Evaluate the expression when c= 1/4 and d= 2/4. 3 (1/4 + c) + 2d

The value of the expression ⁴P₄ is 24 because when we simplified ⁴P₄ then we get the factorial 4 whose value is 24.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements .

The formula of  ⁿ[tex]P[/tex]ₓ [tex]=[/tex] [tex]\frac{(n)!}{(n-x)!}[/tex]

Similarly ⁿPₙ = n!

The value of 0! is 1

n! = n × (n - 1)!

According to the question ,

⁴P₄ [tex]=[/tex][tex]\frac{(4)!}{(4-4)!}[/tex] = [tex]\frac{4!}{0!}[/tex] = [tex]\frac{4!}{1}[/tex] =[tex]4![/tex]

Thus , 4! = (4) (3) (2) (1)

              = 24

Hence, the value of ⁴P₄ = 24 .

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Answer:

[tex]2 {}^{ - 15} {a}^{3} b {}^{15} c {}^{6} {d}^{ - 27} [/tex]

Answer:

[tex]\dfrac{a^{3} b^{15}c^{6}}{2^{15}d^{27}}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left[\dfrac{2^{-3}ab^0(c^{-2}d^3)^{-2}}{2^2a^0(b^5c^{-2})^{-1}d^3} \right]^3[/tex]

Following the order of operations, begin by applying exponent rules to the parentheses in the numerator and denominator.

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left[\dfrac{2^{-3}ab^0c^{(-2 \cdot -2)}d^{(3 \cdot -2)}}{2^2a^0b^{(5 \cdot -1)}c^{(-2 \cdot -1)}d^3} \right]^3[/tex]

[tex]\implies \left[\dfrac{2^{-3}ab^0c^{4}d^{-6}}{2^2a^0b^{-5}c^{2}d^3} \right]^3[/tex]

Notice there are two terms with a zero exponent.

[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]

[tex]\implies \left[\dfrac{2^{-3}a(1)c^{4}d^{-6}}{2^2(1)b^{-5}c^{2}d^3} \right]^3[/tex]

[tex]\implies \left[\dfrac{2^{-3}ac^{4}d^{-6}}{2^2b^{-5}c^{2}d^3} \right]^3[/tex]

Separate the terms:

[tex]\implies \left[\dfrac{2^{-3}}{2^2} \cdot \dfrac{a}{b^{-5}} \cdot \dfrac{c^{4}}{c^{2}} \cdot \dfrac{d^{-6}}{d^3} \right]^3[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \left[2^{(-3-2)} \cdot \dfrac{a}{b^{-5}} \cdot c^{(4-2)} \cdot d^{(-6-3)}\right]^3[/tex]

[tex]\implies \left[2^{-5} \cdot \dfrac{a}{b^{-5}} \cdot c^{2} \cdot d^{-9}\right]^3[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^{-n}}=a^n:[/tex]

[tex]\implies \left[2^{-5} \cdot a \cdot b^{5} \cdot c^{2} \cdot d^{-9}\right]^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 2^{(-5 \cdot 3)} \cdot a^{(1\cdot 3)} \cdot b^{(5\cdot 3)} \cdot c^{(2\cdot 3)} \cdot d^{(-9\cdot 3)}[/tex]

[tex]\implies 2^{-15} \cdot a^{3} \cdot b^{15} \cdot c^{6} \cdot d^{-27}[/tex]

[tex]\implies 2^{-15} a^{3} b^{15} c^{6} d^{-27}[/tex]

To give the expression as a rational with positive exponents,

[tex]\textsf{apply exponent rule} \quad a^{-n}=\dfrac{1}{a^{n}}:[/tex]

[tex]\implies \dfrac{1}{2^{15}} \cdot a^{3} \cdot b^{15} \cdot c^{6} \cdot \dfrac{1}{d^{27}}[/tex]

[tex]\implies \dfrac{a^{3} b^{15}c^{6}}{2^{15}d^{27}}[/tex]

Note: I have left 2¹⁵ as an exponent with base 2.  As 2¹⁵ = 32768, you can substitute 2¹⁵ for 32768 in the final answer, if you so wish.

If a and b are disjoint, then the value = 1.

If two events are mutually exclusive then the probability of them happening or occurring simultaneously is by definition zero. However, the described setting is impossible.

Let’s review the situation. At a given point in time there are four possible states of the world:

We know that

Pr(S4) = 0,

since A and B are mutually exclusive. We also know that the probability of A happening is 0.2, which is in states S2 and S4, so

Pr(S2) + Pr(S4) = 0.2.

Moreover, the probability of B happening is 0.8, which is in states S3 and S4, so

Pr(S3) + Pr( S4) = 0.8.

Since PR(S4) = 0, it follows that

P(S2)= 0.2

and

Pr(S3) = 0.8.

However, that means that the probabilities of all possible states do not sum to 1 as they should for a probability distribution, since Pr(S2) + Pr(S3) is already 1. So the problem definition describes an impossible situation.

Hence the answer is if a and b are disjoint, then the value = 1.

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It takes 9.96 hours to travel the same distance (24,900 miles) now that the rocket is faster.

Distance covered in one hour = 2500 miles

Total distance = 24,900 miles

D₁ / T₁ = D₂ / T₂

2500 / 1 = 24900 / x

x = 24900/2500

x = 9.96  hours

Hence, It takes 9.96 hours to travel the same distance (24,900 miles) now that the rocket is faster.

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A

source: trust me bro

The function that gives the rate of change for the given situation is R9x) = 2 + 2.6x

Rate of change

Rate of change refers a  rate that describes how one quantity changes in relation to another quantity.

Given,

Brooklyn's cab company charges a one-time pickup fee of $2 for every ride, as well as a $2.60 charge for each mile traveled.

Here we need to find the rate of change.

Let as consider that the number of mile travelled is modeled as x.

And R(x) is the function that defines the rate of change.

So, in the given question we know that, the one time charge is $2 and the charge per mile is $2.60.

Therefore, the rate of change is calculated as,

R(x) = 2 + 2.60x.

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Answer:

2.60

Step-by-step explanation:

2.60 for each mile

Answer:

1.4

Step-by-step explanation:

An equation of the parabola that models the cross section of the mirror is y=x²/28.

Given that, a mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The pipe is located 7 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 7 inches from the vertex (0,0)

7 inches is the focus of the mirror

The distance between the vertex and the focus = 7

Since parabola is upwards and vertex is (0,0) we use formula 4py=x²

Where p is the distance between the vertex and focus p = 7

Now, 4×7×y=x²

⇒ 28y=x²

Now isolate y by dividing 28 on both sides, we get

y=x²/28

Therefore, an equation of the parabola that models the cross section of the mirror is y=x²/28.

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Number of side of polygon will be 18.

What is polygon?

A plane figure may be a figure that's delineated by a finite variety of line segments connected to create a closed plane figure chain is called polygon.

Main body:

Since the sum of the exterior angles of a polygon is 360° and an angle of the regular polygon is 20°, then 360° / 20° is the number of sides. Let the number of sides be n.

n = 18, an octadecagon.

Measure of Each Interior Angle

If you imagine a regular octadecagon (or any polygon), you will notice that the exterior angle is the supplement of the interior angle.

20° = 180° - I, where I is the interior angle.

[20°] + I = [180° -I] + I

[20° + I] - 20° = [180°] - 20°

I = 160 degrees

Sum of the Interior Angles:

Sum of interior angles is 180° (n - 2). The way I remember this equation is by remembering that the equation contains 180° and the number of sides, and that the sum of interior angles of a triangle is 180°.

=180° (18 - 2)

=180° (16)

=(200 - 20)° (16)

=(3200 - 320)°

=2880°

Sum of the Exterior and Interior angles

360° + 2880° = 3240°

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The value of angle E  in the ΔDEF is 121°.

Given,

∠B = (96 + y)°

∠E = (6y - 29)°

EF = BC

AB = DE

AC = DF

Therefore, ΔABC ≅ ΔDEF

So, ∠ABC = ∠DEF or ∠B = ∠E

     96 + y = 6y - 29

      6y - y = 96 + 29

           5y = 125

             y = 125/5

             y = 25

∠E = 6y - 29

     = 6(25) - 29

     = 150 - 29

     = 121

Hence, ∠E = 121°.

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Answer:

y=2/3x-3

Step-by-step explanation:

first we fill in the values for y=2/3x to find y intercept

-5=2/3(-3)

-5=-6/3

-5=-2

We know in order to make this equation true we have to subtract 3 so we write the new equation like this

y=2/3x-3

And we can test it

-5=2/3(-3)-3

-5=-6/3-3

-5=-2-3

-5=-5

Hopes this helps please mark brainliest

Answer:

given that

26 + (-42) =0

-16 =0

-46 + (-52) = 0

=-46-52

= - 98 is answer

Step-by-step explanation:

given that

26 + (-42) =0

= -16 =0

-46 + (-52) = 0

=-46-52

= - 98 is answer

Answer:

Eric made a mistake on the slope of the graph.

Explanation:

The slope of the graph that Eric made has a slope of 1/2 not 2, as written in the equation. Instead, Eric should have moved up 2 units and left 1 unit on his graph.

In the first step by open bracked students forgot to multiply the negative sign with 9 by doing the correct step the answer is -17/2.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

An equation is said to be linear if the maximum power of the variable is consistently unity.

As per the given equation,

1 - (x + 9) = -(-x - 9)

Open the bracket

1 - x - 9 = x + 9 (students did a mistake he/she write +9 instant of -9)

1 - (x + 9) = x + 9

1 = 2(x + 9)

x + 9 = 1/2

x = 1/2 - 9 = -17/2

Hence "In the first step by open bracked students forgot to multiply the negative sign with 9 by doing the correct step the answer is -17/2".

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The correct choice is C. If she earns $50,000 a year, he will pay $5,000 in federal income tax.

federal taxable income is That portion of gross income known as “taxable income” is used to determine your tax liability for a particular tax year. It can be loosely defined as adjusted gross income less allowable standard or personal deductions.

we can calculate federal income tax  as below:

Your adjusted gross income determines your total federal income tax (AGI). The 1040 form and accompanying schedule must record all income from multiple categories, including wages, interest and dividends, and business income.

So if your income is $50,000, your federal income tax is $5,000. The correct answer is C. If she earns $50,000 a year, he will pay $5,000 in federal income tax.

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Answer:

Just count all of the cubes  = 12

Step-by-step explanation:

12 cubes in all

The equation for profit relating to N(number of book ) is P = 15.21N - 650 .

In the question ,

it is given that

the small publishing company is releasing a "new book" ,

the cost(c) for the production of books is = 17.59*N + 650 ,

where N denotes the number of books .

total Revenue earned (in dollars) from selling the books is given by the function R = 32.80*N .

So , the Profit(P) = Revenue - Cost

Substituting the value of Revenue and Cost ,

we get ,

Profit = 32.80*N - (17.59*N + 650)

P = 32.80N - 17.59N - 650

P = 15.21N - 650

Therefore , The equation for profit relating to N(number of book ) is P = 15.21N - 650   .

The given question is incomplete , the complete question is

A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book printed.

The total production cost C (in dollars) is given by the function C= 17.95 N + 650, where N is the number of books.

The total revenue earned (in dollars) from selling the books is given by the function R=32.80N.

Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible

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There are 630 more strings of ten letters that do not include the consecutive letter stts.

Total number of combinations possible with 10 letters =2∧10

                                                                                          =1024

Calculating using inclusion method;

There are 7 possible spots for the 4 characters, from 1-4 through 7-10, and 26 options for the remaining 6 slots if we have a specific 4 character string that fits within a range of 10 characters. Then, for the double counts, we can either have the strings joined (1-7, 2-8, 3-9, and 4-10), with 23 other values, equaling 4*8=32, or the strings separated (2-5 and 6-9, 7-10, or 3-6, 7-10, equaling 6), with 22 = 4 other values, equaling 6*4 = 24, and one 10-character sequence that contained the pattern three times. STTSTTSTTS.

Number of combination containing consecutive letter stts will be

= 448 - (32 + 24) + 1

= 393.

Then,

Total Strings without the sequence stts = 1024 - 393

                                                                    = 631

Since, one is already provided in the question 631-1=630 more strings can be formed.

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The equation of the proportional relationship is [tex]y=\frac{1}{4}x[/tex].

Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship can be represented as follow:

y = kx

where

Therefore, the value of y is 4 when x is 16. Let's find the relationship in the form y = kx

4 = 16k

divide both sides by 16

4 / 16 = 16k / 16

k = 1 / 4

Therefore, the equation is [tex]y=\frac{1}{4}x[/tex]

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Answer:

142 ft2

Step-by-step explanation:

3/4 is eaqaul to 0.75 so 17.75 x 8

The preimage of the point C'(x, y) = (- 3, - 10) is the point C(x, y) = (5, - 14).

In this question we find the coordinates of a point that is result of a translation. Translations are examples of rigid transformations, whose vector formula is shown below:

C'(x, y) = C(x, y) + T(x, y)

Where:

Please notice that the original point C(x, y) is the preimage of C'(x, y).

If we know that C'(x, y) = (- 3, - 10) and T(x, y) = (- 8, 4), then the preimage of the point C is:

(- 3, - 10) = C(x, y) + (- 8, 4)

C(x, y) = (- 3, - 10) - (- 8, 4)

C(x, y) = (- 3, - 10) + (8, - 4)

C(x, y) = (5, - 14)

The preimage is the point C(x, y) = (5, - 14).

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Depending on the scale factor, the dilation picture will either be larger or smaller than the preimage.

What is an example of a scale factor?

What in mathematics are preimage and image?

Preimages are parts of the range, and images are the range's elements.

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Since Maya is estimating the product of 88 and 12, the statements that are true include the following:

In order to determine the statements that are true, we would have to evaluate each of the statement as follows:

"If she rounds both values to the nearest ten, her estimate will be 800."

Rounding up 88 and 12 to the nearest ten, we have the following:

Rounded up number = 88 ≈ 90

Rounded up number = 12 ≈ 10

Therefore, the product of 90 and 10 is given by:

Product = 90 × 10

Product = 900.

"If she rounds 88 to the nearest hundred and 12 to the nearest ten, her estimate will be 1,000."

Rounding up 88 to the nearest hundred, we have the following:

Rounded up number = 88 ≈ 100

Rounding up 12 to the nearest ten, we have the following:

Rounded up number = 12 ≈ 10

Therefore, the product of 100 and 10 is given by:

Product = 100 × 10

Product = 1,000.

In this context, we can reasonably and logically deduce only two statements are true while all of the other statements are false and incorrect.

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Complete Question:

Maya is estimating the product of 88 and 12. Which statements are true? Check all that apply.

If she rounds both values to the nearest ten, her estimate will be 800.

If she rounds both values to the nearest ten, her estimate will be 900.

If she rounds 88 to the nearest hundred and 12 to the nearest ten, her estimate will be 1,000

If she rounds both values to the nearest ten, her estimate will be 1,600.

If she rounds 88 to the nearest hundred and 12 to the nearest ten, her estimate will be 2,000.

The equation 6x²+64x-222 = -8x is in form of (x+6)² = 73

Given: 6x²+64x-222 = -8x

To change the given equation to the form (x+a)² = b, the steps below will be all intermediate steps involved:

6x²+64x-222 = -8x

2(3x²+32x-111) = 2(-4x)

3x²+32x-111 = -4x

3x²+32x+4x-111 = 0

3x²+36x = 111              (Divide through by 3)

x²+12x = 37

Using completing the square by adding the square of half of the coefficient of x to both sides of the equation:

x²+12x+(6)² = 37 +(6)²

(x+6)²  = 73

Therefore, the equation 6x²+64x-222 = -8x is in form of (x+6)² = 73.  The intermediate steps are as shown above

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Answer:

[tex]x = \frac{-3}{2}[/tex]

and / or

[tex]x = 6[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Zach has invested a total of 100,000

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

the ratio 1 : 2 : 0.5 can be written in whole number ratios
by multiplying the ratio by 2 so that it becomes

2:4:1

Total shares = 2 + 4 + 1 = 7

Zach's share = 2/7 x 350,000

Zach's share = 2 x 50,000, which is 100,000

In conclusion, Zach's share of the total money invested is 100,000

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The modified function will be  f(p²) = [tex]p^{4}[/tex] - 3p² +1.

What is a function?
A function is a special kind of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation instead of a function is depicted in the above graph as one is mapped to intermediate values. However, if someone were instead mapped to the a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly. The function machine receives the x-values as input. After finishing its operations, the function machine outputs the y-values. Any function may be the one within.

The given function f(x) = x²-3x+1

So we can replace x ---→ p²

So f(p²) = [tex]p^{4}[/tex] - 3p² +1

Hence the modified function will be  f(p²) = [tex]p^{4}[/tex] - 3p² +1
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Answer:

f ubiquitous uniform 8th Nii coffin stubby chin

Answer:

5029

Step-by-step explanation:

The figures that are given above are not similar because their corresponding side lengths have different ratios.

To determine if two figures are similar to each other, find out if their corresponding side lengths have the same ratio, or are proportional to each other.

Note also that if two figures are similar, their corresponding angles will have the same angle measures.

The corresponding angles of the two figures above given are congruent, that is they are equal to each other.

Thus, the ratio of their corresponding sides are:

4.2/7 = 0.6

7.7/11 = 0.7

The ratios are not the same, therefore, the figures are not similar.

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The pyramid is 13 units long with polygon as a base.

A pyramid is a 3D polyhedron with the base of a polygon along with triangle-shaped faces that meet at a point above the base.

The triangular sides are called faces and the point above the base is called the apex.

A pyramid is made by connecting the base to the apex.

Looking at the object shown,

The base of the pyramid is Hexagon , a polygon with 6 sides

The height of the pyramid is 13 units.

The vertex of the pyramid is E , A ,Y ,P ,T ,A ,N

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