Rewrite in simplest rational exponent from √x × \(\sqrt[4]{x}\)

Answer:

10

Step-by-step explanation:

Formula :

Finding a₅ :

Finding a₆ :

The surface area that must be covered when painting the exterior of the silo is \(700\pi\)square feet.

To calculate the surface area of the grain silo, we need to find the sum of the lateral surface area of the cylinder and the surface area of the hemispherical dome.

Surface area of the cylinder:

The lateral surface area of a cylinder is given by the formula: A_cylinder \(= 2\pi rh\), where r is the radius and h is the height.

Given the diameter of the cylinder is 20 ft, we can find the radius (r) by dividing the diameter by 2:

\(r = 20 ft / 2 = 10 ft\)

The height of the cylinder is given as 25 ft.

Therefore, the lateral surface area of the cylinder is:

A_cylinder =\(2\pi(10 ft)(25 ft) = 500\pi ft^2\)

Surface area of the hemispherical dome:

The surface area of a hemisphere is given by the formula: A_hemisphere = 2πr², where r is the radius.

The radius of the hemisphere is the same as the radius of the cylinder, which is 10 ft.

Therefore, the surface area of the hemispherical dome is:

A_hemisphere \(= 2\pi(10 ft)^2 = 200\pi ft^2\)

Total surface area:

To find the total surface area, we add the surface area of the cylinder and the surface area of the hemispherical dome:

Total surface area = Acylinder + Ahemisphere

                 \(= 500\pi ft^2 + 200\pi ft^2\)

                 \(= 700\pi ft^2\)

So, the surface area that must be covered when painting the exterior of the silo is \(700\pi\) square feet.

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The surface area that must be covered is \(\(700\pi\)\) sq ft, or approximately 2199.11 sq ft.

To calculate the surface area of the grain silo that needs to be painted, we need to consider the surface area of the cylinder and the surface area of the hemispherical dome.

The surface area of the cylinder can be calculated using the formula:

\(\(A_{\text{cylinder}} = 2\pi rh\)\)

where r is the radius of the cylinder (which is half the diameter) and h is the height of the cylinder.

Given that the diameter of the cylinder is 20 ft, the radius can be calculated as:

\(\(r = \frac{20}{2} = 10\) ft\)

Substituting the values into the formula, we get:

\(\(A_{\text{cylinder}} = 2\pi \cdot 10 \cdot 25 = 500\pi\)\) sq ft

The surface area of the hemispherical dome can be calculated using the formula:

\(\(A_{\text{dome}} = 2\pi r^2\)\)

where \(\(r\)\) is the radius of the dome.

Since the radius of the dome is the same as the radius of the cylinder (10 ft), the surface area of the dome is:

\(\(A_{\text{dome}} = 2\pi \cdot 10^2 = 200\pi\)\) sq ft

The total surface area that needs to be covered is the sum of the surface area of the cylinder and the surface area of the dome:

\(\(A_{\text{total}} = A_{\text{cylinder}} + A_{\text{dome}} = 500\pi + 200\pi = 700\pi\)\)sq ft

Therefore, the surface area that must be covered is \(\(700\pi\)\) sq ft, or approximately 2199.11 sq ft.

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Answer:

Commission = $768

Total amount commission in 2011 = $41,472

Step-by-step explanation:

Commission = Sales × 12% of sales

Commission = $6,400 × .12

Commission = $768

Number of weeks in a year = 52 weeks

Total amount commission in 2011 = Commission per month × Number of

                                                            weeks in a year

Total amount commission in 2011 = $768 × 52

Total amount commission in 2011 = $41,472

Answer:

Step-by-step explanation:

85°

Answer:

60

Step-by-step explanation:

All the sides are equal

Answer:

Option (b) is correct.

The expression is equivalent, but the   term is not completely factored.

Step-by-step explanation:

Given :  a student factors  to

We have to choose the correct statement  about   from the given options.

Given   is factored to

Consider    

Using algebraic identity,

comparing  and b = 4, we have,

Thus, the factorization is equivalent but we can simplify it further also, as

Using algebraic identity,

Thus,

Can be written as

Thus, the expression is equivalent, but the   term is not completely factored.

Option (b) is correct.

The minimum surface area of the container is: 96.00 cm² in the given case.

Let's call the length and width of the square base "x", and the height of the container "h". Since the container has a volume of 256 cm^3, we can write:

V = \(x^2 * h = 256\)

We want to minimize the surface area of the container, which consists of the area of the base plus the area of the four sides. The area of the base , and the area of each side is xh. Therefore, the total surface area of the container is:

A = \(x^2 + 4xh\)

We can solve for h in terms of x using the volume equation:

h = \(256 / (x^2)\)

Substituting this expression for h into the surface area equation, we get:

A(x) =

To find the minimum surface area, we need to find the critical points of the function A(x).

We can do this by taking the derivative of A(x) with respect to x, setting it equal to zero, and solving for x:

\(dA/dx = 2x - 1024 / x^2 = 0\\2x = 1024 / x^2\\x^3 = 512\\x = ∛512\\x ≈ 8.00 cm\)

To confirm that this is a minimum, we can check the second derivative:

\(d^2A/dx^2 = 2 + 2048 / x^3\)

This is positive, so A(x) has a minimum at x =\(∛512\). Therefore, the minimum surface area of the container is:   96.00 cm²

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The critical points for the rational function defined as \(p(x) = \frac{ x - 4}{-4x² + 4}\) are equal to the \(x =\ frac{ -4 ± \sqrt {13}}{ 3} \).

A critical point of a function y = f(x) is a point say (c, f(c)) on graph of f(x) where either the derivative is 0 (or) the derivative is not defined. Steps to determine the critical point(s) of a function y = f(x):

\(p(x) = \frac{ x - 4}{-4x² + 4}\)

We have to determine the critical points for function. Using the above steps, p'(x) = 0

=> \(p'(x) = \frac{(-4x² + 4) -( x - 4)(-8x)}{(-4x² + 4)²}\)

\( = \frac{(-4x² + 4) - 8x² - 32x)}{(-4x² + 4)²}\)

\( = \frac{(-12x² - 32x + 4)}{(-4x² + 4)²}\)

so, \(\frac{(-12x² - 32x + 4)}{(-4x² + 4)²} = 0\)

=> - 12x² - 32x + 4 = 0

=> 3x² + 8x + 1 = 0

solve the Quadratic equation by quadratic formula,

=> \(x = \frac{ -8 ± \sqrt { 64 - 12}}{ 6} \)

\(x = \frac{ -4 ± \sqrt {13}}{ 3} \).

Hence, required value are \(x = \frac{ -4 ± \sqrt {13}}{ 3} \).

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The value of b is -6

We know that the difference between two vectors with components (a1, a2) and (b1, b2) is given by (b1-a1, b2-a2).

So in this case, we have

[b1 - 3, b2 - 4] = [(-6) - 3, b - 4]

Simplifying the right-hand side gives us

[-9, b - 4]

So we can set the components of the left-hand side equal to the corresponding components of the right-hand side

b1 - 3 = -9

b2 - 4 = b - 4

Solving for b in the first equation gives us

b1 = -9 + 3 = -6

Substituting this into the second equation and simplifying gives us

-6 - 4 = b - 4

-10 = b - 4

b = -10 + 4 = -6

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Answer:

T = 11.77

18% Tip = 2.12

Total with tip = $13.89

This should be right :)

Lmk how I did!

To calculate a 95% confidence interval for the slope on the line, we would need to perform linear regression on the data to obtain an estimate for the slope and its standard error. In summary, we can use the confidence interval for the slope as evidence for a linear relationship between GRE score and chance of admission if the interval does not contain zero.

We can then use this estimate and standard error to construct the confidence interval. Assuming α = 0.05, if the confidence interval does not contain zero, we can use this as evidence that there is a linear relationship between GRE score and chance of admission. This is because if the slope is significantly different from zero, it suggests that there is a non-zero relationship between the two variables.
To calculate a 95% confidence interval for the slope of a linear regression line, you'll need to know the standard error of the slope and the critical t-value. Here are the steps:
1. Calculate the slope (b) and the standard error of the slope (SEb) using your dataset. This usually requires a statistical software package, as it involves complex calculations.
2. Find the critical t-value (t*) corresponding to α/2 (0.025) and the degrees of freedom (df) of the dataset. You can use a t-distribution table or online calculator for this.
3. Calculate the lower and upper bounds of the confidence interval for the slope:

  Lower Bound = b - (t* × SEb)
  Upper Bound = b + (t* × SEb)
If the calculated 95% confidence interval for the slope contains zero, it means that there's a possibility the true slope is zero, and thus, there might not be a linear relationship between GRE score and chance of admission. On the other hand, if the interval doesn't contain zero, it serves as evidence of a linear relationship between the variables.
Remember that the confidence interval only provides evidence for a relationship, and not a definitive conclusion.

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Since d(1) = 1, we can assert that the induction proves that the value of n is true for n = 1, and there is only one dot. Also, the mathematical induction is true for all natural numbers (n).

A mathematical approach known as mathematical induction is used to demonstrate that a claim or statement is true for each and every natural number.

You must demonstrate the following proposition using an inductive step of proof such that d(k) and d(k+1) are both true if d(k) is true.

To Prove:

\(\mathbf{d(n) = \dfrac{n(n+1)}{2}}\)

For n = 1

\(\mathbf{d(1) = \dfrac{1(1+1)}{2}}\)

\(\mathbf{d(1) = \dfrac{1 \times 2}{2}}\)

\(\mathbf{d(1) = \dfrac{2}{2}}\)

d(1) = 1   this is true for n = 1, there is only one dot.

b.

Now, let us assume that the result is true for n = k + 1 such that:

\(\mathbf{d(k+1) = \dfrac{(k+1) ((k+1) + 1) }{2}}\)

\(\mathbf{d(k+1) = \dfrac{(k+1) (k+2) }{2} ---- (1)}\)

Now, Let n = k, then:

\(\mathbf{d(k) = \dfrac{k(k + 1)}{2} ----(2)}\)

Recall that, the total number of dots d(n) increases by 'n' each time.

i.e. d(n+1) = d(n) + n

Therefore;

d(k) = d(k+1) + k

To prove:

\(\mathbf{\dfrac{k(k + 1)}{2} + (k + 1) = \dfrac{(k+1) (k+2) }{2}}\)

\(\mathbf{ \dfrac{k(k+1)+ (2k+2) }{2}= \dfrac{(k+1) (k+2) }{2}}\)

\(\mathbf{ \dfrac{(k+1) (k+2) }{2}= \dfrac{(k+1) (k+2) }{2}}\)

L.H.S    =   R.H.S

Therefore, we can conclude that the mathematical induction is true for all natural numbers (n).

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Answer:

Step-by-step explanation:

A.

We have repeat values of x with different values of y:

This is not a function of x.

B.

C.

D.

Answer:

y=4x-7

Step-by-step explanation:

first, find b

5=4*3+b

5=12+b

b=-7

Answer:

-3/4

Step-by-step explanation:

The slope of a line is the rise (change in y-value) over the run(change in x-value). From the graph we can see that the rise is -3 and the run is 4.

Therefore, the slope will be: -3/4

Hope this helps!

Answer:

11/2=k

Step-by-step explanation:

Write equation in number format

8+3k=5k-3

Solve for k

Combine like terms

11=2k

Divide by 2

(11/2)=k

The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4

The second derivative of v with respect to t, we will differentiate v twice.

v = 2t² + 7t + 11

First, let's find the first derivative of v with respect to t (dv/dt):

dv/dt = d/dt (2t² + 7t + 11)

Using the power rule of differentiation, we differentiate each term separately:

dv/dt = 2(2t) + 7(1) + 0

dv/dt = 4t + 7

Now, let's find the second derivative of v with respect to t (d²v/dt²):

d²v/dt² = d/dt (4t + 7)

Again, using the power rule of differentiation, we differentiate each term separately:

d²v/dt² = 4(1) + 0

d²v/dt² = 4

Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.

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Step-by-step explanation:

that is really a problem ?

come on !

you know, the area of a square is side length × side length = length²

that is basically all of us learn as the very first thing when we are learning about squaring and multiplication.

how do we get the regular side length out of length² ?

we pull the square root. you have a calculator (at least on your computer, cell phone,...).

sqrt(121) = .... .... .... 11 ! tada !

and the perimeter of a square ... you really have to ask ?

it is the way all around the whole square. you need to go along every one of the 4 sides.

so, it is side length × 4 = 11×4 = 44 cm

again - you really needed help with THAT ?

Answer:

D.

Step-by-step explanation:

Use a protractor if available and it is a paper assignment. However, if not, please look for the protractor tool.

Answer:

126 degrees

Step-by-step explanation:

Making a system of equations of both given equations because they are vertical angles is 90-12b = -3b+63. Solving this equation gives you b = 3. Take this value and plug it in to 90-12b to get 90-36 = 54. Take that value and subtract it from 180 degrees because the requested angle is supplementary, so the other side is just 180-54 is 126 degrees. Hope that helps!

To conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts, we can use a chi-square test for independence.

The null hypothesis states that the proportions of good parts in each shift are equal, while the alternative hypothesis states that they are not equal.
Assuming a significance level of .05, we can calculate the p-value of the test. If the p-value is less than .05, we reject the null hypothesis, indicating that there is evidence to suggest that the population proportions are not equal. On the other hand, if the p-value is greater than .05, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that the population proportions are not equal.
After performing the test, we obtain a p-value of .02. Since this value is less than .05, we reject the null hypothesis and conclude that there is evidence to suggest that the population proportions of good parts are not equal for all three shifts. Therefore, we can conclude that there is a significant difference in the proportion of good parts produced by each shift.

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the value today of the money machine is approximately $29,499.48.

The formula to calculate the present value of an annuity is:

PV = C * (1 - (1 + r)^(-n)) / r

PV is the present value

C is the cash flow per period

r is the interest rate per period

n is the number of periods

Cash flow per year (C) = $4,161.00

Number of years (n) = 23.00

Interest rate (r) = 15.00%

First, let's convert the annual interest rate to a decimal and calculate the interest rate per period:

r = 15.00% / 100 = 0.15

PV = $4,161.00 * (1 - (1 + 0.15)^(-23)) / 0.15

Using a calculator, we find that the present value (PV) is approximately $29,499.48.

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Answer:

y = -2x - 4

Step-by-step explanation:

y = mx +b is the slope intercept form of a line.  The m is the slope and the b is the y intercept.

The y intercept is where the line crosses the y axis.  It crosses at the point (0,-4).  The -4 is where the line crosses the y axis.  It is the b.

The slope is the change in y over the change in x.  To go from point (0,-4) to the point (-2,0)  You go up 4 units and the left 2 units.  Up is positive and left is negative. 4/-2 which simplifies to -2.  This is your m.

Assuming that you can choose only one type of sandwich, one size, one type of bread, and any combination of fillings, you can personalize your sandwich in the following way : 5 (types of sandwich) x 3 (sizes) x 4 (types of bread) x 2^6 (choices of fillings) = 5 x 3 x 4 x 64 = 3840

So, you can personalize your sandwich in 3840 different ways by choosing one type of sandwich, one size, one type of bread, and any combination of six different fillings.
Hi! I'd be happy to help you determine the number of ways you can personalize your sandwich at this shop.

1. Sandwich type: There are 5 types of sandwiches to choose from.
2. Sandwich size: There are 3 different sizes available.
3. Bread type: You can select from 4 different kinds of bread.

Now, let's consider the fillings. Since there are 6 fillings, each one can either be included or not included. This results in 2 options (yes or no) for each filling.

To calculate the total number of personalized sandwiches, we can multiply the options for each aspect of the sandwich:

5 (types) * 3 (sizes) * 4 (breads) * 2^6 (fillings) = 5 * 3 * 4 * 64 = 3840

Therefore, you can personalize your sandwich in 3840 different ways.

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The product of (-9 + i) and (2 + i) in standard form is -19 - 7i.

Given the expression in the question:

( -9 + i )( 2 + i )

To determine the product of ( -9 + i )( 2 + i ), we expand using the FOIL method.

( -9 + i )( 2 + i )

-9( 2 + i ) + i( 2 + i )

Expand:

-9 × 2 -9 × i + i × 2 + i × i

-18 -9i + 2i + i²

Replace i² with -1

-18 -9i + 2i + ( -1 )

-18 -9i + 2i - 1

Simplifying, we get:

-18 - 1 -9i + 2i

-19 - 7i

Therefore, the product of the expression is -19 - 7i.

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when a sample statistic is measured with nominal data, the only appropriate proportion measure is sample percentage.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol %.

when a sample statistic is measured with nominal data, the only appropriate proportion measure is sample percentage.

A small portion of the population is surveyed to produce sample percentages. A sample percentage is what you get when you calculate a percentage from a small portion of the population.

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The probability of Angela rolling another three on her next roll, after rolling nine consecutive threes, is still 1/6.

If Angela rolls a fair die nine times and each time she rolls a three, it means that she has already rolled nine consecutive threes. Each roll of a fair die is an independent event, which means the outcome of one roll does not affect the outcome of another roll.

The probability of rolling a three on any given roll of a fair die is 1/6, as there are six possible outcomes (numbers 1 to 6) and only one favorable outcome (rolling a three).

Therefore, the probability of Angela rolling another three on her next roll, after rolling nine consecutive threes, is still 1/6. The previous rolls do not influence the probability of rolling a three on the next roll, as each roll is independent of the others.

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The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.

The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value of the investment can also be determined using an online finance calculator, as follows.

Then the interest is the difference between the future value and the present value.

Initial deposit = $8,241.78

Interest rate = 5.5% compounded daily

Investment period = 31 days

N (# of periods) = 31 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $8,241.78

PMT (Periodic Payment) = $0

Results:

FV = $8,280.37

Total Interest $38.59 ($8,280.37 - $8,241.78)

Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.

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Answer:

x = 13.8 ft

The triangle is obtuse

Step-by-step explanation:

Using the cosine rule to determine x:

\(x=\sqrt{(11.7)^{2}+(7.4)^{2} -2(11.7)(7.4) * cos90 } \\=13.8 ft\\\)

Testing whether or not the Pythagoras theorem applies

\(r^{2} =x^{2} +y^{2} \\(13.8)^{2} = (7.4)^{2} +(11.7)^{2} \\190.44\neq 191.65\)

Therefore the triangle is obtuse

The largest possible area for the right triangle is 1250 in² in which the sum on the lengths of the two shorter sides is 100 in.

we know that in a right triangle the two shorter sides are the base and the perpendicular. Here we have to find the largest possible area of the triangle in which the sum of the shorter sides is 100 in.

Let the base and perpendicular be x and y respectively.

Therefore,

x+y = 100

  y = 100 -x

Also, Area A

= 1/2 xy

= 1 x(100-x)/z

= 100x-x²/2

so the coordinate of vertex = -b/2a

= - 50/2(1-1/2)

= 50

Also,

y = 100-50 [Putting the value of x in equation 1]

= 50

Therefore Maximum, area:

= 1/2 (50)(50)

= 1250 in²

Hence we get the required maximum area.

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Answer:131

Step-by-step explanation:

2 * 2 * 2 * 2 + 20 * 5 + 15 = 2^4+100+15=16+115=131

Answer:

Step-by-step explanation:

2 * 2 * 2 * 2 + 20 * 5 + 15 =            (remember PEMDAS)

16 + 100 + 15 =

131