A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states.
a) At α = 0.05, is there enough evidence to conclude that there is a difference in the interest rates paid by the two states?
State A:
Sample size 60
Mean interest rate (%) 3.2
Population variance .02
State B:
Sample size 60
Mean interest rate (%) 3.4
Population variance .05

The value of the account is $47226.73.

The compound interest formula is equal to  

A = P( 1 + r/n )^{nt}

where  A is the Final Investment Value, P is the Principal amount of money that is to be invested, r is the rate of interest, t is the Number of Time Periods, and n is the number of times interest is compounded per year.

Now, we have:

t = 21 years

Principal amount, P = $9000

Rate, r = 8% = 0.08 and

n = 12 as a year has 12 months.

Substituting these values in the formula,

\(A = P( 1 + \frac{r}{n} )^{nt}\)

A = 9000 × ( 1 + 0.08/12)²⁵²

A = 9000 × ( 1 + 0.0066)²⁵²

A = 9000 × ( 1.0066)²⁵²

A = 9000 × 5.247

A = 47226.73

The value of the account will be $47226.73.

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Answer:

I don't know the answer am sorry to say

Step-by-step explanation:

ask someone else I just wasted your time

Answer:

Step-by-step explanation:

The equation is:

Simplify:

Solve for x if required:

Answer:

Square based pyramid

Step-by-step explanation:

Answer:

The given figure is a square based pyramid

Using compound interest, it is found that he must invest his money at a rate of 8.78% a year.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

In this problem, the parameters are as follows:

t = 3, A(t) = 60000, P = 46150.3, n = 12.

Hence:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(60000 = 46150.3\left(1 + \frac{r}{12}\right)^{12 \times 3}\)

\(\left(1 + \frac{r}{12}\right)^{36} = 1.3\)

\(\sqrt[36]{\left(1 + \frac{r}{12}\right)^{36}} = \sqrt[36]{1.3}\)

\(1 + \frac{r}{12} = (1.3)^{\frac{1}{36}}\)

\(1 + \frac{r}{12} = 1.00731451758\)

\(\frac{r}{12} = 0.00731451758\)

r = 12 x 0.00731451758

r = 0.0878.

He must invest his money at a rate of 8.78% a year.

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Answer:

7\(\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{98}\) = 7\(\sqrt{2}\)

The exponential equation having y- intercept of 5 and a multiplier of 1.7 is

Hence

, wwhen x = 0

Therefore the correct answer is

Answer:

Simplifying

6x + 32 = 180

Reorder the terms:

32 + 6x = 180

Solving

32 + 6x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-32' to each side of the equation.

32 + -32 + 6x = 180 + -32

Combine like terms: 32 + -32 = 0

0 + 6x = 180 + -32

6x = 180 + -32

Combine like terms: 180 + -32 = 148

6x = 148

Divide each side by '6'.

x = 24.66666667

Simplifying

x = 24.66666667

6x + 32> -4

6x > -4 - 32

6x > -36

x > -6

Answer:

Free Coins!!!

Quadrant 1 if that's what your talking about

The graph below shows a couple of plotting points, one of them being 0,1.

Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

Answer:1296 if I’m not wrong please

Step-by-step explanation:

Step-by-step explanation:

Appropriate Question :

\( \frak{\red{Given}} \begin{cases} & \sf {Area\ of\ the\ square\ field\ is\ 5184m^2.} \\ & \sf {Perimeter\ of\ rectangular\ field\ is\ equal\ to\ perimeter\ of\ square\ field.} \\ & \sf {Length\ of\ the\ rectangular\ field\ is\ twice\ to\ the\ breadth\ of\ the\ square\ field.} \end{cases}\)

Need to find : We have to find the area of the rectangular field.

Let the side of the square field be a.

SidE :-

∴ Hence, the side of the square field is 72m. Now, let's find out the perimeter of square.

⠀⠀⠀⠀⠀━━━━━━━─━━━━━━━

\( \red \bigstar \sf{\underline{Finding\ perimeter\ of\ square:-}} \)

\( \sf \dashrightarrow {Perimeter\ of\ square\ =\ 4a} \\ \\ \sf \dashrightarrow {4 \times 72} \\ \\ \dashrightarrow {\underline{\boxed{\purple{\frak{288m}}}}} \)

∴ Hence, the perimeter of the square field is 288m. Now, let us find out the length and breadth of the rectangular field.

⠀⠀⠀⠀⠀━━━━━━━─━━━━━━━

\( \sf : \implies {Perimeter\ of\ rectangle\ =\ Perimeter\ of\ square} \\ \\ \sf : \implies {2(l\ +\ b)\ =\ 288} \\ \\ \sf : \implies {2(2b\ +\ b)\ =\ 288} \\ \\ \sf : \implies {4b\ +\ 2b\ =\ 288} \\ \\ \sf : \implies {6b\ =\ 288} \\ \\ \sf : \implies {b\ =\ \dfrac{\cancel{288}}{\cancel{6}}} \\ \\ : \implies {\underline{\boxed{\purple{\frak{b\ =\ 48m}}}}} \)

∴ Hence, breadth of the rectangular field is 48m. Now, let's find out the length of the rectangular field.

LengtH :-

∴ Hence, the length of the rectangular field is 96m. Now, let's find out the area of the rectangular field.

⠀⠀⠀⠀⠀━━━━━━━─━━━━━━━

\( \red \bigstar \sf{\underline{Finding\ area\ of\ the\ rectangular\ field:-}} \)

\( \sf : \implies {Area\ of\ rectangle\ =\ l \times b} \\ \\ \sf : \implies {Area\ of\ rectangle\ =\ 96 \times 48} \\ \\ : \implies {\underbrace{\boxed{\pink{\frak{Area\ of\ rectangle\ =\ 4608m^2}}}}_{\sf \blue{\tiny{Area\ of\ the\ field}}}} \)

∴ Hence, area of the rectangular field is 4608m².

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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The use of volunteer sampling means that the result of the survey is potentially misleading.

Volunteer sampling is a sampling technique in which each participant in the sample opts to join the research, as is the case for this problem, as each participant opted to join in the project to compare their cold lengths.

The drawback of this type of sampling is that it should contain lots of participants that share similar characteristics, such as desiring to weight/diet, and this may influence their recovery to cold. The participants also may lie, which can cause misleading results to the study.

Options to remove misleading conclusions is to use a different type of sampling, such as stratified sampling, as groups of people that are either short or long sleepers are compared to reach a conclusion.

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Answer:

A

Step-by-step explanation:

A). Will find you the area so you can find how much soil to cover the entire area

Answer:

(x-1)(-3x-1)

Step-by-step explanation:

A=(b)(h)

Area is base times height and in order to know how much soil to put in you need to find the area of the garden.

Answer:

84.37 %.

Step-by-step explanation:

The question is shown in the attached figure.

We have,

\(f(t)=2t^3+10,\ t=3\)

We can find the value of f(t) at t = 3,

\(f(3)=2(3)^3+10\\\\f(3)=64\)

Finding f'(t).

\(f'(t)=6t^2\)

Finding f'(t) at t = 3

\(f'(3)=6(3)^2\\\\=54\)

The relative change is calculated as :

\(\dfrac{f'(t)}{f(t)}=\dfrac{54}{64}\\\\=0.8437\)

In percentage rate of change,

\(\dfrac{f'(t)}{f(t)}=0.8437\times 100\\\\=84.37\%\)

Hence, the required percent change is 84.37 %.

The value of x in the figure is calculated using the linear pair theorem to be 6 degrees

The linear pair postulate or linear pair theorem in mathematics states that the sum of the measurements of two angles that make up a linear pair is 180°.

Because o the linear pair postulate we have that

150 + 5x = 180

collecting like terms

5x = 180 - 150

5x = 30

Isolating x

5x / 5 = 30 / 5

x = 6

hence x is solved to be 6

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Answer:

Below

Step-by-step explanation:

A vertical line is of the form   x = ....

For this question it would just be    x = 8    

   this line will go through ALL values of 'y'

The equation of the linear relationship in slope-intercept form is y = 2x - 8. Option A is the correct answer.

To determine the equation of the linear relationship in slope-intercept form based on the table, we need to find the slope and y-intercept.

By observing the table, we can calculate the slope by selecting any two points. Let's choose the points (0, -8) and (4, 0).

Slope (m) = (change in y) / (change in x)

= (0 - (-8)) / (4 - 0)

= 8 / 4

= 2

Now that we have the slope, we can find the y-intercept by substituting the values of one point and the slope into the equation y = mx + b and solving for b.

Using the point (0, -8):

-8 = 2(0) + b

b = -8

Therefore, the equation of the linear relationship in slope-intercept form is: y = 2x - 8. Option A is the correct answer.

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Answer:

V = (1/3)π(3^2)(11) = 33π = 103.4

we know the diameter of the cone is 6, so its radius must be half that, or 3.

\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=11 \end{cases}\implies V=\cfrac{\pi (3)^2(11)}{3} \implies V\approx 103.7\)

Answer:

a)

The probability that a newborn elephant weighs between 250 and 275 pounds

P(250≤ x ≤275) = 0.1577

b)

The probability that a newborn elephant weighs more than 210 pounds

P(x >210 ) = 0.6293

Step-by-step explanation:

Step(i):-

Given mean of the Population = 225

Given standard deviation of the population = 45

Let 'X' be the random variable in normal distribution

Let x₁ = 250

\(Z = \frac{x-mean}{S.D} = \frac{250-225}{45} = 0.55\)

Let x₂ = 275

\(Z = \frac{x-mean}{S.D} = \frac{275-225}{45} = 1.11\)

The probability that a newborn elephant weighs between 250 and 275 pounds

P(250≤ x ≤275) =P(0.55≤ Z≤1.11)

                        = P(Z≤1.11) - P(Z≤0.55)

                       = 0.5 + A( 1.11) - ( 0.5 + A(0.55)

                       =  A(1.11) - A(0.55)

                       = 0.3665 - 0.2088

                       = 0.1577

Step(ii):-

The probability that a newborn elephant weighs between 250 and 275 pounds

P(250≤ x ≤275) = 0.1577

b)

Let x = 210

\(Z = \frac{x-mean}{S.D} = \frac{210-225}{45} = - 0.33\)

The probability that a newborn elephant weighs more than 210 pounds

P(x >210 ) = P( Z> -0.33)

                = 1- P( Z < -0.33)

               = 1 - ( 0.5 - A(-0.33))    

               = 0.5 + A( -0.33)

              = 0.5 +  A(0.33)                  (∵ A(-0.33) = A(0.33)  

             = 0.5 + 0.1293  

            = 0.6293

Final answer:-

The probability that a newborn elephant weighs more than 210 pounds

P(x >210 ) = 0.6293

Answer:

See below.

Step-by-step explanation:

1)

So we have:

\(\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2\)

This can be interpreted as:

"There exists a natural number x and an integer y such that x² is equal to y²."

2)

So we want even numbers are in the set of integers.

\(\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}\)

This is interpreted as:

"The set of even numbers (2n such that n is an integer) is in the set of integers"

The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Let the missing number be 'x'. Then the equation is given as,

25 - x = 13

Simplify the equation, then the value of the variable 'x' will be given as,

25 - x = 13

x = 25 - 13

x = 13

The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.

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The maximum and minimum value of η at q = 10 and q = 85 respectively.

The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.

η is the elasticity of demand.

Then, the elasticity of demand is given as:

η = ( dq/ dp) × ( p / q )

Now, we have p = 190/ (q + 10)

Therefore,

p ( q + 10 ) = 190

pq + 10p = 190

q = ( 190 - 10p ) / p

Now,

dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )

dq / dp =  ( -190/ p² )

Substituting these values in the elasticity demand,

η = ( dq/ dp) × ( p / q )

η = ( -190/ p² ) × ( p / q )

η = ( -190/ pq )

η = ( -190/ [190 / (q + 10 ) ]q )

η = [ - ( q + 10 ) / q ]

| η | = | - ( q + 10 ) / q |

η =  ( q + 10 ) / q = 1 + 10/q

The critical point is when | η' | = 0.

η' = ( d / dq ) ( 1 + 10/q )

η' = - 10/ q²

- 10/ q² = 0

Hence, - 10/ q² is not defined.

Therefore, the function is not defined at q = 0.

Therefore, q = 0 is not a solution.

We have 10 ≤ q ≤ 85

The value of functions at the endpoint,

At q = 10,

η = ( 1 + 10/q )

η = ( 1 + 10/10 )

η = 1 + 1 = 2

At q = 85,

η = ( 1 + 10/q )

η = ( 1 + 10/85 )

η = 1.11764

Therefore, the absolute value of the elasticity of demand is maximum at q = 10.

The absolute value of the elasticity of demand is minimum at q = 85.

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Answer:

Vertical (A) The first graph is the correct one

Step-by-step explanation:

The "slope" of a vertical line. A vertical line has undefined slope because all points on the line have the same x-coordinate. As a result the formula used for slope has a denominator of 0, which makes the slope undefined..

The first graph shows the line with undefined slope.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have some graphs as shown in the image.

The slope of the line is the tangent of the angle that the line makes with [+x] axis. So -

tan (90) = sin (90)/cos(90) = 1/0 = undefined

θ = 90 degree

Therefore, the first graph shows the line with undefined slope.

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The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Answer:

500500

Step-by-step explanation:

intergers are whole numbers which are not fractions

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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The sentence which show correct verb tense usage is The overall outlook is favorable.

Verbs are a necessary component of communication in every language, including English, without which it would be difficult to convey what the subject is doing. All acts, including those motivated by sentiments and emotions, are included.

Verbs exist in a variety of forms and kinds so they can function in many ways to convey the whole meaning. Let's have a look at how different dictionaries define the word "verb" before we examine the many kinds of verbs and their forms.

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The graph of the inequality y ≤ 1/3x + 1 is added as an attachment and it is represented with option (c)

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

y ≤ 1/3x + 1

The above expression is an inequality that implies that

Next, we plot the graph

See attachment for the graph of the inequality

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