Jill planted two flowers in her garden. The first flower is 2 inches tall, and it is growing 2.25 inches each week. The second plant is 5.75 inches tall, and it is growing 1.5 inches each week. How many weeks will it be until the two plants are the same height?

Answer:

Coefficient of determination = 0.149769  

Step-by-step explanation:

We are given the following in the question:

Coefficient of correlation, r = -0.387

We have to find the coefficient of determination.

Coefficient of determination =

[tex]r^2 = (-0.387)^2 = 0.149769 = 14.98\%[/tex]

Coefficient of determination:

Answer:

f(c) = 3c + 5

Step-by-step explanation:

c is independent variable, p is dependent variable, so p = f(c)

6c = 2p -10

3c = p - 5

p = 3c + 5

f(c) = 3c + 5

Answer:

F(c) = 3c +5  

Step-by-step explanation:

6c=2p-10

If c is considered to be as the independent variable, then p is the dependent variable

So we will clear and solve for variable p

6c = 2p-10

Dividing both sides by 2. We will have  

6c/2 = 2(p-5)/2

3c= p-5  

Adding 5 on both sides

3c+5= p

So p =3c+5

By writing the above equation in the functional notation form  

F(c) = 3c +5  

Answer:

A. It is an equivalence relation on R

B. In fact, the set [0,1) is a set of representatives

Step-by-step explanation:

A. The definition of an equivalence relation demands 3 things:

And the relation ∼ fills every condition.

∼ is Reflexive:

Let a ∈ R

it´s known that a-a=0 and because 0 is an integer

a∼a, ∀a ∈ R.

∼ is Reflexive by definition

∼ is Symmetric:

Let a,b ∈ R and suppose a∼b

a∼b ⇒ a-b=k, k ∈ Z

b-a=-k, -k ∈ Z

b∼a, ∀a,b ∈ R

∼ is Symmetric by definition

∼ is Transitive:

Let a,b,c ∈ R and suppose a∼b and b∼c

a-b=k and b-c=l, with k,l ∈ Z

(a-b)+(b-c)=k+l

a-c=k+l with k+l ∈ Z

a∼c, ∀a,b,c ∈ R

∼ is Transitive by definition

We´ve shown that ∼ is an equivalence relation on R.

B. Now we have to show that there´s a bijection from [0,1) to the set of all equivalence classes (C) in the relation ∼.

Let F: [0,1) ⇒ C a function that goes as follows: F(x)=[x] where [x] is the class of x.

Now we have to prove that this function F is injective (∀x,y∈[0,1), F(x)=F(y) ⇒ x=y) and surjective (∀b∈C, Exist x such that F(x)=b):

F is injective:

let x,y ∈ [0,1) and suppose F(x)=F(y)

[x]=[y]

x ∈ [y]

x-y=k, k ∈ Z

x=k+y

because x,y ∈ [0,1), then k must be 0. If it isn´t, then x ∉ [0,1) and then we would have a contradiction

x=y, ∀x,y ∈ [0,1)

F is injective by definition

F is surjective:

Let b ∈ R, let´s find x such as x ∈ [0,1) and F(x)=[b]

Let c=║b║, in other words the whole part of b (c ∈ Z)

Set r as b-c (let r be the decimal part of b)

r=b-c and r ∈ [0,1)

Let´s show that r∼b

r=b-c ⇒ c=b-r and because c ∈ Z

r∼b

[r]=[b]

F(r)=[b]

∼ is surjective

Then F maps [0,1) into C, i.e [0,1) is a set of representatives for the set of the equivalence classes.

Answer:

Step-by-step explanation:

A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it's width. Let the width of the rug be represented by w. This means that the length of the rug will be w + 2

The total area of the rug (in square inches ) based on the width W of the rug (in inches ) is given by

A(w) = w (2+w)

If the desired area of the rug is 15 square inches,,the width will be determined by substituting 15 for A(w). It becomes

15 = w^2 + 2w

w^2 + 2w - 15 = 0

w^2 + 5w - 3w - 15 = 0

w(w+5) -3(w+5)

w - 3 = 0 or w+ 5 = 0

w = 3 or w = -5

w cannot be negative. So w = 3 inches

Answer:

0.33

Step-by-step explanation:

Two fair number cubes can be thought as dice with sides numbered from 1 to 6. The throw of two dice may result in one of the following combinations in which (d1,d2) are the results of die 1 and 2 respectively:

Ω={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

There are 36 as many possible combinations

The sum of both quantities will produce 11 possible results

S={2,3,4,5,6,7,8,9,10,11,12}

The combinations which produce a sum of 4 are (1,3)(2,2),(3,1), 3 in total

The combinations which produce a sum of 5 are (1,4)(2,3),(3,2),(4,1) 4 in total

The combinations which produce a sum of 6 are (1,5)(2,4),(3,3),(4,2),(5,1) 5 in total

If we want to know the probability that the sum of the results of the throw is 4,5, or 6, we compute the total ways to produce them

T=3+4+5=12 combinations

The probability is finally computed as

[tex]P=\frac{T}{36}=\frac{12}{36}=\frac{1}{3}=0.33[/tex]

Final answer:

To find the probability of getting a sum of 4, 5, or 6 when two dice are rolled, all possible combinations are listed, resulting in 12 favorable outcomes. Those outcomes are then divided by the total number of possible outcomes, 36, resulting in a probability of 1/3.

Explanation:

The question asks about the probability of getting a sum of 4, 5, or 6 when throwing two fair number cubes (dice). Each die has six faces, with numbers ranging from 1 to 6. When rolling two dice, there are 36 possible outcomes (6 outcomes from the first die multiplied by 6 outcomes from the second die).

To find the probability of obtaining a sum of 4, 5, or 6, we first want to identify all the possible combinations that lead to these sums:

Altogether, there are 3 + 4 + 5 = 12 outcomes that result in either a 4, 5, or 6 as the sum. Therefore, the probability is the number of favorable outcomes (12) divided by the total number of outcomes (36), which simplifies to 1/3. Hence, the probability is 1/3.

Answer:

65

Step-by-step explanation:

Answer: 2.33, 1.87, 3.6, 7.1

Step-by-step explanation:

2.33, 1.87, 3.6, 7.1 is not arranged from smallest to the largest. Arranging the number will be 1.87, 2.33, 3.6, 7.1.

Answer:

B. 2.33, 1.87, 3.6, 7.1

Step-by-step explanation:

This option is not in order from smallest to largest.

Hope it helped!

Answer:

Answer is

=950

Answer:

[tex]y=-30x+2380[/tex]

Step-by-step explanation:

[tex]x\rightarrow[/tex] represent price per video game.

[tex]y\rightarrow[/tex] represent demand.

The linear equation in slope intercept form can be represented as:

[tex]y=mx+b[/tex]

where [tex]m[/tex] is slope of line or rate of change of demand of game per dollar change in price and [tex]b[/tex] is the y-intercept or initial price of game.

We can construct two points using the data given.

When price was $66 each demand was 400. [tex](66,400)[/tex]

When price was $36 each demand was 1300. [tex](36,1300)[/tex]

Using the points we can find slope [tex]m[/tex] of line.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{1300-400}{36-66)}[/tex]

[tex]m=\frac{900}{-30}[/tex]

[tex]m=-30[/tex]

Using point slope form of linear equation to write the equation using a given point.

[tex]y-y_1=m(x-x_1)[/tex]

Using point [tex](66,400)[/tex].

[tex]y-400=-30(x-66)[/tex]

⇒ [tex]y-400=-30x+1980[/tex]    [Using distribution]

Adding 400 to both sides:

⇒ [tex]y-400+400=-30x+1980+400[/tex]

⇒[tex]y=-30x+2380[/tex]

The linear relationship between price and demand can be written as:

[tex]y=-30x+2380[/tex]

Answer:

First  quartile  list of number median is 23

Step-by-step explanation:

List of numbers = 42,24, 30 , 22 , 26, 19, 33, 35

Arrange them in a sequence:

List of numbers = 19, 22, 24, 26, 30, 33, 35, 42

The median of {19, 22, 24, 26, 30, 33, 35, 42} is= 26+30/2 = 28

Numbers that are less than the median are { 19 , 22 , 24 , 26}

then

median of the list = 22+24/2 = 23

So the first  quartile  list of number median is 23.

The median of the first quartile list is 23.

The given set of numbers {42, 24, 30, 22, 26, 19, 33, 35} can be arranged in ascending order as follows:

{19, 22, 24, 26, 30, 33, 35, 42}.

The median of this sequence is calculated as (26 + 30) / 2, resulting in 28.

The numbers less than the median are {19, 22, 24, 26}.

Next, the median of this subset is found by taking (22 + 24) / 2, yielding 23. Therefore, the median of the first quartile list is 23.

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The researcher's prediction of an interaction between training and gender is true. An interaction occurs when the effect of one variable on an outcome depends on the level of another variable.

The researcher's prediction of an interaction between training and gender is True.

An interaction occurs when the effect of one variable on an outcome depends on the level of another variable. In this case, the researcher predicts that the training course will have a different effect on females compared to males.

For example, if the researcher conducts a study where both males and females participate in the training course, and finds that females benefit significantly from the course while males do not, this would support the researcher's prediction of an interaction between training and gender.

Answer: length = 8 units

Width = 2 units

Step-by-step explanation:

Let the length of the rectangle be represented by L

Let the width of the rectangle be represented by W

The sum of 5 times the width of a rectangle and twice its length is 26 units. This means that

5W + 2L = 26 - - - - - - - - 1

The difference of 15 times the width and three times the length is 6 units. It means that

15W - 3L = 6 - - - - - - - - 2

The system equations are equation 1 and equation 2.

Multiplying equation 1 by 3 and equation 2 by 2, it becomes

15W + 6L = 78

30W - 6L = 12

Adding both equations,

45W = 90

W = 90/45 = 2

15W - 3L = 6

15×2 - 3L = 6

-3L = 6 - 30 = - 24

L = - 24/ -3 = 8

The length of the rectangle is 8 units, and the width is 2 units. This solution satisfies both equations given.

Let's denote the width of the rectangle as ( w ) units and the length as ( l ) units.

According to the given information, we have two equations:

1. ( 5w + 2l = 26 )  (sum of 5 times the width and twice the length is 26 units)

2. ( 15w - 3l = 6 )  (difference of 15 times the width and three times the length is 6 units)

We can set up a system of equations using these two equations.

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

First, we'll multiply the second equation by 2 to eliminate the ( l ) term:

( 2 x (15w - 3l) = 2 x 6 )

This gives us:

( 30w - 6l = 12 )

Now, we have the system of equations:

1. ( 5w + 2l = 26 )

2. ( 30w - 6l = 12 )

We can now eliminate the ( l ) term by adding these equations together.

( (5w + 2l) + (30w - 6l) = 26 + 12 )

This simplifies to:

( 35w - 4l = 38 )

Now, we have one equation with only ( w ) as a variable.

Now, we can solve for ( w ):

( 35w - 4l = 38 )

( 35w = 38 + 4l )

[tex]\( w = \frac{38 + 4l}{35} \)[/tex]

Now, we can substitute this value of ( w ) into one of the original equations to solve for ( l ).

Let's use the first equation:

( 5w + 2l = 26 )

Substituting[tex]\( w = \frac{38 + 4l}{35} \)[/tex], we get:

[tex]\( 5\left(\frac{38 + 4l}{35}\right) + 2l = 26 \)[/tex]

Now, we can solve this equation for ( l ).

[tex]\( \frac{190 + 20l}{35} + 2l = 26 \)[/tex]

Multiply both sides by 35 to clear the fraction:

( 190 + 20l + 70l = 910 )

Combine like terms:

( 90l + 190 = 910 )

Subtract 190 from both sides:

( 90l = 720 )

Now, divide both sides by 90 to solve for ( l ):

[tex]\( l = \frac{720}{90} \)[/tex]

( l = 8 )

Now that we have the value of ( l ), we can substitute it back into one of the original equations to solve for ( w ). Let's use the first equation:

( 5w + 2(8) = 26 )

( 5w + 16 = 26 )

Subtract 16 from both sides:

5w = 10

Now, divide both sides by 5 to solve for ( w ):

[tex]\( w = \frac{10}{5} \)[/tex]

w = 2

So, the length of the rectangle is 8 units and the width is 2 units.

Answer:

a) 0.30

b) 0.90

c)   0.15

Step-by-step explanation:

When two events are independent then conditional probability take place.

Answer:

The answer to your question is  x - 5 or x = 5

Step-by-step explanation:

                                           [tex]\frac{x^{2} -3x - 10}{x + 2}[/tex]

1.- Factor the numerator

                                       x² - 3x - 10

    find 2 numbers that added equal -3 and multiply equal -10.

    These numbers are -5 and + 2

                                     (x - 5)(x + 2)

2.- Simplify

                                     [tex]\frac{(x - 5)(x + 2)}{x + 2)}[/tex]

Delete (x +2) in both numerator and denominator

3.- Result                       x - 5

                                      x = 5

Answer:

Step-by-step explanation:

In general, wherever a function is tending from the upper left to the lower right, it is decreasing; wherever a function is tending from the lower left to the upper right it is increasing.  Constant functions are horizontal lines.

Our function is tending from upper left to lower right on negative infinity to an x-value of -4.  Then it runs as a horizontal line from x values of -4 to +4.  Then it tends from lower left to upper right from +4 to infinity.

Answer:

The proof is completed below

Step-by-step explanation:

1) Definition of info given

We have the function that we want to maximize given by (1)

[tex]P(L,K)=bL^{\alpha}K^{1-\alpha}[/tex]   (1)

And the constraint is given by [tex]mL+nK=p[/tex]

2) Methodology to solve the problem

On this case in order to maximize the function on equation (1) we need to calculate the partial derivates respect to L and K, since we have two variables.

Then we can use the method of Lagrange multipliers and solve a system of equations. Since that is the appropiate method when we want to maximize a function with more than 1 variable.

The final step will be obtain the values K and L that maximizes the function

3) Calculate the partial derivates

Computing the derivates respect to L and K produce this:

[tex]\frac{dP}{dL}=b\alphaL^{\alpha-1}K^{1-\alpha}[/tex]

[tex]\frac{dP}{dK}=b(1-\alpha)L^{\alpha}K^{-\alpha}[/tex]

4) Apply the method of lagrange multipliers

Using this method we have this system of equations:

[tex]\frac{dP}{dL}=\lambda m[/tex]

[tex]\frac{dP}{dK}=\lambda n[/tex]

[tex]mL+nK=p[/tex]

And replacing what we got for the partial derivates we got:

[tex]b\alphaL^{\alpha-1}K^{1-\alpha}=\lambda m[/tex]   (2)

[tex]b(1-\alpha)L^{\alpha}K^{-\alpha}=\lambda n[/tex]   (3)

[tex]mL+nK=p[/tex]   (4)

Now we can cancel the Lagrange multiplier [tex]\lambda[/tex] with equations (2) and (3), dividing these equations:

[tex]\frac{\lambda m}{\lambda n}=\frac{b\alphaL^{\alpha-1}K^{1-\alpha}}{b(1-\alpha)L^{\alpha}K^{-\alpha}}[/tex]   (4)

And simplyfing equation (4) we got:

[tex]\frac{m}{n}=\frac{\alpha K}{(1-\alpha)L}[/tex]   (5)

4) Solve for L and K

We can cross multiply equation (5) and we got

[tex]\alpha Kn=m(1-\alpha)L[/tex]

And we can set up this last equation equal to 0

[tex]m(1-\alpha)L-\alpha Kn=0[/tex]   (6)

Now we can set up the following system of equations:

[tex]mL+nK=p[/tex]   (a)

[tex]m(1-\alpha)L-\alpha Kn=0[/tex]   (b)

We can mutltiply the equation (a) by [tex]\alpha[/tex] on both sides and add the result to equation (b) and we got:

[tex]Lm=\alpha p[/tex]

And we can solve for L on this case:

[tex]L=\frac{\alpha p}{m}[/tex]

And now in order to obtain K we can replace the result obtained for L into equations (a) or (b), replacing into equation (a)

[tex]m(\frac{\alpha P}{m})+nK=p[/tex]

[tex]\alpha P +nK=P[/tex]

[tex]nK=P(1-\alpha)[/tex]

[tex]K=\frac{P(1-\alpha)}{n}[/tex]

With this we have completed the proof.

Using the Poisson distribution to determine the probability that a page contains exactly 2 errors is 0.0163

Given that, a book contains 400 pages.

There are 80 typing errors randomly distributed throughout the book,

We have to use the Poisson distribution to determine the probability that a page contains exactly 2 errors.

The Poisson distribution formula is given as:

[tex]\text { Probability distribution }=e^{-\lambda} \frac{\lambda^{k}}{k !}[/tex]

Where, [tex]\lambda[/tex] is event rate of distribution. For observing k events.

[tex]\text { Here rate of distribution } \lambda=\frac{\text { go mistakes }}{400 \text { pages }}=\frac{1}{5}[/tex]

And, k = 2 errors.

[tex]\begin{array}{l}{\text { Then, } \mathrm{p}(2)=e^{-\frac{1}{5}} \times \frac{\frac{1}{5}}{2 !}} \\\\ {=2.7^{-\frac{1}{5}} \times \frac{\frac{1}{5^{2}}}{2 \times 1}} \\\\ {=\frac{1}{2.7^{\frac{1}{5}}} \times \frac{\frac{1}{25}}{2}}\end{array}[/tex]

[tex]\begin{array}{l}{=\frac{1}{\sqrt[5]{2.7}} \times \frac{1}{25} \times \frac{1}{2}} \\\\ {=\frac{1}{50 \sqrt[5]{2.7}}} \\\\ {=0.0163}\end{array}[/tex]

Hence, the probability is 0.0163

Answer:

Fraction of cake that was left for Amber = [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given:

Amber had [tex]\frac{3}{8}[/tex] of a cake left after her party.

Amber wrapped a piece of cake for her friend that was [tex]\frac{1}{4}[/tex] of the original cake.

To find the fractional part of cake that was left for Amber.

Solution:

Fraction of cake left Amber had after party = [tex]\frac{3}{8}[/tex]

Fraction of cake she wrapped for her friend = [tex]\frac{1}{4}[/tex]

To find the fractional part of cake that was left for Amber we will subtract [tex]\frac{1}{4}[/tex] of the cake from  [tex]\frac{3}{8}[/tex] of the cake.

∴ Fraction of cake that was left for Amber = [tex]\frac{3}{8}-\frac{1}{4}[/tex]

To subtract fractions we need to take LCD

⇒  [tex]\frac{3}{8}-\frac{1}{4}[/tex]

LCD  will be =8 as its the least common multiple of 4 and 8.

To write [tex]\frac{1}{4}[/tex] as a fraction with common denominator 8 we multiply numerator and denominator with 2.

So, we have

⇒  [tex]\frac{3}{8}-\frac{1\times 2}{4\times 2}[/tex]

⇒  [tex]\frac{3}{8}-\frac{ 2}{8}[/tex]

Then we simply subtract the numerators.

⇒  [tex]\frac{3-2}{8}[/tex]

⇒  [tex]\frac{1}{8}[/tex]

∴ Fraction of cake that was left for Amber = [tex]\frac{1}{8}[/tex]

Answer:

5y = -× + c

Step-by-step explanation:

If two lines are perpendicular, the product of their gradient equals -1.

We should note that the general equation of a line is y = mx + c, where m is the gradient.

For the line y = 5x - 2 , the slope is 5. The line that will be perpendicular to this line will have a slope of -1/5.

A line like 5y = -x + c fits the description

To find the maximum value of f(x) = xa(1−x)b, use calculus to find the derivative of f(x), set it equal to 0, and solve for x to find the critical points. Evaluate f(x) at the critical points and the endpoints of the interval to find the maximum value.

To find the maximum value of f(x) = xa(1−x)b, we can use calculus. First, find the derivative of f(x) with respect to x: f'(x) = a(1 - x)b - bx(1 - x)b-1. Set the derivative to 0 and solve for x to find the critical points. The maximum value of f(x) occurs at one of these critical points or at the endpoints of the interval [0, 1]. Plug the values of x into f(x) to find the corresponding maximum values.

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To find the maximum value of f(x)=xa(1−x)b, where a and b are positive numbers and 0≤x≤1, we need to find the critical points by finding when the derivative of the function is equal to zero or does not exist. Then, we evaluate the function at the critical points and the endpoints to determine the maximum value.

To find the maximum value of the function f(x)=xa(1−x)b, where a and b are positive numbers and 0≤x≤1, we need to determine when the function reaches its maximum. This can be done by finding the critical points, which occur when the derivative of the function is equal to zero or does not exist.

First, let's find the derivative of f(x):

f'(x) = a(1-x)^{b-1}(bx - (b-1)x -1).

To find the critical points, we set f'(x) = 0 and solve for x.

Solving the equation, we find that the critical point occurs when x = \frac{b}{2b-1}.

Next, we evaluate f(x) at the critical point x = \frac{b}{2b-1} and also at the endpoints x = 0 and x = 1. The maximum value of f(x) will be the largest value among these.

Finally, we compare the values to find the maximum value.

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Divide the total cards by 18:

236 / 18 = 13.111

Use the whole number and multiply by 18:

13 x 18 = 234

This means 234 cards would be in storage boxes.

236 - 234 = 2 cards would be left over.

Answer:

x-intercepts: -2; 1; 5

Average rate of change: 1.8

Step-by-step explanation:

x- intercepts as per graph are:

Average rate of change over the interval (-1, 4) is:

The radius of the bowl R as a function of the angle theta is [tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]

Solution:

The figure is attached below

If we consider the centre of hemisphere be A

The radius be AC and AD

According to question,  

A bowl in the shape of a hemispere is filled with water to a depth h=3 inches .i.e. BC = h = 3 inches

And radius of the bowl is R inches .i.e. R = AD =AC

Now , using  trigonometric identities in triangle ABD we get

[tex]\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{A B}{A D}[/tex]

[tex]\begin{array}{l}{\sin \theta=\frac{A B}{R}} \\\\ {A B=R \sin \theta}\end{array}[/tex]

Since , AC = AB + BC

R = R Sinθ + 3

R - R Sinθ = 3

R (1 – Sinθ ) = 3

[tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]

Which is the required expression for the radius of the bowl R as a function of the angle theta

Answer:

The percentage of boys students in Jamie's class is 20 %

Step-by-step explanation:

Given as :

The total number of boys in the Jamie's class = [tex]\frac{1}{5}[/tex] of the total student

Let the total number of student's in the class = x

So, The number of boys =  [tex]\frac{1}{5}[/tex] × x

I.e The number of boys =  [tex]\dfrac{x}{5}[/tex]

So , in percentage the number of boys students in class = [tex]\dfrac{\textrm Total number of boy student}{\textrm Total number of students}[/tex] × 100

OR, % boys students = [tex]\dfrac{\dfrac{x}{5}}{x}[/tex] × 100

or, % boys students = [tex]\frac{100}{5}[/tex]

∴ % boys students = 20

Hence The percentage of boys students in Jamie's class is 20 %  . Answer

Answer:

Step-by-stejfnqe ruhrhe ye\

The Answer is C) Inches

Answer:

  a_n = 2^n + 3

Step-by-step explanation:

The first differences have a geometric progression, so the explicit definition will be an exponential function. (It cannot be modeled by a linear or quadratic function.) The above answer is the only choice that is an exponential function.

__

First differences are ...

  (7-5=)2, 4, 8, 16

Answer: [tex]a_n = 2^n + 3\ \ \ \, n=1,2,3,4,5...[/tex]

Step-by-step explanation:

The given sequence = 5, 7, 11, 19, 35,....

[tex]7-5=2\\11-7=4=2^2\\19-11=8=2^3\\35-19=16=2^4[/tex]

Here , it cam be observe that the difference between the terms is not common but can be expressed as power of 2.

We can write the terms of the sequence as

[tex]2^1+3=5\\2^2+3=4+3=7\\2^3+3=8+3=11\\2^4+3=16+3=19\\2^5+3=32+3=35[/tex]

Then , the required explicit definition that defines the sequence will be

[tex]a_n = 2^n + 3\ \ \ \, n=1,2,3,4,5...[/tex]

Answer:

Step-by-step explanation:

Let x represent the amount invested at 6.25%. Then the total interest earned is ...

  0.0625x + 0.0600(150,000 -x) = 9212.50

  0.0025x = 212.50 . . . . . . subtract 9000, collect terms

  x = 212.50/0.0025 = 85,000

  150,000 - 85,000 = 65,000 . . . . amount invested at the lower rate

$85,000 is invested at 6.25%; $65,000 is invested at 6%.

Answer:

A. decreases if banks increase their desired reserve ratio

Step-by-step explanation:

Since, the money multiplier is the amount of money produced by banks with each dollar of reserves,

In other words,

It estimates, how an initial deposit can lead to a bigger final increase in the total money supply.

For example :

If a commercial bank gains deposits of 1 crore and this leads to a final money supply of 10 crore, the money multiplier would be 10.

That is,

[tex]\text{Money multipliers}=\frac{1}{\text{Reserve ratio}}[/tex]

[tex]\implies \text{Money multipliers}\propto \frac{1}{\text{Reserve ratio}}[/tex]

Therefore, the money multiplier decreases if banks increase their desired reserve ratio

The money multiplier decreases when banks increase their desired reserve ratio, as they lend out less money, reducing the multiplier effect.

The money multiplier is a key concept in understanding how the banking system can increase the money supply within an economy. It is defined as the quantity of money that the banking system is able to generate from each dollar of bank reserves. The question relates the behavior of the money multiplier in response to changes in the reserve ratio and the currency drain ratio.

Answering the student's query, the money multiplier decreases if banks increase their desired reserve ratio because as they keep more reserves relative to deposits, they can lend out less money, effectively reducing the multiplier effect. Conversely, when banks decrease their reserve ratio, they can lend out a larger proportion of their deposits, which leads to an increase in the money multiplier. Therefore, the correct option is A: decreases if banks increase their desired reserve ratio.

Answer:

176 199 pounds

Step-by-step explanation:

To answer this it is first useful to find the proportionality constant.

F= kx

8080 pounds = k.88 in

k = 91.81 pound/inch

So what force is required to stretch the spring to 1919 inches?

F = kx

  = 91.81 pound/inch * 1919 inches

  = 176 199 pounds

It is worth noting that this force seems rather large and the spring might have long reached its elastic limit