How long does it take for an investment of $6,400 to increase to $14,000 if
it is invested at 5% per year compounded continuously? Round to the
nearest tenth of a year.

Answer:

25

Step-by-step explanation:

A. y = 3x-1; slope is 3 and y-intercept is -1

B. -x+3 = y; slope is -1 and y-intercept is 3

C. x-3 = y; slope is 1 and y-intercept is -3

D. y = 1-3x; slope is -3 and y-intercept is 1

In math, slope interceptor form is the method of writing an equation for a line in the form y = mx + b.

Slope-Intercept form

The slope - intercept form equation with slope m and y intercept c is given by, y = mx+c

Option A:

y = 3x-1

slope m = 3

y-intercept c = -1

Option B:

-x+3 = y

slope m = -1

y-intercept c = 3

Option C:

x-3 = y

slope m = 1

y-intercept c = -3

Option D:

y = 1-3x

slope m = -3

y-intercept c = 1

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The required inverse function of the given function is given as f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and the range of the inverse function is all real numbers.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
f(x) = -x + 9 / [8 + 9x]
Now,
y = f(x)
y = -x + 9 / [8 + 9x]
x = 9 - 8y / [1 + y]
Now,
x ⇄ y
y = 9 - 8x / 1 + x
Now y = f⁻¹[x]
f⁻¹(x) = [9 - 8y] / [1 + y],

Thus, the required inverse function is f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and its range is all real numbers.

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The value of /BD/ in the quadrilateral is 16.9m

A quadrilateral is polygon with four sides, four angles, four vertices, two diagonals  whose sum of angles is 360 degrees

The diagonal of the quadrilateral forms a triangle.

From the triangle ΔABD, two sides are given with an included angle.

/AB/=16m

/AD/=19m

/BD/=?

To find the length /BD/

let it be a.

Using cosine rule, we have

a²=b²+d²-2bdcosA

a²=19²+16²-2*19*16*cos57⁰

Simplifying the formula

a²=361+256-608*0.5446

a²=617-311.1168

a²=285.8832

taking the square of both sides we have

a=√285.8832

a=16.9m

Therefore the length of the side /BD/ = 16.9m

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The probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.

What is a probability distribution?

A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.

In the case of rolling a die until the first time that a six turns up, the probability distribution for t (the number of rolls it takes to get a six) would describe the probability of getting a six on each roll.

The probability of getting a six on the first roll is 1/6, since there is a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the second roll is 1/6, since there is still a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the third roll is also 1/6, and so on.

The probability distribution for t in this case can be represented by the following table:

t Probability

1 1/6

2 1/6

3 1/6

4 1/6

5 1/6

... ...

This probability distribution indicates that the probability of getting a six on the first roll is 1/6, the probability of getting a six on the second roll is 1/6, and so on.

Hence, the probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.

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Yes, it is possible to use the law of cosines to solve for one angle in a triangle.

The law of cosines states that in any triangle, the square of the length of any side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those sides and the cosine of the angle between them (C):

c^2 = a^2 + b^2 - 2ab * cos(C)

If you know the lengths of all three sides of a triangle (a, b, and c), you can use the law of cosines to solve for the cosine of one of the angles (C). Once you have the cosine of the angle, you can use the inverse cosine function (also known as the arccosine) to find the measure of the angle in degrees.

For example, if you know the lengths of sides a and b and the measure of angle C in a triangle, you can use the law of cosines to find the length of side c:

c = sqrt(a^2 + b^2 - 2ab * cos(C))

Alternatively, if you know the lengths of sides a and c and the measure of angle B in a triangle, you can use the law of cosines to find the length of side b:

b = sqrt(c^2 - a^2 - 2ac * cos(B))

In both cases, once you have found the value of one of the sides, you can use the law of sines to find the measure of the remaining angle in the triangle.

The dimensions giving the minimum surface area are  r = 0.98 cm approx. and h = 1.998 cm .

What is surface area?

The surface area of a solid object could be a live of the full area that the surface of the article occupies.

Main body:

The surface area of the closed cylinder is given by,

S = 2πr²+2πrh

And volume is given by,

V = πr²h

Where, R is radius and h is height of cylinder.

Volume is given to be  6 cm³.

V = πr²h = 6

h = 6/πr²

Inserting this value of h in Surface area equation, we get,

S = 2πr²+ 2πr ( 6/πr²)

S = 2πr² + 12 /r

Now differentiating wrt x to find minimum, inserting ds/dr = 0 , we get,

4πr = 12/r²

r = (3/π)¹/³

r = 0.98 cm approx.

h = 6/π *(0.98)²

h = 6/3.017

h = 1.998 cm

Hence ,the dimensions giving the minimum surface area are  r = 0.98 cm approx. and h = 1.998 cm .

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Answer: 10

Step-by-step explanation: As I said in your previous question, we can make this an addition problem, to make it easy, and make more sense. S0, it would be 5+5, which is our answer; 10. I hoped this helped

Pseudocode doesn't depend on the syntax and subtitles of a particular programming language, so his readers will be able to understand it as long as they know at least one language.

In computer science, pseudocode is a undeniable language description of the stairs in an set of rules or any other system. Pseudocode frequently makes use of structural conventions of a regular programming language, however is supposed for human studying as opposed to gadget studying. Pseudocode is known via way of means of the programmers of all types. it allows the programmer to pay attention most effective at the set of rules a part of the code development. It can't be compiled into an executable program.

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Complete question:

Ryland is creating an article about commonly used compression algorithms for an online educational site.

He's debating whether to express each algorithm in natural language, flow charts, pseudocode, or C++, a general-purpose programming language.

Which of these is a good argument for expressing the algorithm in pseudocode?

Answer:

a) [tex]A(x)=360x-2x^2[/tex]

b) [tex]90m[/tex]

c) [tex]16200m^2[/tex]

Step-by-step explanation:

This is related to a differential topic called optimisation.

We here have two sides of the field that are equal to [tex]x[/tex], and another unknown (that we will call [tex]y[/tex]). Maya has 360m of fencing, so we will say that [tex]2x+y=360[/tex], and this means that [tex]y=360-2x[/tex].

Our first task is to find a function for the area of the field. We know that the area of a field is length × width. We know we have a length of [tex]y[/tex] which is [tex]360-2x[/tex] and a width of [tex]x[/tex], therefore:

[tex]A(x)=x(360-2x)=360x-2x^2[/tex]

To find the maximum value of [tex]x[/tex], we must first differentiate the function:

[tex]A'(x)=360-4x[/tex]

We must then set the equation equal to 0 and solve for [tex]x[/tex], where the line/curve would be stationary.

[tex]360-4x=0[/tex]

[tex]4x=360[/tex]

[tex]x=90[/tex]

Finally, to find the maximum area, we would substitute this value of [tex]x[/tex] back into the original equation:

[tex]A(x)=360x-2x^2\\\\A(90)=360(90)-2(90)^2\\\\A(90)=16200[/tex]

For the following:

(a) To find a function A(x) that gives the area of the field in terms of x, use the information given about the fencing and the shape of the field.

Let the length of the other two sides (perpendicular to the side with length x) be y (in meters).

The perimeter of the rectangle is given by the sum of all four sides:

Perimeter = 2x + 2y

According to the problem, the perimeter is 360 meters, set up an equation:

2x + 2y = 360

Now, solve this equation for y in terms of x:

2y = 360 - 2x

y = (360 - 2x) / 2

y = 180 - x

The area A(x) of the rectangle is given by the product of its length (x) and width (y):

A(x) = x × y

A(x) = x × (180 - x)

(b) To find the side length x that gives the maximum area for the field, maximize the function A(x) from part (a). To do that, take the derivative of A(x) with respect to x, set it equal to zero, and solve for x:

A(x) = x × (180 - x)

dA/dx = (180 - x) - x

dA/dx = 180 - 2x

Now, set dA/dx = 0 and solve for x:

180 - 2x = 0

2x = 180

x = 90

So, the side length x that gives the maximum area is 90 meters.

(c) Now there is the value of x, find the maximum area by substituting x = 90 into the area function A(x) from part (a):

A(x) = x × (180 - x)

A(90) = 90 × (180 - 90)

A(90) = 90 × 90

A(90) = 8100

The maximum area that the field can have is 8100 square meters.

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Answer:

Deepak have taken 5 days leave from the start of the work.

The numbers of each beads that Sharon will need to make all of the key chains is given as follows:

The amounts for each bead are obtained applying the proportions built from the image given at the end of the answer.

From the images, for a single key chain, the amounts needed are given as follows:

Hence, for each 4 green beads, 3 red beads are needed. For 20 green beads, the number of red beads needed is given as follows:

3/4 x 20 = 60/4 = 15 red beads.

For each 4 green beads, 6 blue bears are needed. For 20 green beads, the number of blue beads needed is given as follows:

6/4 x 20 = 120/4 = 30 blue beads.

The image is given at the end of the answer.

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The probability states that- (r+w+b+g)min =21,

Probability refers to possibility.

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

According to our question-

r−3=4w,r−2=3b,r−1=2g

r=4w+3,r=3b+2,r=2g+1

rmin=11⇒w min=2⇒bmin​=3⇒g min =5

Hence,  (r+w+b+g)min =21,

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At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n, then E(Y1) = w

Let W be the total weight of all people in the elevator at a given time and N be the number of people in the elevator at a given time.

E(W) = E[E(W|N)]

Since N and Y are independent, we can also write with mean:

E(W|N) = E[E(W|N,Y)]

Since the weight of each person is independent of the others, we can write:

E(W|N,Y) = E[E(W|N,Y1)]

Since Y is a continuous random variable and the weights of each person are independent, we can further write:

E(W|N,Y1) = E(Y1) = w

Therefore, we can conclude that:

E(W) = E[E(W|N)] = E[E(W|N,Y)] = E[E(W|N,Y1)] = E(Y1) = w

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Answer isn't one of your options, it is 34.

[tex]f(9) = (3(9)+7)[/tex]

[tex]f(9) = (27+7)\\ \\f(9) = 34[/tex]

[tex]f(9) = 34[/tex].

Answer: correct answer is A

Step-by-step explanation:The numbers of sets which cannot represent the lengths of the sides of a triangle are 8, 9, 11.We have to determineWhich set of numbers cannot represent the lengths of the sides of a triangle?According to the questionThe length of sides which can not form a triangle is determined in the following steps given below.

Answer:

The correct answer is A.

Step-by-step explanation:

You have to look at the triangle inequality theorem where a + b ≥ c. Any two sides of a triangle must be greater than or equal to the third, in this case, 1 ft + 3 ft only = 4. Therefore A does not represent the length of 3 sides of a triangle.

Hope this helps, Have an amazing day!

After 26 years Judy purchased the home for $109,000.

What is function?

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.

A function is a relationship between a set of inputs and a set of potential outputs, where each input is related to exactly one output.

Given:

Judy purchased a home in 1956.

The function represents y, the value of the home x years since 1956.

f(x) = 11,500(1.09)^x

Let Judy purchased the home for $109,000.

We have to find the the number of years when Judy purchased the home for $109,000.

Plug f(x) = 109,000 in the above equation.

109,000 = 11,500(1.09)^x

218/23 = (1.09)^x

Taking log on both sides,

ln(218/23) = ln(1.09)^x

ln(218/23) = x ln(1.09)

             x = ln(218/23)/ln(1.09)

             x = 26.097

⇒           x ≈ 26

Hence, after 26 years Judy purchased the home for $109,000.

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Answer:

in the picture

Step-by-step explanation:

in the picture

As per the least-squares regression,

a) The residual for the high school senior with a foot length of 20cm and a height of 160cm is 2.94

b) As per the given standard deviation, the value of the context 5.9

The term standard deviation in math is defined as a measure of how dispersed the data is in relation to the mean.

Here we have given that the random sample of 65 high school seniors was selected from all high school seniors at a certain high school.

And we need to find following.

While we looking into the given question, as per the least-squares regression line, here the estimated height for a high school senior with a foot length of 20 cm is calculated as,

=> y = 2.599x + 105.08

Now, we have to apply the value of x as 20, then we get,

=> y = 2.599(20) + 105.08

=> y = 157.06

Therefore, the residual is calculated as,

=> 160 − 157.06 = 2.94

b) As per the given standard deviation, here the differences between each data point and its corresponding estimate varies with a standard deviation of 5.9 cm.

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A study about the diet of undergraduate students,

5) Chi-square statistic test , would use to determine if the observed and expected frequencies of diets are consistent. With null hypothesis as the observed and expected frequencies of diets are consistent.

6) The excepted students to eat

meat = 165

exclusively vegetarian= 6

strict vegetarian= 1

7) Chi-square statistic value is 62.755 and degree of freedom are 2 . The critical value for Chi-square statistic is 0.00001

8) P-value< 0.05, so reject the null hypothesis.

Therefore there is no sufficient evidence to support that the observed and expected frequencies of diets are consistent.

A random sample of undergraduates in the University of Virginia dining hall.

Sample size , n = 175

Three categories are given as shown in above table with percentage of report eating a diet.

Report also consists observed values about the number of students diet including the three different categories

5) The Chi-square test would use to determine the required result. Consider Null and alternative hypothesis as :

H₀ : the observed and expected frequencies of diets are consistent

Hₐ : the observed and expected frequencies of diets are not consistent

χ² =∑(Oᵢ - Eᵢ)²/Eᵢ

where, χ² --> chi-square cofficient or value

Oᵢ --> observed values which are provided

Eᵢ --> excepted values

Excepted values , Eᵢ = n× p

here we assume that,

6) The number of students would you expect to eat meat = 168

The number of students would you expect to eat exclusively vegetarian

= 6.125 ~ 6

The number of students would you expect to eat strict vegetarian = 0.875 ~ 1

7) Degree of freedom,df = k - 1 = 2, where k denotes total number of categories here

Chi-square statistic, χ² = ∑(Oᵢ - Eᵢ)²/E

χ² = 62.755

Using chi-square table, the critical chi-square value for χ² = 62.755 and degree of freedom 2 is 0.00001 ..

8) Significance level, alpha = 0.05

As we see that p-value = 0.00001< alpha = 0.05

So, we reject the null hypothesis.

Thus, there is no sufficient evidence to support null hypothesis.

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We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.

  y=mx+b is the slope intercept formula

The given equation is y=2x-7.

By comparing to slope intercept formula y=mx+b,

   m=2 and b=-7.  

   So the slope of the given equation is 2 and y-intercept is (0,-7).

we know that,

             m=rise/run

             so rise=2 and run=1 that means Sam needs to count up 2 and right 1 to graph the equation using the given slope.

We can use the concept of Line Intercept form . She should count up 2 and right 1 . So the correct option is D.

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For the number of calls greater than 140, the plan [1] is more economical than plan [2].

Given is that a telephone company offers two billing plans for local calls. Plan 1 charges ​$25 per month for unlimited calls and Plan 2 charges ​$18 per month plus ​$0.05 per call.

For the part [1] -

25 < 18 + 0.05x

25 < 18 + 0.05x

25 - 18 < 0.05x

7 < 0.05x

x > (7/0.05)

x > 140

For part [2] -

For the number of calls greater than 140, the plan [1] is more economical than plan [2].

Therefore, for the number of calls greater than 140, the plan [1] is more economical than plan [2].

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Answer:

for g(-2)

we wil take -1/4 x -1

so g(-2) = - 1/2

for g(1)

we will take (x+1)²

so g(1) = (1+1)² = 4

for g(2)

we will take (x+1)²

so g(2)= ,(2+1)² = 9

Answer:

good job

Step-by-step explanation:

Answer:

[tex]61.8^{\circ}[/tex]

Step-by-step explanation:

Vertical angles are congruent

Answer:

61.8

Step-by-step explanation:

The measure of angle C is 61.8 degrees.

Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. They are called "vertical" because they are opposite each other and share the same vertex (the point at which the two lines intersect). Because vertical angles share the same vertex, they are always congruent, which means that they have the same measure.

In this case, angles C and E are a pair of vertical angles, so they are congruent. Since the measure of angle E is 61.8 degrees, the measure of angle C must also be 61.8 degrees. Therefore, the answer is 61.8 degrees.

Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. the length of FG is  x + 1.

Generally, A distance may be measured in terms of its length. A quantity that has the dimension distance in the International System of Units is referred to as length. In the vast majority of measuring systems, a length base unit is selected, and it is from this unit that all other units are derived.

The meter serves as the fundamental measuring device for length in accordance with the International System of Units.

Since the ratio of the sides of the two pentagons is 4:1, the length of FG is 1/4 of the length of AB.

Therefore, the length of FG is

(1/4)(4x + 4) = x + 1.

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Complete Question not found

Image not found

Answer:

its 1/4

Step-by-step explanation:

Step 1: Calculate the ratio of the side lengths for the original image to the corresponding side lengths of the transformed image using side FG and its corresponding side in

The kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.

In the given question, the charge on an electron is 1.60218 x 10^(-19) C and its mass is 9.10939 x 10^(-31) kg.

We have to find the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT.

E = 0.18 kV/m

B = 1.1 mT

mass m = 9.10939*10^(-31) kg

Then force on a moving charge in electric and magnetic field = Lorentz force

F = qE+ q*VB

So,

F = qE+ q*VB = 0

E = V*B

Find V , so

V = E/B

V = 0.18*10^3 /( 1.1*10^-3)

V =163637 m/s

so KE = 1/2*m*v^2

Then put values..

KE = 0.5*9.11*10^(-31)*163637^(2)

KE = 1.2197*10^(-20) J

in eV = 1.2197*10^-20 / ( 1.6*10^-19 )

eV = 0.07623125 eV

Hence, the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.

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Answer:

Step-by-step explanation:

986