ind the present value that will grow to ​$4000 if the annual interest rate is ​8.5% compounded quarterly for 9 yr.

Equation that represents the total time t (in minutes) Ken spent running is = 10 + m/6.30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Total time t (in minutes) =Initial Time + distance/speed

Given :-

Thus,

t = 10 + m/6.30.

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Using a system of equations, it is found that there were 4,000 children tickets sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given by:

The attendance at the amusement park is 5,000 attendees, hence:

x + y = 5000 -> y = 5000 - x.

Considering the cost of parking and that the total money earned by the park is $100,000, we have that:

15x + 40y = 100000

Applying the multiplication of the matrices, these equations are the same that the system gives. Replacing the second equation into the first:

15x + 40(5000 - x) = 100000

25x = 100000

x = 100000/25

x = 4000.

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Using the distance between two points, it is found that you travel approximately 41 meters.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, we have that:

Hence the distance is:

D = sqrt[(-15 - (-25))² + (15 - (-25))²] = sqrt(10² + 40²) = 41 meters.

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Answer: 2

Step-by-step explanation:

[tex]y=\frac{1}{3}x^2 +2x+5 \longrightarrow \frac{dy}{dx}=\frac{2}{3}x+2[/tex]

Setting this equal to 0 yields [tex]x=-3[/tex].

When [tex]x=-3[/tex], [tex]y=2[/tex]

Answer:

Step-by-step explanation:

Given quadratic equation:

Its leading coefficient is positive, so it has minimum value at vertex.

The x-coordinate of the vertex is:

Substitute the coefficients:

Find the value of y at vertex:

The matching answer choice is A.

Answer:

1) (3,1)

2) (4,1)

3) No solution

Step-by-step explanation:

The solution is point where the graphs cross.  It is a little hard to see the pictures, but I think that I have the right ordered pairs.  The ordered pairs are in the order (x,y).  The x tells you how far (in these cases), the point is right of the origin (0,0 the middle of the whole graph).  The y tells us (in these cases) how high the point is from the origin (0,0).

The last answer has no solution because the lines are parallel and they do not cross.

We need to use a technique called dot multiplication. In this technique, we multiply the magnitude of two given vectors by the value of the angle between them.

In the question, the value of the angle between two vectors [tex]cos(45^0)[/tex] and the coordinates of the two vectors are given. Let's multiply them by the dot product to get the result.

Formula: [tex]u.v=|u||v|cos(a)[/tex]

[tex]u=3i+2j[/tex]
[tex]v=i+5j[/tex]
[tex]cos(a)=\frac{1}{\sqrt{2}}[/tex]

To find the magnitude of a vector, we square the coordinates, add them up and take the square root of the result.

Result: [tex]u.v=|\sqrt{(3^2)+(2^2)}||\sqrt{(1^2)+(5^2)}|.\frac{1}{\sqrt{2}}=(13\sqrt{2})\frac{\sqrt{2}}{2} =13[/tex]

The area of the rhombus is 100 mm². The correct answer is D.

A rhombus is one type of parallelogram and has 4 sides and 4 vertices.

Every side is equal in length and opposite angles are equal.

Given:

A rhombus with horizontal diagonal length 25 millimeters,

and vertical diagonal length 8 millimeters.

Let d₁ = 25 mm and, d₂ = 8 mm.

Let A be the area of rhombus.

To find the area of rhomus:

Using diagonals,

A = (1/2) × d₁× d₂.

Substituting the values of diagonals,

A = 1/2 x 25 x 8

A = 200/2

A = 100 mm².

Therefore, 100 mm² is the area of the rhombus.

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Using the hsd test qcrit = 3.65  

HSD testis used to check differences among sample way for significance. The Tukey's HSD assessments all pairwise variations at the same time as controlling the probability of making one or greater type I errors.

A Tukey-Kramer test lets us check the null speculation of no distinction between the population approach for all pairs of businesses. The Tukey-Kramer check (also known as a Tukey sincere importance test, or Tukey HSD), is carried out in R inside the function.

solution

given;

   using HSD test, the degree of freedom = 16

                                                         and α=0. 05

                                                         groups = 3

                         Hence,                    Qcrit = 3.65    {using HSD table}

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The zeroes of the function g(x) = x² +3x -4 as given in the task content is; x = -4 and x = 1.

It follows from the task content that the function g(x) given in the task content is; g(x) = x² +3x -4.

On this note, it follows that the zeroes of the function can be determined by solving the quadratic function as follows;

x² +4x -x -4 = 0

(x+4) (x-1) = 0

Ultimately, it can be concluded that the values of x which represents the zeroes of the function are; x = -4 and x = 1.

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Answer:

$2,450

Step-by-step explanation:

21:150 is the ratio of people who will donate $5.

21:150 / 3 = 7:50

7:50 x 2 = 14:100

14:100 = 21:50

14:100 x 35 = 490:3500

490 out of 3500 people will contribute $5.

490 x 5 = $2,450

See attachment for the graph of cell phone plan 1: y= 7.5x and cell phone plan 2: y= 5.5x + 10.1

Linear equations are equations that have constant average rates of change, slope or gradient

The cell phone plans are given as:

Cell phone plan 1: y= 7.5x

Cell phone plan 2: y= 5.5x + 10.1

To plot the graph of both plans, we make use of the following domain for both cell phone plans

Domain: x >= 0

Next, we set x = 0, 1, 2, 3, 4 and 5 for both plans

So, we have:

Cell phone plan 1

y= 7.5x

When x = 0, y = 7.5 * 0 = 0

When x = 1, y = 7.5 * 1 = 7.5

When x = 2, y = 7.5 * 2 = 15

When x = 3, y = 7.5 * 3 = 22.5

When x = 4, y = 7.5 * 4 = 30

When x = 5, y = 7.5 * 5 = 37.5

Cell phone plan 2

y= 5.5x + 10.1

When x = 0, y = 5.5*0 + 10.1 = 10.1

When x = 1, y = 5.5 * 1 + 10.1 = 15.6

When x = 2, y = 5.5 * 2 + 10.1 = 21.1

When x = 3, y = 5.5 * 3 + 10.1 = 26.6

When x = 4, y = 5.5 * 4 + 10.1 = 32.1

When x = 5, y = 5.5 * 5 + 10.1= 37.6

Next, we plot both graphs on the domain x >= 0

See attachment for the graph of cell phone plan 1: y= 7.5x and cell phone plan 2: y= 5.5x + 10.1

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If the side are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].

Given that area of a shape of 37 [tex]mm^{2}[/tex] in which 60% is green.

We are required to find the area of green region if the side is increased by 45%.

Area is basically part of a surface covered by a shape.

When the side is increased by 45% then the area will increase by 45%*45%=20.25%.

Increased area =37*20.25%=7.4925

New area=37+7.4925

=44.4925

We have been given that 60% is the area of green.

Area of green region=44.4925*60/100

=26.6955 [tex]mm^{2}[/tex]

Hence if the sides are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].

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Answer: (x) = x^3 − x^2 − 4x + 4End behavior- Falls to the left rises to the righty intercept-(0, 4)Zeros- (1,-2,2)g(x) = x^3 + 2x^2 − 9x − 18

Step-by-step explanation:

Answer:

Option A - 32 cm³

Step-by-step explanation:

Volume of a pyramid is given by the formula :

V = [tex]\frac{lwh}{3}[/tex]

Substituting values given gives us :

V = (4)(4)(6)/3

V = (16)(6)/3

V = 96/3

V = 32

Units will be cm³ as this is volume

Hope this helped and have a good day

Answer:

A. 32 cm³

Step-by-step explanation:

V = (1/3)(area of base)(height)

The base is a square of side 4 cm.

area of base = side × side

V = (1/3)(4 cm × 4 cm)(6 cm)

V = 32 cm³

Using proportions, the length of x is of 2.9.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The triangles are similar, that is, they have the same angles, hence the corresponding sides are proportional, by the following rule of three:

x/7 = 5/12

Applying cross multiplication:

12x = 35

x = 35/12

x = 2.9.

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The measure of Arc AU of the given Circle Geometry is; 50°

The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”

We can express the above theorem as;

Angle at the center = 2 × Angle at the circumference

From the attached image below  and from the given statement in the question, we are given that; ∠QUA = 111°

Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA

m∠QDA = 2 × 111° = 222°

Which gives;

∠QOA =  = 360° - 222° = 138°

∠QOA = ∠QOU + ∠UOA (by angle addition property)

Thus;

∠QOA = 138° = 88° + ∠UOA

∠UOA = 138° - 88° = 50°

Thus, the measure of Arc AU is;

Arc AU = ∠UOA = 50°

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Answer: b

Step-by-step explanation:

Answer:

1.36mph

Step-by-step explanation:

The escalator is moving at 2ft/s, lets convert this to miles/second.

2ft/s = 0.000378788miles/s.

Now that we have the miles/second lets multiply this value by 3600 to get the miles/h, because there are 3600 seconds in an hour.

2ft/s=1.3636368miles/h

Or approximately 1.36miles/h.

The correct function that has been represented on the graph is,

f(x) = { 2 if -1 < x ≤ 2 as the values of f(x) for the other two parts, -6 ≤ x ≤ -1 and 2 ∠ x ≤ 6 are (2x+17)/5 and (16-7x)/2 respectively.

This can be broken into three parts :

   y-3/x+1 = 2/5

  5y -15 = 2x +2

  2x - 5y = -17

 y-1/x-2 = -7/2

 2y -2 = -7x + 14

2y + 7x = 16

Thus function becomes

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Answer:

25.0

Step-by-step explanation:

Notice that points A, B, and C form a right triangle. This allows us to use the Pythagorean theorem, a^2 + b^2 = c^2, to find the missing side. AB is the hypotenuse, so substitute 55 for c, and BC is the leg, so substitute 49 into either a or b in the formula.

a^2 + b^2 = c^2

49^2 + b^2 = 55^2

b^2 = 3025 - 2401

b^2 = 624

b = sqrt (624)

b = 24.9799919936

The coordinate of P is (A) ( 40, 96).

To find What are the x- and y- coordinates of point p on the directed line segment from K to J:

It can be seen from the figure the coordinates of K and J:

The coordinates of P can be determined as:

[tex]x=\frac{m}{m+n} (x_{2}-x_{1})+x_{1} } \\y=\frac{m}{m+n} (y_{2}-y_{1})+y_{1} } \\[/tex]

So, as the P point divides the line into three-fifths of the length,

Which gives the ratio as 3: 2.

m:n = 3:2

Therefore, the coordinate of P is (A) ( 40, 96).

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The complete question is shown below:

What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J?

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

(A) (40, 96)

(B) (85, 105)

(C) (80, 104)

(D) (96, 72)

Using proportions, it is found that it took 15 days for the students to finish the project.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, we have that:

The compound rule of three is given as follows:

1 project - 5 students - 15 days

0.4 project - 2 students - x days

Increasing the number of students, the number of days is reduced, hence the measures are inverse proportional and the rule of three is given by:

[tex]\frac{15}{x} = \frac{2}[5} \times \frac{1}{0.4}[/tex]

[tex]\frac{15}{x} = \frac{2}{2}[/tex]

15/x = 1

x = 15 days.

It took 15 days for the students to finish the project.

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logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x

What is logarithmic equation?

The given logarithmic equation is;

[tex]log x = 4[/tex]

Since, log with base 10 is written as [tex]log x[/tex]  simply, therefore, we have:

[tex]log_{10} x[/tex] = 4

Using the definition of logarithm, we get;

[tex]x = 10^{4}[/tex]

Equivalently, [tex]10^{4} = x[/tex]

Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x

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The complete question is -

Which exponential equation is equivalent to this logarithmic equation?

log x = 4

0.9544 = 95.44% of scores lie between 220 and 380 points.

Normal distribution problems can be solved using the Z-score formula.

With a set of means and standard deviations, the Z-score for measure X is given by: After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is less than X. H. Percentile of X. Subtract 1 from the p-value to get the probability that the value of the measure is greater than X.

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

We are given mean 300, standard deviation 40.

This means that µ= 300, σ = 40

What proportion of scores lie between 220 and 380 points?

This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.

X = 380

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

Z= (380-300)/40

Z= 2

Z=2 has a p-value of 0.9772.

X=300

[tex]z = \frac{x - \mu}{\sigma} \,[/tex]

Z= (220-380)/40

Z=-2

Z=-2 has a p-value of 0.9772.

0,9772 - 0,0228 = 0,9544

0.9544 = 95.44% of scores lie between 220 and 380 points.

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The number has over positive integer divisors. One of them is chosen at random. If each divisor has the same probability, then the likelihood that a random one will be odd is precisely 1/19. This assumes that all divisors have the same probability. This is further explained below.

Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.

In conclusion, The number may be divided into more than positive integers. A selection is made at random from among them. If each divisor has the same probability, then the chance that a random one would be odd is exactly 1/19. This assumes that each divisor has the same probability. This makes the assumption that the probability of each divisor is the same.

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MOV EBX,EAX

SHL EAX,4

SHL EBX,1

ADD EAX,EBX these are the  series of instructions that will multiply eax by 18, using a combination of shift, mov, and add instructions.

STEPS:

1. Copy EAX into another register, say EBX

2. We know that shift left by 'n' bits results in multiplication with 2^'n' , so perform shift left operation of EAX by 4 bits ( results in multiplication of EAX with 16) and perform shift left operation of EBX by 2 bits(results in multiplication of EBX with 2)

3. Now add EAX and EBX which is the required answer ( Since, i*16 + i*2 equals to i*18 )

INSTRUCTIONS:

mov ebx,eax ; make copy

shl eax,4 ; eax * 16

shl ebx,1 ; ebx * 2

add eax,ebx ; answer

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Answer:

[tex] - 0.2026[/tex]

Step-by-step explanation:

I hope it is the right answer

Answer:

(-1, 5) and (3, -3)

Step-by-step explanation:

The solutions are all the points where the two functions intersect. Since the lines intersect at two different points, there are two solutions.

The two points at which the functions appear to intersect are (-1, 5) and (3, -3).

Answer:

ph : perimeter = 4 sides of the base; p*h = the area of the sides of that prism

B : 2 areas of the base = top and bottom

A right prism consists of a rectangle and two undersides S night prism =

 S rectangle + 2S base

the length of the rectangle is the circumference of the base which is P  so A = ph + 2B