in the expression 7a + b-12 which is a constant

The real zeros in the given equation y = (x-12)³ - 7 will be x =  13.912.

For the real solutions, we know that a real zero is a real number which makes the value of the function zero. By the question, let

y = 0  ..........(1)

Put values of 'y' in equation (1), and we get.

(x-12)³ - 7 = 0         .........(2)
Adding '7' on both sides of equation (2), we get

(x-12)³ = 7
Taking the cube root on sides, the resulting equation will be:

[tex]\sqrt[3]{(x-12)^{3} }[/tex]  =  [tex]\sqrt[3]{7}[/tex]
x - 12 = 1.912
By adding '12' on both sides.
x =  13.912

So the only real zeros for the given equation will be 13.912. Other solutions are imaginary zeros.

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The fraction of height at which the collision occured is , y/y₀ = 1/2 + v₀²/(2 g y₀) .

For ball A

Given that the ball is dropped and its initial velocity is zero, the equation is

= - 2 g (y₀-y)

For ball B

v {B}^2 = v₀² - 2 g y

We swap out

2v {B}^2 = -2 g (y₀ -y)

g y0 + 2 g y = -v B2

v {B}^2 = v₀² - 2gy

It can be solved because it is a system of two equations with two unknowns. Let's add and multiply by -1.

0 = g y₀ + v₀² -2gy

Bypassing the height

y = (g yo plus v02) / 2g

y = yo / 2 + v₀² / 2g

In this exercise, we'll assume that the building's height and ball B's initial velocity are both known.

The percentage is

y/yo

= 1/2 + v₀²/(2gyo) (2gyo)

Velocity and speed describe how quickly or slowly an object is moving. We frequently encounter circumstances when we must determine which of two or more moving objects is going faster.

If the two are travelling on the same route in the same direction, it is simple to determine which is quicker.

It is challenging to identify who is moving the fastest when their motion is in the other direction.

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Answer:

n = 16

Step-by-step explanation:

-1/2 n = -8

(-1/2 * n = -8) * 2  ==> multiply the equation by 2 to remove fractions

-1 * n = -16

-n = -16 ==> simplify

n = 16

Answer: 16

Step-by-step explanation:

-1/2n=-8

Divide by -1/2

n=16

By using the fact that segment DC bisects the angle  BCA, we will see that:

m∠DCB =  67.38°

First, we know that the angle CDB is an angle of 90°, and the angle ACB has a measure of 134.76°.

Now, notice that the segment DC bisects that angle (bisects means that it "cuts it" right in half), then the angle BCD is half of that, we will have:

∠DCB = 134.76°/2 = 67.38°

In this way we conclude that the measure we wanted to find is  67.38°.

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Answer:

55000 grams

Step-by-step explanation:

1 kg = 1000 grams  ==> kilo means 1000, so 1 kilogram = 1000 grams

Now multiply 55 kg with the grams-kilograms conversion factor to get the total number of grams Shaina weighs.

55 kg* 1000 grams / 1 kg =

55 * 1000 grams / 1 =  ==> cancel out the kg

55 * 1000 = 55000 grams

The balance of Carlos account after this period, using simple interest, is of:

$2,339,488.08.

This is a simple interest problem, hence the balance of the account can be obtained using an exponential function, defined as follows:

[tex]B(n) = B(0)(1 + r)^n[/tex]

In which the parameters of the exponential function are defined as follows:

In the context of this problem, the values of these parameters are given as follows:

B(0) = 1500000, r = 0.025, n = 18, as one and a half year = 18 months.

Then the balance of Carlos account is obtained as follows:

B(18) = 1500000(1.025)^18 = $2,339,488.08

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In the picture we can see the graph represents of the function f(x)=-x²+5 that is curve graph.

Given that,

We have to find the graph represents the function f(x)=-x²+5.

We know that,

The quadratic function is f(x)=-x²+5.

This is a vertical parabola open downward

The vertex is a maximum

We know,

A vertical parabola's equation in vertex form is equal to

y= a(x-h)²+k

where

a is a coefficient

(h,k) is the vertex

Here

a=-1

(h,k)=(0,5) is vertex

The y-intercept is the point (0,5) is value of y when the value of x is equal to zero (is the same point that the vertex)

The x-intercepts are the points is values of x when the value of y is equal to zero  

Therefore, In the picture we can see the graph represents of the function f(x)=-x²+5.

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$9483.774 money should be deposited in the account.

Let the amount to be invested be P=$x so that the amount accumulated is A = $12000. We have t=3 years. The rate of interest is r=0.04 per year.     n  = 2 as interest will be compounded twice a year.

Interest, in its most simple form, is calculated as a percent of the principal.

Interest is the amount of money a lender or financial institution receives for lending out money. Interest can also refer to the amount of ownership a stockholder has in a company, usually expressed as a percentage.

Now,

                         [tex]x (1 + \frac{0.04}{2} )^{2 * 3}[/tex] [tex]= 12000[/tex]

                                 [tex]x(1.04)^{6}[/tex] [tex]= 12000[/tex]

                                           [tex]x = \frac{12000}{(1.04)^{6} }[/tex]

                                              ≈ 9483.774

                   ∴ Amount invested  ≈  $9483.774.

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The average rate of change from 1992 to 2000 is -1.025 percent per decade.

What is the average rate of change?

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

the average rate of change :

A(x) = 34.5 - 42.7 / 2000 - 1992

A(x) = -8.2 / 8

A(x) = -1.025

Hence, the average rate of change from 1992 to 2000 is -1.025 Percent per decade.

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As a result, the second table agrees with the formula y= 3x -3.

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. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

-3x - 3 = -6

y= 3x -3

Therefore, the second table matches the equation y= 3x -3.

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The subtended arc is 2.14 times as long as the circle's radius.

What is radius of circle?

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of those line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

Given:

A circle with a radius 7 cm long is centered at an angle's vertex, and the angle's rays subtend an arc length of 15 cm along the circle.  

The radius of the circle is 7 and length of the subtend are is 15 cm. The required value is given by:

Subtended arc / Radius = 15 / 7 = 2.14

Therefore, option (e) is the correct answer.

Hence, the subtended arc is 2.14 times as long as the circle's radius.

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The mean score is 6.48. If we were to give this quiz to more and more students, the mean score for these students would approach 6.48.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

To find the mean score, we need to calculate the expected value of the score. The expected value is calculated by multiplying the score by its probability and summing over all possible scores.

The expected value is:

(5 * 0.06) + (6 * 0.18) + (7 * 0.37) + (8 * 0.22) + (9 * 0.11) + (10 * 0.06) = 6.48

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The solution of Neumann problem, ∇²u= 0 if r < R , Uₙ (R,θ) = f(θ) is u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ) with boundary conditions uᵣ (r,θ) = ∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ) and

Aₙ=∫(f(θ)cosnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Bₙ=∫(f(θ)sinnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Given that

The solution of Numann problem

∇²u= 0 if r < R , Uₙ (R,θ) = f(θ)

Use polar co-ordinates (r,θ)

uᵣᵣ + 1/r uᵣ+ 1/uᵣ (uθθ) = 0 ,0 < r< R,

0 <θ <2π and ∂u/∂r(R,θ) = f(θ) is directional derivative

r²d²u/dr² + rdu/dr + d²u/dθ² = 0

Let , r = ε⁻ᵗ , u(r(t),θ)

uₜ = uᵣ(rₜ) = - e⁻ᵗ uᵣ

uₜₜ =( - e⁻ᵗ uᵣ )ₜ = ε⁻ᵗuᵣ + e⁻²ᵗ uᵣᵣ

= r uᵣ+ r²uᵣᵣ

Thus we have, uₜₜ + uθθ = 0

Let u(t,θ) = X(t)Y(θ)

Which gives X''(t)Y(θ) + X(t)Y"(θ) = 0

X"(t)/X(t) = - Y"(θ)/Y(θ) = λ

From Y"(θ) + λ Y(θ) = 0

We get, Yₙ(θ) = aₙ cosnθ + bₙ sinnθ

λ= n² , n =0, 1, ...

With these values of λn we solve,

X"(t) - n² X(t) = 0

If n = 0 , X₀(t) = c₀t + d₀

X₀(r) = -c₀log (r) + d₀

If n not equal to 0 then

Xₙ (t) = cₙeⁿᵗ + dₙ e⁻ⁿᵗ

Xₙ(r) = cₙ(r)⁻ⁿ + dₙ (r)ⁿ

We have u₀(r, θ) = X₀(r)Y₀(θ)

= a₀ ( - c₀(log r) + d₀)

uₙ(r,θ) = Xₙ(r) Yₙ(θ)

= (cₙ r⁻ⁿ+ dₙrⁿ)(aₙ cosnθ + bₙ sinnθ)

But u must be positive at t =0

So, cₙ = 0 ; n = 0,1,2....

u₀ (r,θ) = a₀ d₀

uₙ(r,θ) = dₙ rⁿ( aₙ connθ + bₙ sinnθ)

By superposition , we can write as

u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ)

Boundary conditions gives

uᵣ (r,θ)=∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ)

the coefficients aₙ , bₙ for n ≥ 1 are determined are Fourier series for f(θ)

but a₀ is not determined from f(θ) therefore , it may take arbitrary value. By using Fourier series,

Aₙ= Integration of(f(θ)cosnθ dθ/π n R⁽ⁿ⁻¹⁾) where θ∈[-π, π]

Bₙ= Integration of (f(θ) sinnθ dθ/π nR⁽ⁿ⁻¹⁾) where θ∈[-π, π]

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Answer: 2

Step-by-step explanation:

The total amount of ticket sales on this day is $1900.

Math has several different subfields, including algebra. Algebra, a common thread that runs through nearly all of mathematics, is the study of mathematical symbols and the rules for using them in formulas.

Elementary algebra is crucial for all mathematical applications since it deals with the manipulation of variables, which are frequently represented by Roman letters, as though they were numbers. The study of algebraic structures such as groups, rings, and fields is known as abstract algebra, mostly in education (the term is no more in common use outside educational context). In contemporary presentations of geometry, linear algebra—which deals with linear equations and linear mappings—is used.

Given,

Number of adult tickets sold by zoo=43

And number of child tickets sold by zoo=80

Also given that,

The cost of each adult ticket=$20

And the cost of each child ticket=$13

20 x 43 = 860

80 x 13 = 1040

860 + 1040 = 1900

Therefore, the total amount of ticket sales on this day is $1900

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The complete question is:

"Question A zoo sells 43 adult tickets and 80 child tickets in one day. Each adult ticket costs $20 and each child ticket costs $13.

What is the total amount of ticket sales on this day?

Enter your answer in the box.

$="

Answer:

It is a observational study

Step-by-step explanation:

An angle is formed when two lines or rays meet at a common point. The common point is known as the vertex.

An angle measurement can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measures in degrees. There are many kinds of angles in geometry such as acute, obtuse, reflex, straight and right angle. Each angle has a different measure.

Angle relationship between the angles made when a line intersects a pair of parallel lines.

In geometry, there are five fundamental angle pair relationships such as complementary angles, supplementary angles, adjacent angles, linear pair, vertical angles.

The more familier unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°. Two angles are complementary if the sum of their measures is 90°.

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Total $234.95 is the cost of 5 band shirts and 5 pair of pants.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given, Molly bought 4 band shirts and 3 pair of pants for $159.99.

And Christian bought 3 band shirts and 2 pair of pants for $113.00.

Let x be the band shirts and y be the pair of pants.

So, according to the question;

4x + 3y = 159.99         equation 1

3x + 2y = 113                equation 2

Now, we have the system of the equations.

In order to solve the system of equations:

Multiply 4 to the equation 2 and multiply 3 to the equation 2.

12x + 9y = 479.97

12x + 8y = 452

Subtracting the transformed equation 2 to transformed equation 1.

y = 27.97

Then 12x = 479.97 - 251.73

 12x = 228.24

x = 228.24 / 12

x = 19.02.

To find the amount of 5 band shirts and 5 pair of pants:

5x + 5y

= 5 (19.02) + 5(27.97)

= 95.1 + 139.85

= 234.95

Therefore, 5 band shirts and 5 pair of pants cost $234.95.

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Answer:

Solution of the given equation by elimination method is x=0.5 and y=5.

Step-by-step explanation:

8x + 7y = 39 --------------(1)

4x - 14y = -68 ------------(2)

Multiply the equation 2 by -2, then add the equations along.

Equation (2) multiply by -2 :  -8x +28y = 136

8x + 7y = 39 --------------(1)

-8x +28y = 136-----------(2)

Add these equations to eliminate x:

0x+35y=175

35y=175

y=5

Substitute y=5 in 8x+7y=39:

8x+(7)(5) =39

8x+35=39

8x=39-35

8x=4

X=8/4

x=0.5

Solution of the given equation by elimination method is x=0.5 and y=5.

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77532 is the total cost to Russell

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Russell Slater bought 700 shares of Disney stock at $106.50 per share

The amount for 700 shares is 700×106.5

74550

commission of 4% of the purchase price.

We have to convert 4% to decimal value by dividing 4 by 100

0.04

Now multiply 0.04 with 74550 to get the commission

0.04×74550

2982

Now add this commission amount with 74550 to find total cost,

2982+74550

77532

Hence, 77532 is the total cost to Russell

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The difference between the numbers 4.7 and 2.3 is 2.4

what is number line ?

The visual representation of numbers on a straight line is called a number line. On an endless line that extends on both sides, either horizontally or vertically, this line is used to compare numbers that are spaced at equal intervals. The numbers on a horizontal number line grow as we approach towards the right side and drop as we move towards the left.

Between 4 and 5 , there are 10 divisions. Each division shows the value 0.1.

So, 4.7 is marked as shown in the figure.

To find the difference 4.7 - 2.3 , reverse the direction by 2.3 units from 4.7, will give us 2.4..

So, the difference between 4.7 and 2.3 is 2.4

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The reasonable 95% confidence intervals for the population mean difference is (7.83, 12.13) , the correct option is (a) .

In the question ,

it is given that ,

90% confidence interval is given as (8.21 , 11.75)

using this interval , we have to find the 95% confidence interval .

Now, [tex]x_{d}[/tex]  - E = 8.21

[tex]x_{d}[/tex] + E = 11.75 , where E is the margin of Error .

Solving the equations ,

we get ,

E = 1.77  and [tex]x_{d}[/tex] = 9.98

So , the margin of error E is given as

E = [tex]t_{\frac{0.10}{2},15 } \times \frac{S.D.}{\sqrt{n} }[/tex]

we have to find standard deviation from this ;

given n = 16 and [tex]t_{\frac{0.10}{2},15 }[/tex] = 1.7531

Substituting in the margin of error equation ,

we get ,

S.D. = (1.77 × 4)/1.7531

= 4.0386

So , the 95% confidence interval is given as [tex]x_{d}[/tex]  ± [tex]t_{\frac{0.10}{2},14 } \times \frac{S.D.}{\sqrt{n} }[/tex] .

from t table , [tex]t_{\frac{0.10}{2},14 }[/tex] = 2.1314

Substituting ,

we get ,

CI = (9.98 ± 2.1314×4.0386/√16)

= (9.98 ± 2.1519)

= ( 9.98 - 2.1519 , 9.98 + 2.1519)

= (7.83 , 12.13)

Therefore , the correct option is (a) (7.83 , 12.13)    .

The given question is incomplete , the complete question is

Based on the 90% confidence interval of (8.21, 11.75) points, which of the following are reasonable 95% confidence intervals for the population mean difference in exam scores before and after taking an exam prep course? Select any that may apply:

(a) (7.83, 12.13)  

(b) (7.53, 11.83)

(c) (8.45, 11.51)

(d) (8.63, 11.33)

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y = 3 + tan (π/4)x , this is the equation of transformed graph of tangent with period 4 that has been shifted vertically up 3 units.

Our parent function:

y = tan x

Let's apply the vertical shift now:

y = 3 + tan x

Now the period. This is a little tricky because we have to remember that the period is equal to π/b, because tangent functions normally have a period of π, and the b is the value placed in front of the x.

In this case, that value would have to be π/4

π/(π/4) = 4

Therefore, our b-value is π/4 and our final equation is as follows:

y = 3 + tan (π/4)x

The question is :

write the equation of the transformed graph of tangent with period 4 that has been shifted vertically up 3 units

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A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. then P(A and B) = 0.18

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

If A and B are events defined on the sample space with P(A) = 0.6 and P(BIA) = 0.3.

To find P(A and B),

we use the formula of conditional probability,

P( A and B ) = P (BIA) P(A)

P( A and B ) = 0.6 × 0.3

P( A and B ) = 0.18

Therefore, P ( A and B ) is 0.18.

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Answer:

  (b)  y=(x+1)²−9

Step-by-step explanation:

You want the vertex form equation of the graphed parabola, which opens upward and has its vertex at (-1, -9).

The vertex form equation for a parabola with vertex (h, k) is ...

  y = (x -h)² +k

The vertex of the parabola shown is (h, k) = (-1, -9). Using these values in the equation gives ...

  y = (x +1)² -9

__

Additional comment

The equation may include a scale factor that multiplies the square. Here, the curve rises 1 unit for 1 unit either side of the vertex, so the scale factor is 1. (The rise at ±1 from the vertex is the scale factor.)

Steps: (1) read the vertex coordinates from the graph; (2) put those coordinates in the vertex form equation; (3) check to see that the vertical scale factor is 1.

The values of x in the triangles are (a) 15 and (b) 4

From the question, we have the following parameters that can be used in our computation:

Triangle 1 and Triangle 2

Solving triangle 1

In this triangle, we can see that the side lengths of the triangles are congruent

This means that the triangles is an equilateral triangle

The individual angles in an equilateral triangle are 60 degrees

So, we have the following representation

4x = 60

Divide both sides of the equation by 4

x = 15

So, the value of x is 15

Solving triangle 2

In this triangle, we can see that the length KM of the triangle divides the length JL into congruent parts

This means that the JM and LM are congruent

So, we have the following representation

x + 1 = 5

Subtract from both sides of the equation by 1

x = 4

So, the value of x is 4

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A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .

Given :

Let N be set of New England states {ME, NH, VT, MA, CT, RI }. (See map provided.) (Note that Maine is abbreviated as ME and Massachusetts as MA.) For each of the following parts, either give an example of a relation on the set of New England states N that has the noted properties, or else show that no such relation exists.

a )

A relation R on N that is reflexive and symmetric but not transitive of example is { N , ME , MA } .

b )

A relation S on N that is reflexive and transitive but not symmetric is { MA , CT , RI } .

c )

A relation T on N that is transitive and symmetric but not reflexive is { ME , NH , VT } .

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The number of seashells that Joan gave to Sam is 43   .

In the question ,

it is given that ,

the total number of seashell that Joan found on the beach is = 70 ,

let the  number of seashells that she gave to Sam be "x" .

the number of seashells that Joan has with her is = 27 .

So , the equation that represents the above situation about the number of seashells is

27 + x = 70

subtracting 27 from both sides of the equation ,

x = 70 - 27

Simplifying further ,

we get ,

x = 43

Therefore , the number of seashells given is 43 .

The given question is incomplete , the complete question is

Joan found 70 seashells on the beach . she gave Sam some of her seashells . She has 27 seashell . How many seashells did she give to Sam ?

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The possible domain of the convergence are b. (-1,3) and c. (-1,3]

Domain of convergence.

In statistics, domain of the convergence also known as interval of convergence means an interval associated with a given power series such that the series converges for all values of the variable inside the interval and diverges for all values outside it.

Given,

Here we need to identify in which of the options are domain of convergence.

As per the definition of domain of convergence, the interval of the convergence is (-∞ , ∞).

So, the possible convergence in the given options are (b) and (c).

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Answer:

b = a - 6

Step-by-step explanation:

Solve for b:

6 + b = a

6 + b - 6 = a - 6

b + 0 = a - 6

b = a - 6