Which of these values for P and a will cause the function f(x)-Pa to be an
exponential growth function?
O
○ A P = 1²; a = 2
OB. P= 5; a = 1
C. P = 5; a = 1/1/2
○ D. P= 1/2; 0 = 1/1/2

The expression of log₄405 in terms of the logarithms of prime numbers is; 4 log₄3 + log₄ 5

One of the laws of logarithm is that;

log (a * b) = log a + log b

Now, we are given the logarithmic expression as; log₄405

We can express 405 in terms of prime numbers as;

405 = 81 * 5 = 3⁴ × 5

Thus, we have;

log₄405 =  log₄(3⁴ × 5)

Since log (a * b) = log a + log b, then;

log₄(3⁴ × 5) =  log₄3⁴ +  log₄ 5

= 4 log₄3 + log₄ 5

3 and 5 are prime numbers because they are divisible by only themselves or 1.

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Answer:

75287520

Step-by-step explanation:

Combination formula: [tex]\frac{n!}{r!(n-r)!}[/tex]

n = the amount of members of the US senate (100)

r = number of members chosen to be committee (5)

= [tex]\frac{100!}{5!(100-5)!}[/tex]

= [tex]\frac{100!}{5! * 95!}[/tex]

=   75287520

Explanation:

Use the trigonometric ratio cosine.

Remember that [tex]\cos(x) = \dfrac{\textrm{adjacent}}{\textrm{hypotenuse}}[/tex].

So, we can construct the following equation using the given triangle:

[tex]\cos(23\textdegree)=\dfrac{11}{x}[/tex]

And solve for x. First, take the reciprocal of both sides (flip both sides).

[tex]\dfrac{\cos(23\textdegree)}{1}=\dfrac{11}{x}[/tex]

        ↓

[tex]\dfrac{1}{\cos(23\textdegree)}=\dfrac{x}{11}[/tex]

Then, multiply both sides by 11.

[tex]11\cdot\left(\dfrac{1}{\cos(23\textdegree)}\right)=\left(\dfrac{x}{11}\right) \cdot 11[/tex]

[tex]\dfrac{11}{\cos(23 \textdegree)} = x[/tex]

[tex]x = \dfrac{11}{\cos(23 \textdegree)}[/tex]

Finally, plug this fraction into your calculator as 11/cos(23) to get approximately 11.95.

Also, make sure that your calculator's mode is degrees, NOT radians.

The value of x that will make the equation of the model true is: x = 5.8.

Create an equation using the model given, then isolate the variable in order to determine its value, which will make the equation true.

Given the model above, the following equation would be created below:

x + x + 9.4 = 21

Combine like terms

2x + 9.4 = 21

Subtract 9.4 from both sides

2x + 94 - 9.4 = 21 - 9.4 [subtraction property of equality]

2x = 11.6

Divide both sides by 2:

2x/2 = 11.6/2 [division property of equality]

x = 5.8

The value of x is: 5.8.

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When the sum of 5 and y is greater than or equal to -19, the inequality is y ≥ - 24.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since the sum of 5 and y is greater than or equal to -19, this will be:

5 + y ≥ - 19

y ≥-19 - 5.

y ≥ - 24

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Complete question

The sum of 5 and y is greater than or equal to -19. Express the inequality.

Answer:

x = 3 and -2/3

Step-by-step explanation:

(6x - 18) (3x + 2) = 0

6x - 18 = 0

6x = 18

x = 3

3x + 2 = 0

3x = -2

x = -2/3

The Answer is 38 seats for the 30th row! Because...

It is Adding up by 4 seats:)

Glad to help....

Mark me brainlyest ty!

The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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The system of inequalities that is represented by the graph is given as follows:

The system of linear inequalities is defined with linear functions, which have the slope-intercept format given as follows:

y = mx + b.

In which the parameters are given as follows:

For the upper bound of the inequality, we have that the linear function:

Then the upper bound of the inequality has the definition given by:

y ≤ -x + 1.

For the lower bound of the inequality, we have that the linear function:

Hence the lower bound of the inequality has the definition given by:

y ≥ -0.75x + 0.5.

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Answer:

mean is the average of all the values:

( 15.07 + 15.47 + 15.93 + 15.86 + 15.07 ) / 5 = 15.48g

median is the middle value AFTER it has been arranged in increasing order:

the increasing order is: 15.07, 15.07, 15.47, 15.86, 15.93

the middle value is 15.47g making it the median.

the mode is the most repeated value: 15.07g

The solution to the given simultaneous equations are;

x = 5/3 and y = 7/3

We are given the two simultaneous equations as;

x + y = 4  

y = 2x -1

Rearranging the second equation to have all the variables on one side gives; 2x - y = 1

Thus, we have the equations;

x + y = 4   ------(1)

2x - y = 1    -----(2)

Add eq 1 to eq 2 to get;

3x = 5

divide both sides by 3 using division property of equality to get;

x = 5/3

Put 5/3 for x in eq 1 to get;

⁵/₃ + y = 4

y = 4 - ⁵/₃

y = ⁷/₃

Thus, those are the solutions to the simultaneous equations.

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Brust's votes equaled 2 times the sum of Pitt's votes and 400:

The total number of votes received was 2012:

Solve for P by substitution:

Find B:

Answer:

a)   Total # of votes:   B + P = 2012

     Brust vs Pitt:   B = 2(P + 400)

b)   1608 = votes for Brust

      404 = votes for Pitt

      Brust won by 1204 votes

Step-by-step explanation:

Given variables:

Given information:

Create a system of linear equations using the given variable and information:

Substitute the second equation into the first equation and solve for P:

⇒ 2(P + 400) + P = 2012

⇒ 2P + 800 = 2012

⇒ 3P = 1212

⇒ P = 404

Substitute the found value of P into the first equation and solve for B:

⇒ B + 404 = 2012

⇒ B = 1608

Therefore:

To find how many votes Brust won by, subtract the total number of votes for Pitt from the total votes for Brust:

⇒ 1608 - 404 = 1204

There are 14 members in the club, and there are 4 leadership positions. Each position can be filled by any of the 14 members, so there are 14 ways to fill the first position, 14 ways to fill the second position, and so on. However, we have overcounted because we have not taken into account that a member cannot serve in two positions simultaneously. To correct for this overcounting, we divide by the number of ways that a member can serve in two positions simultaneously, which is 1. Therefore, the total number of ways that the club leadership can be organized is:

14 * 14 * 14 * 14 / 1 = 14^4 = 20736 ways.

The value of x in the equation x + 5 = 7 is 2

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is:

x + 5 = 7

Collect the like terms

x = 7 - 5

x = 2

Therefore, x is 2.

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Answer:

x = 2

Step-by-step explanation:

Given equation,

→ x + 5 = 7

Now the value of x will be,

→ x + 5 = 7

→ x + 5 - 5 = 7 - 5

→ [ x = 2 ]

Hence, the value of x is 2.

Answer:

To avoid consecutive b's, the string of b's must be divided into one or more groups of 1, 2, or 3 b's. There are a total of 5 + 1 = 6 possible places to insert the dividers to create these groups. For example, suppose we have a string of 7 b's and we insert dividers between the 3rd and 4th b's, and between the 5th and 6th b's. This would create the following groups of b's: bb|bb|b. In general, the number of possible ways to divide the string of b's into groups of 1, 2, or 3 b's is equal to the number of ways to insert 6 dividers into a string of 7 b's. This is equal to the number of ways to choose 6 of the 8 possible places to insert the dividers, which is equal to $\binom{8}{6} = 28$.

Since the 5 a's and the 1 c must be arranged in a specific order, there is only 1 way to arrange these letters. Therefore, the total number of words consisting of 5 letter a's, 7 letter b's, and 1 letter c is equal to $1 \times 28 = 28$.

Answer:

-----------------------------------------------

According to the question there are 7 'b' s  and we can't have them together. We assume more than two consecutive 'b' s contain two consecutive 'b' s and hence not considering any option of having 3, 4, 6 or 7 'b' s.

There is only one way to place 'b' s apart which leaves us with 6 gaps.

There are 5 + 1 = 6 other letters which is just the number to fill in the gaps between 7 'b' s.

We have only an option for 'c' to have any of the 6 gaps, it gives us 6 options and no other options for 'a' s.

Therefore in total we have 6 possible ways.

Answer:

1/2

Step-by-step explanation:

When you roll a 6-sided die, there are 6 possible outcomes:

1, 2, 3, 4, 5, 6

3 of the outcomes are even, and 3 of the outcomes are odd.

p(A) = p(even) = 3/6 = 1/2

p(Ac) = 1 - p(A) = 1 - 1/2 = 1/2

Answer:the answer is 17  

Step-by-step explanation:

The required simplified solution of the given expression is 17.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 4×5 -10 -2 (1 - 2) + 5
Following the PEMDAS rule,
= 20 - 10 - 2(-1) + 5
= 20 - 10 + 2 + 5
= 20 + 2 + 5 - 10
= 27 - 10
= 17

Thus, the required simplified solution of the given expression is 17.

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$10.6375 she tip if she wants to give a 23% tip of the whole bill when  tab for the nice supper that Kristyn and her sister had was $ 46.25.

Given that,

The tab for the nice supper that Kristyn and her sister had was $ 46.25.

We have to find how much should she tip if she wants to give a 23% tip of the whole bill.

We know that,

The tab for the nice supper that Kristyn and her sister had was $ 46.25.

So,

23% tip of the whole bill is

=$ 46.25×23%

=10.6375

Therefore, $10.6375 she tip if she wants to give a 23% tip of the whole bill when  tab for the nice supper that Kristyn and her sister had was $ 46.25.

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The correct option C: r = √(√3)² + (√3)² = √6; θ  = arctan (1) = π/4.

The complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

The polar coordinates r (a radial coordinate) and in Cartesian space (the angular coordinate, generally termed as  polar angle),

x = rcosθ  .....(1)

y = rsinθ,  .....(2)

where is indeed the counterclockwise angle first from x-axis and r is the radial distance to the origin. Considering x and y,

r² = x² + y²  ...eq 3

θ  = arc tan (y/x)

Using the polar coordinates explanation from above, we can deduce that;

r² = x² + y²  .

r² = √3² + √3²  .

r = √(√3)² + (√3)²

and

θ  = arc tan (√3/√3) = arctan (1) = π/4.

Thus, the complex number z=x+iy is represented by the rectangular coordinates (√3,√3) and polar coordinates (6,π/4) respectively.

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The compete question is attached.

Answer:

A Yard

Step-by-step explanation:

Yards are 36 inches and feet are 12

The percentile rank of score 71 on the test is 26.7 and The score of the 60th percentile on the test is 84.

The figure that a particular percentage falls within is referred to as the percentile. For instance, 80% of the kids in a group of 20 are shorter than you, and Ben is the fourth tallest.

Given:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

Calculate the percentile of score 71 as shown below,

[tex]Percentile= n / N \times 100[/tex]

Here, n is the number of scores below 71 and N is the total number of scores,

Percentile = 4 / 15 × 100

Percentile = 0.267 × 100

Percentile = 26.7 percentile

Therefore, the percentile rank of score 71 on the test is 26.7

(B)

Substitute the value in the formula given below,

60 = n / 15 × 100

n / 15 = 60 / 100

n = 0.6 ×  15

n = 9

Thus, the 9th term here is 84,

Therefore, the score of the 60th percentile on the test is 84.

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The congruent angles of the statements are;

∠1 + ∠3 = 180° by Vertical angles theorem.

∠5 + ∠6 = 180° by Linear pair theorem.

∠1 + ∠3 = ∠5 + ∠6 by both are supplementary angles.

∠3 = ∠6 by consecutive interior angles

∠1 = ∠5 by corresponding angles.

We want to prove that ∠1 = ∠5.

Corresponding angles; When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal.

From the given question, we see that;

∠1 + ∠3 = 180°: This is because ∠1 and ∠3 are vertical angles by the vertical angles theorem.

∠5 + ∠6 = 180°: This is because ∠5 and ∠6 are linear pairs by the Linear pair theorem.

∠1 + ∠3 = ∠5 + ∠6 ; 180° = 180° ; Both are supplementary angles.

∠3 = ∠6 ; Consecutive interior angles

Now, ∠1 = ∠5, Corresponding angles.

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The solution of the z-score of the standard deviation is [tex]0.5[/tex].

What is the standard deviation?

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Here given that,

The weight for twelve month old baby boys are normally distributed wih the mean [tex]22.5[/tex] pounds and a standard deviation of [tex]2.2[/tex] pounds.

Here, [tex]mean=22.5[/tex] , standard deviation [tex]=2.2[/tex]

z-score = (Blood pressure reading - mean)/standard deviation

[tex]=\frac{23.6=22.5}{2.2}\\\\=\frac{1.1}{2.2}\\\\=0.5[/tex]

Hence, the percentage is [tex]0.5[/tex].

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Answer:

-2, 8/3

Step-by-step explanation:

You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...

 A = (1/2)(f(a) +f(4))(4 -a)

 = (1/2)((3a -1) +(3·4 -1))(4 -a)

 = (1/2)(3a +10)(4 -a)

We want this area to be 12, so we can substitute that value for A and solve for "a".

 12 = (1/2)(3a +10)(4 -a)

24 = (3a +10)(4 -a) = -3a² +2a +40

 3a² -2a -16 = 0 . . . . . . subtract the right side

 (3a -8)(a +2) = 0 . . . . . factor

Values of "a" that make these factors zero are ...

 a = 8/3, a = -2

The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.

Alternate solution

The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.

Based on the storage capacity, Lunanne's car has 13 gallons of gas left in the tank.

Storage capacity of car = distance covered in total ÷ distance covered in one gallon

Keep the values in formula to find the storage capacity of car

Storage capacity of car = 675 ÷ 45

Performing division on Right Hand Side of the equation

Storage capacity of car = 15 gallons

Amount of gas left in tank = 15 - 2

Performing subtraction on Right Hand Side of the equation

Amount of gas left in tank = 13 gallons

Hence, 13 gallons of gas is left.

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Answer:

Step-by-step explanation:

[tex]i=\sqrt{-1} \ \ \ \ \ \ \ \ i^2=(\sqrt{-1})^2=-1[/tex]

a) ±2, 3

[tex](x-2)(x-(-2))(x-3)=\\\\(x-2)(x+2)(x-3)=\\\\(x^2-4)(x-3)=\\\\x^3-4x-3x^2+12=\\\\x^3-3x^2-4x+12[/tex]

b) -2, ±i

[tex](x-(-2))(x-i)(x-(-i))=\\\\(x+2)(x-i)(x+i)=\\\\(x+2)(x^2-i^2)=\\\\(x+2)(x^2-(-1))=\\\\(x+2)(x^2+1)=\\\\[/tex]

[tex]x^3+x+2x^2+2=\\\\x^3+2x^2+x+2[/tex]

c) 3, -1 ±i

[tex](x-3)(x-(-1-i))(x-(-1+i)=\\\\(x-3)(x+1+i)(x+1-i)=\\\\(x-3)((x+1)+i)((x+1)-i)=\\\\(x-3)((x+1)^2-i^2)=\\\\(x-3)((x+1)^2-(-1))=\\\\(x-3)((x+1)^2+1)=\\\\(x-3)(x+1)^2+(x-3)(1)=\\\\(x-3)(x^2+2x+1)+(x-3)=\\\\x^3+2x^2+x-3x^2-6x-3+x-3=\\\\x^3-x^2-4x-6[/tex]

d) -1, -2±√2

[tex](x-(-1))(x-(-2-\sqrt{2}))(x-(-2+\sqrt{2}))=\\\\ (x+1)(x+2+\sqrt{2})(x+2-\sqrt{2})=\\\\(x+1)((x+2)+\sqrt{2})((x+2)-\sqrt{2})=\\\\ (x+1)((x+2)^2-(\sqrt{2})^2)=\\\\(x+1)((x+2)^2-2)=\\\\(x+1)(x+2)^2-2(x+1)=\\\\(x+1)(x^2+4x+4)-2x-2=\\\\x^3+4x^2+4x+x^2+4x+4-2x-2=\\\\x^3+5x^2+6x+2[/tex]

Displacement from the origin will be 16.76 block

Pythagoras Theorem:

                                   Pythagoras theorem can be used to find the unknown side of a right-angled triangle.Theorem stats that,

                c² = a² + b²

                         where 'c' is the hypotenuse and 'a' and 'b' are the two legs.

In figure,

              O is origin,

             First travel 21 block north that means OA = 21 block.

             then,

                         travel 16 block East that means AB = 16 block.

             again finally,

                        travel 26 block South that means BC = 26 block.

Join OC,

            OC = 16 block

            CD = 5 block

we have to find the value of OD

Apply Pythagoras theorem,

                                                OD² = OC² + CD²

                                                OD = √(OC² + CD²)

                                                OD =√(16² + 5²)

                                                OD =√(256 + 25)

                                                 OD = √(256 + 25)

                                                 OD = √281 block

                                                 OD = 16.76 block

Thus,

              Displacement from the origin will be 16.76 block

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Según el método de diferenciales, el cambio aproximado del volumen del prisma es aproximadamente igual a 60 centímetros cúbicos.

Las diferenciales son una generalización del concepto matemático de cambio para funciones de una o más variables. Las versiones de una sola variable involucran derivadas ordinarias, mientras las versiones multivariables utilizan derivadas parciales.

El volumen del prisma es igual al producto del área de la base (A), en centímetros cuadrados, y la altura (h), en centímetros.

V(h, A) = h · A

El área de la base es igual al área de un cuadrado, es decir:

A(x) = x²

Donde x es la longitud del lado, en centímetros.

Según el enunciado, la altura del prisma es constante, mientras la longitud del lado de la base es una variable. En consecuencia, tenemos un diferencial que emplea derivadas ordinarias, esto es:

ΔV = (dV / dx) · Δx

V(x) = 15 · x²

dV / dx = 30 · x

Si sabemos que x = 10 cm y Δx = 0.02 cm, entonces el cambio en el volumen del prisma es:

ΔV = 30 · (10 cm)² · (0.02 cm)

ΔV = 60 cm³

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y = 7 x is the situation's linear equation in two variables and 7 is Slope of line.

To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.

The faucet leakage rate is shown here to be 7 gallons per hour.

Since y gallons could leak in x hours , we have

Leakage rate is expressed as gallons per hour divided by the number of hours.

Given that our leakage was y gallons, and

The duration of the leaking is x hours, as well.

7 gallons per hour is the leakage rate, so we have;

Amount of gallons leaked = Gallons leaking per hour × Number of hours

The situation is represented by the linear equation =

y = 7 × x.

By comparing this with y=mx+c, Slope of line is 7

y = 7 x is the situation's linear equation in two variables and 7 is Slope of line.

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Two angles are called complementary when their measures add up to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Complementary angles add up to 90°- example: 15° & 75° are complimentary

For example:

Suppose if one angle is x then the other angle will be 90° – x.

Now, to find the complement of 2x + 52°, subtract the given angle from 90 degrees.

90o –  (2x + 52o) =  90o – 2x – 52o  = -2x + 38o

The complement of 2x + 52o is 38o – 2x.

Supplementary angles add up to 180°- example: 50° & 130° are supplementary

if the two angles form a linear angle, such that, if one angle is x, then the other angle is 180° – x

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