A small treasure chest is in the shape of a rectangular prism.
The length of the chest is y feet, the width ½ y feet, and the height
2y feet. The chest holds 8 cubic feet of treasure. What are the
dimensions of the treasure chest?

Using L'Hopital's rule  `18 lim z->8 (1 + 8/z)^(z/8) = 18e^8`

Given information; f(8) = 6 and f'(8) = 4.

Suppose f(8) = 6 and f'(8) = 4. Find the following. Part A: `el (z) - e6`

We know that; $e^0 = 1$ and $e^x > 0$ for all $x$.

Therefore, `el (z) - e6 = e^0 - e^6 = 1 - e^6`

Part B: `lim x->24x - 32 ef(x) -6 - f(x) + 5 x² + 16x + 64`Let, `y = x - 8`

Then, `x = y + 8` and `f(x) = f(y + 8)`

Now, rewrite the expression in terms of `y`;`lim y->0 ((2y + 8)^2 - 32) (f(y + 8) - 6 - f'(8)y + 5y^2 + 32y + 64)`

Using the given values;`lim y->0 ((2y + 8)^2 - 32) (f(y + 8) - 6 - 4y + 5y^2 + 32y + 64)`

Part C: `18 lim z->8 = 8`

Using L'Hopital's rule;`lim z->8 (1 + 8/z)^(z/8) = e^8`

Therefore, `18 lim z->8 (1 + 8/z)^(z/8) = 18e^8`

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The equation of the straight line is y = -2x - 4, the value of x₁ is -1 and the value of y₁ is -2.

To find the equation of a straight line given its slope and one point, we use the point-slope form of the equation:

−y − y₁​ = m(x−x₁ )

where m is the slope of the line, and (x₁, y₁) is the given point.

In this case, m = -2 and the point is (-1, -2). So we have:

x₁ = -1

y₁ = -2

m = -2

Substituting these values into the point-slope form, we get:

y−(−2)=−2(x−(−1))

Simplifying and rearranging terms, we get the equation of the line:

y + 2 = -2x - 2

y = -2x - 4

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For the linear equations provided by the coordinates in the table;

The first equation of this system is y = -2x.

The second equation of this system is y = x - 3.

The solution to the system is (1, -2).

We have four points (-5,10), (-1,2), (0,0), and (11,-22) for first equation, and four points (-8,-11), (-2,-5), (1,-2), and (7,4) the second equation.

The slope (m) is given by the formula (y2 - y1) / (x2 - x1).

For the first line, we can use the points (-5,10) and (-1,2)

m1 = (2 - 10) / (-1 - (-5)) = -8/4 = -2.

the first equation is y = -2x

the second line, we can use the points (-8,-11) and (-2,-5)

m2 = (-5 - -11) / (-2 - -8) = 6/6 = 1.

the second line has a slope of 1,

the equation should have the form y = x + c.

To find c, we can use one of the points, for instance (-2,-5):

-5 = -2 + c => c = -5 + 2 = -3.

So, the second equation is y = x - 3.

the solution to the system, we need to find where the two lines intersect.

y = -2x

y = x - 3

Setting both equation equally

-2x = x - 3

=> 3x = 3

=> x = 1.

Substituting x = 1 into the first equation

y = -2(1) = -2.

the solution to the system of linear equation would be (1, -2).

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Answer:

$90

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 9%/100 = 0.09 per year,

then, solving our equation

I = 2000 × 0.09 × 0.5 = 90

I = $ 90.00

The simple interest accumulated

on a principal of $ 2,000.00

at a rate of 9% per year

for 0.5 years is $ 90.00.

For a repeated measures ANOVA for n = 78, k = 7, SSb = 8, SSw = 8, SSerror = 71 , the value of Mean Square Error Term is  1  .

The Mean Squares Error Term (MSerror) is calculated by dividing the sum of squares error (SSerror) by the degrees of freedom for error (dfe), which is equal to (n - k). So , we have:

⇒ MSerror = (SSerror)/(dfe) ,

For n = 78 and k = 7 ,

We get ,

The degree of freedom for error (dfe) = 78 - 7 = 71 ,

So , MSerror = (SSerror)/(dfe) ,

⇒ MSerror = 71/(78 - 7) ,

⇒ MSerror = 71/71 ,

⇒ MSerror = 1

Therefore, the value of MSerror is equal to 1.

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The given question is incomplete , the complete question is

For a repeated measures ANOVA, given n = 78, k = 7, SSb = 8, SSw = 8, SSerror = 71 . What is the value of the mean squares error term (MSerror)?

Daniel's method is incorrect, as the interquartile range is given by the difference between the third quartile and the first quartile.

The interquartile range of a data-set is by the difference of the 75th percentile(Q3) by the 25th percentile(Q1) of the data-set.

The quartiles are described as follows:

From this, we get that the quartiles are related to the median of the set, that is, neither is given by the highest and by the lowest values, hence the interquartile range is given by the difference between the third quartile and the first quartile.

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The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

Answer: X=74

if you want to be shown step by step comment below

Answer:

The slope of the line is -2.

Step-by-step explanation:

y = mx + b

The "m" variable is the slope.

m = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1}}\)

\(y_{2}\) is the second "y" value given in the table. \(y_{1}\) is the first value given. Same thing for \(x_{2}\) and \(x_{1}\).

m = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1}}\)

m = \(\frac{(-5) - 3}{(-1) - (-5)}\)

m = \(\frac{-8}{4}\)

m = -2

Answer:

b = 6.1 ft

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here A = 10.98 and h = 3.6 , then

\(\frac{1}{2}\) × b × 3.6 = 10.98

1.8b = 10.98 ( divide both sides by 1.8 )

b = 6.1

The  line at the coffee shop during rush hour is 15 people long.

Given:

- 5 people arrive at the coffee shop each minute.

- Each person has to wait for 3 minutes to be served.

Since 5 people arrive each minute,  the rate of people entering the line is 5 people/minute.

Now, Each person has to wait for 3 minutes to be served.

So, Average length of line = Rate of people entering * Time for a person to be served

Average length of line = 5 people/minute * 3 minutes

Average length of line = 15 people

Therefore, on average, the line at the coffee shop during rush hour is 15 people long.

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Answer: both of you have a lead yet but you can get it right away if I can see you guys again in a developer way but I have a game pass

Step-by-step explanation: yes

(a) ∑n=1[infinity]8n7n is a geometric series and it diverges. Answer: DIV.

(b) ∑n=2[infinity]13n is a geometric series and it diverges. Answer: DIV.

(c) ∑n=0[infinity]3n92n+1 is a geometric series and it converges. Sum = 2.452.

(d) ∑n=5[infinity]7n8n is a geometric series and it converges. Sum = 0.0954.

(e) ∑n=1[infinity]7n7n+4 is a geometric series and it converges. Sum = 3.5

(f) ∑n=1[infinity] 7/8*\((7/8)^{(n-1)\) + \(3/8*(3/8)^{(n-1)\). Both of these are geometric series and the series converges. Sum= 1.6.

(a) This series can be rewritten as ∑n=1[infinity]\((8/7)^n\). This is a geometric series with ratio r=8/7 which is greater than 1. Hence, the series diverges. Answer: DIV.

(b) This is a geometric series with first term a=13 and common ratio r=13. Since |r|>1, the series diverges. Answer: DIV.

(c) This series can be written as ∑n=0[infinity] \(3^n/(9^2)^n\) * \(9^{(1/(2n+1))\). The first part of the series is a geometric series with a=1 and r=3/81<1. The second part of the series is also a geometric series with a=\(9^{(1/3)\) and r=\((9^{(1/3)})^2=9^{(2/3)\)<1. Therefore, the series converges. To find the sum, we use the formula for the sum of an infinite geometric series:

sum = a/(1-r) + b/(1-c)

where a and r are the first term and common ratio of the first geometric series, and b and c are the first term and common ratio of the second geometric series. Substituting the values, we get:

sum = 1/(1-3/81) + \(9^{(1/3)}/(1-9^{(2/3))\)

= 1.01 + 1.442

= 2.452

Answer: 2.452.

(d) This series can be written as ∑n=5[infinity] \((7/8)^n\). This is a geometric series with ratio r=7/8 which is less than 1. Hence, the series converges. To find the sum, we use the formula for the sum of an infinite geometric series:

sum = a/(1-r)

where a and r are the first term and common ratio of the series. Substituting the values, we get:

sum = \((7/8)^5/(1-7/8)\)

= \(7/8^4\)

= 0.0954

Answer: 0.0954.

(e) This series can be rewritten as ∑n=1[infinity] \((7/7.4)^n\). This is a geometric series with ratio r=7/7.4<1. Hence, the series converges. To find the sum, we use the formula for the sum of an infinite geometric series:

sum = a/(1-r)

where a and r are the first term and common ratio of the series. Substituting the values, we get:

sum = 1/(1-7/7.4)

= 3.5

Answer: 3.5.

(f) This series can be rewritten as ∑n=1[infinity] \(7/8*(7/8)^{(n-1)\) + \(3/8*(3/8)^{(n-1)\). Both of these are geometric series with ratios less than 1, so the series converges. To find the sum, we add the sums of the two geometric series:

sum = 7/8/(1-7/8) + 3/8/(1-3/8)

= 1 + 3/5

= 1.6

Answer: 1.6.

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The length of arc QS is approximately 2.09 units.

The length of an arc of a circle:

Length of arc = (central angle / 360) × 2 × π × radius

Central angle is the angle in degrees formed by the two radii that define the arc and radius is the radius of the circle.

In this case, we are given that m∠QRS = 30 means that the central angle formed by radii QS and QR is 30 degrees.

We are also given that QR = 4 unit

The radius of the circle is also 4 units.

Substituting these values into the formula, we get:

Length of arc QS = (30 / 360) × 2 × π × 4

Simplifying and rounding to the nearest hundredth we get:

Length of arc QS ≈ 2.09

The length of arc QS is approximately 2.09 units.

An arc of a circle's length:

Arc length equals (central angle / 360) divided by 2 and radius.

Radius is the diameter of the circle, while central angle is the angle, in degrees, produced by the two radii that constitute the arc.

In this instance, we are told that mQRS = 30 denotes the centre angle of 30 degrees created by radii QS and QR.

Also stated is that QR equals 4 units.

The circle also has a radius of 4 units.

When these values are added to the formula, we obtain:

Arc length QS = (30 / 360) 2 4

Rounding to the closest hundredth and simplifying, we obtain:

Arc length QS = 2.09

Arc QS has a length of around 2.09 units.

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The equation representing the cost of each teacup is given as follows:

4c + 18 = 42.

Hence the cost is of: $6.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The meaning of the slope and of the intercept for this problem are given as follows:

Hence the function is given as follows:

C = xc + 18.

(as the cost of the pot is of $18).

4 teacups push the price up to $42, hence the equation is given as follows:

4c + 18 = 42

4c = 24

c = 6.

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Answer:

C

Step-by-step explanation:

11 | 2   means    112

A is wrong because 11 | 2 cannot mean 12.

B is wrong because stem with value 1 doesn't exist.

D is wrong because stems and leaves are not added to give real value.

Hope this helps!

The solution of the system of equations f(x) = 2^x + 1 and g(x) = 3^x is x = 1

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

f(x) = 2^x + 1

g(x) = 3^x

The above expression is a system of exponential equations

We are required to solve by graph

That implies that we graph the equations in the system on the same plane and write out ordered pairs from the point of intersection of the equations in the system

Next, we plot the graph

See attachment for the graph of the equations

The ordered pairs of the intersection point is (1, 3)

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Given the word problem, we can deduce the following information:

1. The ratio of the two complementary angles is 3:7.

To determine the measures of both angles, we must note first that complementary angles are two angles whose measures add up to 90°. So our equation would be:

We simplify the equation above:

We plug in x=9 into 3x to get the first angle:

Angle 1 = 3x = 3(9) = 27

Then, we plug in x=9 into 7x to get Angle 2:

Angle 2= 7x=7(9)=63

Therefore, the measures of both angles are 27° and 63°.

Answer:

3?

Step-by-step explanation:

It depends on the price of the bottle, for example if the bottle is $1 then you can buy 3 but if it's 50¢ then you can buy 6. If there is tax then the amount of bottles you buy will be less than what it be without tax

The greatest possible value of a b ca b c occurs when aa, bb, and cc are the largest possible digits.

This value can be calculated by subtracting the two largest values of b n b_n from c n c_n for different values of nn and finding the maximum result.

Let's consider the largest possible digits for aa, bb, and cc. Since aa, bb, and cc are nonzero digits, the largest possible digit is 9.

To find the greatest possible value of a b ca b c, we need to find the maximum difference between c n c_n and b n b_n for different values of nn. Since a na n ​ has nn digits with all digits equal to aa, the maximum value of a na n ​ is nn times aa.

For b nb n ​, we have nn digits with all digits equal to bb, so the maximum value of b nb n ​ is nn times bb.

Lastly, for c nc n ​, we have 2n digits with all digits equal to cc. The maximum value of c nc n ​ is 2n times cc.

To find the maximum difference between c n c_n and b n b_n, we subtract b nb n ​ from c nc n ​:

c n - b n = (2n * cc) - (nn * bb)

We can calculate this difference for different values of nn and find the maximum result. The largest possible value of a b ca b c occurs when this difference is maximum.

Please note that specific values of nn, aa, bb, and cc are not provided, so we cannot calculate the exact value. However, the approach described above can be used to find the greatest possible value based on the given conditions.

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We have a purchase of $1,300,000.

The downpayment is $150,000 and the rest is financed.

We can calculate the amount that is owed as:

This amount will be paid in equal amounts, monthly for 20 years.

The interest rate is 16% compounded quarterly.

We have to start by converting the interest rate in a monthly-compounded equivalent rate.

A rate of 16% compounded quarterly (m=3) will be equivalent to a monthly rate r. We can calculate r as:

We then can calculate the payments as an annuity with r = 0.013 and 20*12 = 240 payments.

We can calculate the amount he will pay each month as:

Answer: the monthly payment is approximately $15654.45.

Answer:

The anwser to this is 41

Step-by-step explanation:

91 - 7 = 82, 82/2 = 41

Answer:

0.24

Step-by-step explanation:

$1.20 ÷ 5 = 0.24

To check that we are going to multiply \(5 x 0.24 = $1.20\\\)

I hope this helps and have a great day!

Answer:

Which number is missing?

40   38   35   31   26   20   13   5

Pattern: ( -2, -3, -4, etc)

40 - 2 = 38

38 - 3 = 35

35 - 4 = 31

31 - 5 = 26

26 - 6 = 20

20 - 7 = 13

13 - 8 = 5

Step-by-step explanation:

You're welcome.

Answer:

2 solutions

-1 and 3 is the real solutions

Answer:

The answer is : Rational

Answer:

Step-by-step explanation:

Reflection over any line is a rigid transformation that does not change angles or lengths. Dilation is a transformation that changes lengths by the same scale factor, but has no effect on angles. Dilated figures are similar to the original.

When ΔXYZ is reflected over a vertical line, no lengths or angles are changed. When the reflected triangle is dilated by half, we get ...

  Y'X' = (1/2)YX . . . . . . . makes option 3 false

  X'Z' = (1/2)XZ . . . . . . . makes option 4 true

Since no angles are changed, we have ...

  Angle XZY ≅ Angle Y'Z'X'   (another name for angle X'Z'Y')

  ... makes option 2 true

Of course, the resulting triangle is similar to the original, so ...

  △XYZ ~ △X'Y'Z' . . . . . option 1 is true

Answer:

p = 81

Step-by-step explanation:

9 = \(\frac{p}{9}\)  Multiply both sides by 9

9(9) = \(\frac{p}{9}\)\((\frac{9}{1})\)  another name for 9  is \(\frac{9}{1}\)

81 = p