = Rs 17700

Therefore she is left with Rs 17700 .

In the case of a single variable, there is only one viable response. This particular case, in which the variable is accurately referred to as the "unknown," is one to which the term linear equation sometimes relates implicitly.

The Cartesian coordinates of a point on the Euclidean plane can be used to understand each solution in the scenario with two variables. A linear equation's solutions define a line in the Euclidean plane, and each line is the collection of all solutions to a linear equation with two variables.

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Which shows the following expression after the negative exponents have been eliminated

[tex]a^{2} b^{2}[/tex]

Given the algebraic expression:

[tex]\frac{a^{3}b^{-2} }{ab^{-4} }, a\neq 0, b\neq 0[/tex]

We are required to eliminate the negative exponents and find the resulting expression.

Using the Negative Exponent Law of Indices: [tex]x^{-y} = \frac{1}{x^{y} }[/tex]

Using the Division Law of Indices: [tex]\frac{t^{x} }{t^{y} } = t^{x-y}[/tex]

Therefore:

[tex]\frac{a^{3}b^{-2} }{ab^{-4} } = a^{3-1}.b^{-2-(-4)}\\ \\ Simplifying\\ \\a^{3-1}.b^{-2-(-4)} = a^{2}b^{-2+4}\\ \\ =a^{2} b^{2}\\\\Therefore:\\\\\frac{a^{3}b^{-2} }{ab^{-4} } =a^{2} b^{2}\\[/tex]

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Answer:

1 : 4

Step-by-step explanation:

the ratio of

alternative : total

= 15 : 60 ( divide each part by 15 )

= 1 : 4

The simplified expression for the complex expression is -56-52i

What is a complex expression?

A complex expression is an expression of the form a+ ib where a , b are constant and i is the imaginary number known as iota. In a + ib a is the real part and b is the imaginary part.

We are given two complex number as (8-8i) and (8+4i)

We have to simplify the given expression

As Complex number are added multiplied subtracted same as real number we can simplify the expression easily

2(8-8i)-9(8+4i)

We multiply the constants inside the bracket

16-16i-72-36i

Separating the terms and simplifying them we get

-56-52i

Hence the simplified expression is -56-52i

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In a farm composed of cows and chickens, there are total of 13 heads and 42 feet.

Let 'h’ represent the number of hens the farmer has.

Let 'c’ represent the number of cows the farmer has.

Assume that all hens have two legs and all cows have four.

There are a total of 42 legs. So

2h + 4c = 42 (1)

There are 13 animals in total.

h + c = 13 (2)

Now that we have our system of equations, we can solve by either substitution or elimination.

Elimination

(2) x 2

2h + 2c = 26 (3)

(2)—(3)

2c = 6

c=3

From (2):

c + h = 13

3+h = 13

h= 10

Therefore, the farmer has 3 cows and 10 hens.

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The values of the domain is the which satisfies the function is x > - 4.

According to the statement

We have to find the domain of the given function

For this purpose, we know that the

In Mathematics,The domain of a function is the set of values that we are  plug into our function.

The given function is a

[tex]y = \sqrt{x+4}[/tex]

And in this function

The domain is the values of the x which we able to put in the function according to the definition.

x+4=0

x=-4.

It means the value of the domain is the [tex]x > - 4[/tex].

The values according to the upper expression satisfies the domain of the function.

So, The values of the domain is the which satisfies the function is x > - 4.

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