Mr. Wright is investing $1 million. He has options with Bank of Munich, Coralbank, and Lone Star Credit Union.
Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.
Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.
Lone Star Credit Union is offering an interest rate of 1.75% on all funds invested with them.
Mr. Wright plans to leave whatever funds he invests in the account for 15 years.
ROUND ALL ANSWERS TO THE NEAREST TEN THOUSAND AND DO NOT USE COMMAS IN YOUR RESPONSE.
How much money should Mr. Wright expect to have after 15 years if he invests all of his funds with Coralbank?
How much money would he have if he invests everything with Bank of Munich for the full 15 years?
If he plans carefully and invests his funds to gain the maximum amount of interest across all three institutions, how much money will he have in each bank
after 15 years?
Bank of Munich:
Coralbank
Lone Star Credit Union:

We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

The correct interpretation of a 99% confidence interval is that we are 99% confident that the true population mean falls in it.

The probability that it contains the true population mean is 99%.

Given  99% confidence interval : 4.1 < μ < 5.6

Then, the correct interpretation is we are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

Hence the answer is We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

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Using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

A shape's area can be calculated by contrasting it with squares of a known size.

The square meter (abbreviated as m2), which is the area of a square whose sides are one meter long, is the common unit of area in the International System of Units (SI).

Three such squares would be the same size as a form with a three-square-meter area.

The area of any other shape or surface is a dimensionless real number, and the unit square is defined in mathematics to have area one.

So, the area of the square:

A = b²

Where B is the square's long side.

A = 450in²

A = b²

b² = 450

b = √450

b = 15√2 in

Therefore, using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².

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Correct question:
Which represents a side length of a square that has an area of 450 square inches?

a. 15 start root 2 end root inches in.

b. 16 start root 3 end root inches in.

c. 112. 5 in.

d. 115. 5 in.

The number of ways to divide the shares into 10 equal segments is 120

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

Total number of segments, n = 10

Numbers to people, r = 3

The number of ways of dividing the segment is then calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation, so, we have the following representation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have the following representation

Total = 10!/7!3!

Evaluate the quotient

Total = 120

Hence, the number of ways is 120

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Answer:

(2x - 1) (4x + 3)

Step-by-step explanation:

Answer:

x = -2y - 4

Step-by-step explanation:

x + 2y = -4

Subtract 2y from both sides.

x = -4 - 2y

Answer:

x = 2

this is the answer hope u pass

Answer:

C = 50.27

Step-by-step explanation:

Hope this helps!

Answer:

C = 16 pi

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi * r

C = 2 * pi * 8

C = 16 pi

V=Vw-ce^-kt is the velocity V as a function of time t when wind is blowing 20 knots and after 1 half hour the boat moves at 10 knots

Acceleration is a vector quantity that is defined as the rate at which an object's velocity varies. When an object's velocity changes, it is said to be accelerating.

On occasion, sports broadcasters will suggest that a person is accelerating if they are traveling quickly. But speed has nothing to do with acceleration. Even while traveling very quickly, a person may not be accelerating. Changing the speed at which an item is travelling is what acceleration is all about. A substance is not accelerating if its velocity is not changing. The information on the right depicts an object that is speeding as it moves northward. Throughout time, the velocity is shifting. Every second, the velocity is changing by a fixed amount of 10 m/s.

How to solve?

Based on the information from the exercise, we have the equation:

dt/dv=k(Vw−V)

where V is velocity of the boat in knots/hour, tt is time in hours, Vw is velocity of wind.

This equation can be written:

dv/dt = k(Vw -V)

dv/Vw-V =kdt

Now, the variables are separated, tt appears only on the right side, and v only on the left. Integrate the left side in relation to v, and the right side in relation to t:

dv/Vw-V =kdt

∫dv/Vw-V =∫kdt

let Vw -V = u

-dv=du

dv= -du

∫-du/u =k∫dt

-ln|u| =kt +C

-ln|Vw-V| = kt + C

V=Vw-ce^-kt

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Answer:

20 cm²

Step-by-step explanation:

It is a right triangle.

So, using Pythagorean theorem: OS² = OR² - RS²

OR = r (radius) + 8

OS = r

RS = 16

=> r² = (r+8)² - 16²

r² = r² + 16r + 64 - 256

r² = r² + 16r - 192

16r = 192

r = 192 / 16 = 12cm²

a) 12 cm²

b) 12 + 8 = 20 cm²

Answer:

Step-by-step explanation:

The easiest way to do this is to clear the decimal by multiplying the numerator and the denominator by

10

.

You can reduce the fraction later.

40

m

48

m

2) Reduce the fraction to its simplest form

Cancel out

8

from the top and the bottom

5

m

6

m

←

answer

This answer means that the numerator and denominator of the given fraction

4

m

4.8

m

are in a

5

:

6

ratio relationship with each other.

Check

Is

4

4.8

equal to

5

6

?

Cross multiply

(

4

)

(

6

)

should be equal to

(

5

)

(

4.8

)

24

is equal to

24.0

C

h

e

c

k

answer:

1.92 pounds or 23/12 lb

step-by-step explanation:

first convert 3/4 and 1/3 to fractions that have the same denominator such as 9/12 and 4/12. then add the two numbers together and subtract it by 3 to get the answer. hope that helps!

The confidence interval for the true percent of car owners in the city  who received a speeding ticket be, (139.27 , 160.73).

Subtract 1 from your sample size. 1000 – 1 = 999. This provides the degrees of freedom.

Subtract the confidence level from 1, and then divide by two.

(1 – .95) / 2 = .025

Now, df = 999 and α = 0.025

from the table at df = 999 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

150 / √(10) = 4.74

Now, 2.262 × 4.74 = 10.73

So, the confidence interval be,

(150 - 10.73 , 150 + 10.73) = (139.27 , 160.73)

Hence, the confidence interval for the true percent of car owners in the city  who received a speeding ticket be, (139.27 , 160.73).

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The rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces will be M(a²+b²)/3.

Any item that can be rotated has the property of rotational inertia. It is a scalar value that indicates how challenging it is to alter an object's rotational velocity around a certain rotational axis. The role of mass in linear mechanics is analogous to that of rotational inertia in rotational mechanics. Because it measures moment of inertia as it is rotating, this property is also known as rotational inertia. A measurement of an object's resistance to changes in its angular velocity is called rotational inertia. Imagine turning an item with a specific torque. As the torque is being applied, measure the angular acceleration. The rotational inertia of the item increases as the resultant angular acceleration decreases.

Here,

The major calculations are attached in image.

Moment of Inertia of plate passing through O is I = Ma²/12

and, ly = Mb²/12

by perpendicular axis theorem I2 = Ma²/12+Mb²/12

The distance of edge and the center is d = √(a²+b²)/4

So by parallel axis theorem, IA = Ma²/12+ Mb²/12 + Md² = M(a²+b²)/3

M(a²+b²)/3 is the rotational inertia of the block about a rotating axis passing through one of its corners and perpendicular to its large faces.

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The probability that her third child would be a girl is 50%.

Probability:

In math probability means the possible of happening a particular event amount the total number of event.

Given,

Here we need to find if a woman's first child is a girl and her second child is also a girl, what is the probability that her third child would be a girl.

We already know that, there are two sex chromosomes X and Y.

And in the humans are diploid having two sex chromosomes, in females a pair of the X chromosome is found while in males an X and Y chromosome is present.

So, there is  50% chance that the subsequent child is going to be a girl because it entirely depends upon the chromosome of the sperm which fertilizes the ovum.

For each pregnancy features a  50% chance of leading to a boy or girl and this doesn't include the likelihood of multiples.

Here already having 2 girls previously doesn't affect the probabilities of any resulting pregnancy.

Therefore, the prospect of getting a girl remains at  50%.

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The integration of the given function is as follows.

What is anti derivative?

In calculus, an antiderivative, inverse derivative, primitive perform, primitive integral or integral of a perform f could be a differentiable perform F whose spinoff is adequate to the initial perform f. this could be explicit symbolically as F' = f

Main body:

f (x) = x/8 +1/8x + (1/8)^x

to find the anti derivative , we need to integrate the function;

apply sum rule:

[tex]\int\ f{(x)} + g (x)\, dx[/tex] = [tex]\int\ f {(x)} \, dx + \int\ g {(x)} \, dx[/tex]

[tex]\int\ {(x/8)} \, dx[/tex] = x² /16

[tex]\int\ f {(1/8x)} \, dx[/tex] = 1/8 ln|x|

[tex]\int\ f {(1/8^x)} \, dx[/tex] = [tex]-\frac{1}{3\ln \left(2\right)\cdot \:8^x}[/tex]

hence

[tex]\int \frac{x}{8}+\frac{1}{8x}+\frac{1}{8^x}dx[/tex]= [tex]\frac{x^2}{16}+\frac{1}{8}\ln \left|x\right|-\frac{1}{3\ln \left(2\right)\cdot \:8^x}+C[/tex]

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Answer:

-2.8y-7.52

Step-by-step explanation:

multiply 0.4 by each of the numbers in the parentheses then simplify

Answer: -2.8y-7.52

Step-by-step explanation:

Sketching the nyquist plot based on the bode plots for the mentioned systems require a certain understanding of bode plots explained in detail.

In reality, Bode plots are a collection of graphs that display a system's frequency response. This system might be any system (not simply a circuit!) that changes its behavior when its frequency (cycles per second) changes.

Frequency Response simply describes how our system will alter in response to a specific input frequency. This collection of notes will be referred to as our input frequency.

Bode charts often have two graphs. We'll refer to one as the magnitude plot and the other as the phase angle plot.

We'll need something initially called a transfer function. Typically represented as H(s) or H(j). A transfer function often equates to the ratio of the output to the input.

A). >KG ( s) a= K( s+2 ) / s + 10 B.>KG ( s) = K / ( s + 10 )(s+2)2 C).>KG ( s) = K (s+10)(s+10) / (s+100)(s+2)3 D)

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I believe the answer you seek would be that the area of the shaded region would be [tex]64.43 cm^2[/tex].

Hope this helps!

Answer: y=2x-1

Step-by-step explanation:

(1,1) (2,3) (3,5) (4,7)
1=2(1)-1
3=2(2)-1
5=2(3)-1
7=2(4)-1

Answer: 29 inches.

Step-by-step explanation:

The formula to find the hypotenuse is a^2 + b^2 = c^2.

20^2= 400, and 21^2=441. Together, it was 841. Square root that, and your answer is 29.

-

a^2 + b^2 = c^2

20^2 + 21^2 = c^2

400 + 441= c^2

881 = c^2

29=29

The ordered pair that lie on the graph of the exponential function ​f(x)=3(14)ˣ is (-1, 12)

A curve that depicts an exponential function is known as an exponential graph.

The curve have a horizontal asymptote and either an increasing slope or a decreasing slope. this is to say that the curve begins as a horizontal line, increases or drops gradually, and then the growth or decay accelerates. It may or may not cut the x-axis, but it always cuts the y-axis at some point.

An exponential graph will almost always have a y-intercept but not necessarily an x-intercept.

The given function was plotted on a graph and the point that lie on the graph is (-1, 12).

the point (-3,-192)  is way out of the graph

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The population of the small town in 2025 is 22234

The given parameters in the question are

These parameters can be represented as

a = 24597

r = 2%

The equation of the function can be represented as

P(t) = a(1 - r)^t

So, we have

P(t) = 24597 * (1 - 2%)^t

In 2025, we have

Year = 2025

This means that

t = 2025 - 2020

So, we have

t = 5

Substitute t = 5 in P(t) = 24597 * (1 - 2%)^t

P(5) = 24597 * (1 - 2%)^5

Evaluate the expression

P(5) = 22234

Hence, the population is 22234

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The number of revolution per minute for Gear C is 200 rpm

It is given that

The gear ratio r:s is ratio of number of teeth of two connected gear

Also , the gear A is rotated at rate of = 100rpm

Since, Gear A has 20 teeth and Gear B has 60

Ratio = r : s

=> 20 : 60

=> 1 : 3

Thus , the ratio of number of revolution per minute for two gear is s:r

=> 3 : 1

Means Gear A turns at 3 rpm , Gear B turns at 1 rpm

Similarly , for Gear B and Gear C

The ratio of rpms for these two will be =>

10 : 60

=> 1 : 6

That is , when Gear B turns at 1rpm , Gear C turns at 6rpms

Therefore, If Gear A turns at 100 rpms

the Gear B turns at = 100/3 rpms

Hence , Gear C turns at = 100/3 × 6

=> 200 rpms

I've answered the question in general as the question is incomplete

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A right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

The right circular cylinder is a cylinder with circular bases that are parallel to one another.

Three dimensions make up its form.

The two bases of the cylinder are joined at their centers by the cylinder's axis.

Sphere:

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the right circular cylinder will be:

The formula for the volume of a sphere: V = 4/3πr²

Now, substitute r = 12 as shown:

V = 4/3πr²

V = 4/3π12²

V = 4/3π144

V = 7238.22947

Rounding off: 7238 units³

Nw, the formula for the volume of a right circular cylinder:

V = πr²h

Substitute V = 7238 and calculate for r as follows:

V = πr²h

7238 = πr²h

r² = 7238/πh

r = √7238/πh

Therefore, a right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.

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The squares cut from the corners should be large in width and length 6 to hold the box as much as possible. The dimensions of the box with the largest volume are 6 x 6.

If the squares cut from the corners are h × h inches

The open-top box will have

A height of h

A width of 12 - 2h

and a length of 12 - 2h

So its volume will be

V(h) = h × (12 - 2h) × (12 - 2h)

= 4h³ - 48h² + 144h    (square inches)

dV/dh= 12h² - 96h + 144

Critical points occur when the derivative (dV/dh) is zero.

12h² - 96h + 144 = 0

h² - 8h + 12 = 0

(h − 2)(h − 6) = 0

It is clear that h = 6 is not the crucial point for the maximum as it would produce widths and lengths of zero (and so a volume of zero).

In order to cut out squares measuring 6 × 6 inches from the corners of the bigger sheet, the most volume may be obtained.

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The total number of sessions they did in that year will be equal to 20.

Equations are mathematical expressions with two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be similar to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a simple fundamental equation.

As per the data given in the question,

The charge per session = $25

Annual membership charge = $45

Total money paid = $545

Money left after paying for the annual membership = $545 - $45= $500

The total number of sessions in $500 will be,

T = 500/25

T = 20 sessions.  

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The degrees of freedom for goodness-of-fit chi-square tests are calculated with the formula: df=bins(or categories)−1−number of parameters of the distribution and the degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) .

In the given question we have to calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity.

When a categorical variable has more than two levels, a chi-square goodness-of-fit test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.

The degrees of freedom in this case are calculated with the formula:

df=bins(or categories)−1−number of parameters of the distribution.

The degrees of freedom for the chi-square are calculated using the following formula:

df = (r-1)(c-1)

where r is the number of rows and c is the number of columns.

The null hypothesis can be rejected if the observed chi-square test statistic is higher than the crucial value.

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Look at the point in which the x-value is equal to -1

k(-1) = 7