A right prism with height $h$ has bases that are regular hexagons with sides of length $12$. A vertex $A$ of the prism and its three adjacent vertices are the vertices of a triangular pyramid. The dihedral angle (the angle between the two planes) formed by the face of the pyramid that lies in a base of the prism and the face of the pyramid that does not contain $A$ measures $60$ degrees. Find $h^2$.

The cliff-jumper is standing 24.7 meters (or about 81 feet) above the base of the cliff.

What is potential energy (PE)?

The potential energy formula is affected by the force operating on the two objects. The formula for gravitational force is P.E. = mgh, where m is mass in kilograms, g is gravity's acceleration (9.8 m/s2 at the earth's surface), and h is height in meters.

The potential energy (PE) possessed by the cliff-jumper of mass m at height h above the base of the cliff is given by the formula:

PE = mgh

where g is the acceleration due to gravity (9.81 m/s²).

In this problem, the cliff-jumper has a mass of 68.0 kg and possesses 16,800 J of potential energy. We can use the formula above to find the height h:

PE = mgh

h = PE / (mg)

Substituting the given values, we get:

h = 16800 J / (68.0 kg x 9.81 m/s^2)

h = 24.7 meters (rounded to two decimal places)

Therefore, the cliff-jumper is standing 24.7 meters (or about 81 feet) above the base of the cliff.

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As per the information provided, this all indicates that the function f is becoming more of a function r at end.

Three different factors affect the function that determines the balance in this account: the initial deposit amount, the interest rate compounded on this account, and the amount of time the money is kept in the account. The account balance changes if any one or all of these three values is altered.

Let us examine how the interest rate affects this balance. When money is kept in an interest-bearing account, the interest is added as a percentage of the balance to the value of the account. Accordingly, a higher interest rate would result in a larger sum being added to the balance because a larger portion of the balance would be deposited.

Thus, this indicates that the function f is becoming more of a function r at end.

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Note that the correct question is:

The balance, B, in dollars, in a bank account depends on the amount deposited, A dollars, the annual interest rate, r%, and the time, t, in months since the deposit, so B = f(A, r, t).

Is f an increasing or decreasing function of r? Explain your answer.

No, Earline won't have enough money in six weeks

Earline needs to save $367.50 for her summer vacation

She plans on saving $52.50 per week

The amount of money that Earline will get in six weeks can be calculated as follows

= 52.50 × 6

= 315

$315 is lesser that $367.50

Hence Earline will not be able to save enough money in six weeks

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To determine whether these sequences of vertices are paths in this directed graph:

A) path is a series of edges that starts at a vertex and moves along a graph's edges from vertex to vertex.

B) "A circuit begins at the same vertex and terminates there.".

C) "The number of edges determines length.".

D) "A path or circuit is simple if there are no repeated instances of the same edge."

E) No path

F) No path

In most cases, "a simple path" means that you can only enter or exit a vertex once (in the case of cycles, you do both but only once, i. e. It's still ok because there is only one entrance and exit). The phrase "simple path" can mean: simple curve, a continuous injective function from a real number set interval or, more generally, to a topological or metric space.

In graph theory, a simple path is a path through a graph without repeating vertices.

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Note that the graph is: (check attached image)

Option C, center at (0, 0) transverse axis is x - axis vertices at (-11, 0) and (11, 0) foci at ([tex]-\sqrt{265}[/tex], 0) and ([tex]\sqrt{265}[/tex], 0) is the correct option.

The transverse axis is a line segment with vertices as its endpoints that traverses the hyperbola's center. The transverse axis's containing line is where the foci are located. The co-vertices serve as the endpoints of the conjugate axis, which is perpendicular to the transverse axis.

The transverse axis is located on the y-axis because of the equation's form, which is y^2a^2-x^2b^2 = 1. The vertices act as the graph's y-intercepts since the hyperbola is centered at the origin. Set x=0 and then solve for y to discover the vertices. Hence, the formula for a hyperbola with foci along the x-axis is x^2a^2-y^2b^2 = 1. The solution can be seen on the attached image below.

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Question correction:

See attached image below.

The maximum profit that the company will be left with is $11,450 from the laptops and tablets.

Your profit is the amount left over after paying all necessary business expenses. The three main categories of profit are gross, operational, and net. Gross revenue is the most profitable. After paying for the items and services that were sold, the remaining balance is shown.

1.The daily constraints on the company according to the plan are:

70 <= x <= 130 (number of laptops produced)

50 <= y <= 110 (number of tablets produced)

x + y >= 150 (total number of devices produced)

x + y <= 220 (total number of devices produced)

2.The objective function for maximizing profit is:

Profit = 65x + 45y

4.The vertices of the feasible region are:

(70, 80)

(70, 110)

(100, 50)

(110, 40)

(130, 20)

(130, 30)

(130, 50)

(100, 110)

5.Evaluating the objective function at the vertices of each feasible region:

(70, 80): Profit = 65(70) + 45(80) = $8,150

(70, 110): Profit = 65(70) + 45(110) = $9,500

(100, 50): Profit = 65(100) + 45(50) = $8,750

(110, 40): Profit = 65(110) + 45(40) = $8,950

(130, 20): Profit = 65(130) + 45(20) = $9,350

(130, 30): Profit = 65(130) + 45(30) = $9,800

(130, 50): Profit = 65(130) + 45(50) = $10,700

(100, 110): Profit = 65(100) + 45(110) = $11,450

6.To maximize profit, the company should make 100 laptops and 110 tablets.

7.The maximum profit is $11,450.

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98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year by using z-score. The correct answer is (0.1859, 0.2133)

The point estimate for the proportion of American adults who earned money by selling something online in the previous year is:

p-hat = 914/4579 = 0.1995

To construct a 98% confidence interval for the population proportion, we can use the formula:

p-hat ± z*(sqrt(p-hat*(1-p-hat)/n))

where z is the z-score associated with the desired confidence level (98% corresponds to a z-score of 2.33), and n is the sample size. Plugging in the values, we get:

0.1995 ± 2.33*(sqrt(0.1995*(1-0.1995)/4579))

Simplifying this expression, we get:

(0.1859, 0.2133)

Therefore, the correct answer is (0.1859, 0.2133). This means we are 98% confident that the true proportion of American adults who earned money by selling something online in the previous year lies between 0.1859 and 0.2133.

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Cartesian product are A.{aa, ab, ac, ad}   B. {ab}   C. {aa, ab, ad}   D.{ab}

Given the set notations A = {a} B = {b, c} C = {a, b, d}

BUC = {a, b, c, d}

B∩C = {b}

a) A × (BUC) = {aa, ab, ac, ad}

b) A × (B ∩ C) = {ab}

c) (A × B) ∪ (A × C)

A × B = {ab, ac} and A × C = {aa, ab, ad}

(A × B) ∪ (A × C) = {aa, ab, ac, ad}

d) For (A × B) ∩ (A × C)

(A × B) ∩ (A × C) = {ab}

The symbol ∩ represents the intersection of sets. For example, the intersection of two sets X and Y can be expressed as X ∩ Y.

The union of two sets P and Q is denoted by P ∪ Q. This is the set of all distinct elements contained in P or Q. The symbol used to represent the union of sets is ∪. The intersection of two sets P and Q is denoted by P ∩ Q. This is the set of all distinct elements in both P and Q. The symbol for the set intersection is ∩. The intersection of two given sets, H. P and Q, is the set containing all elements common to both P and Q.

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Answer:

15

Step-by-step explanation:

A right angle is 90 degrees

90 - 45 = 45

The remaining angle of 3x is equal to 45 degrees.

45/3 = x     x=15

Answer: a) A 95% confidence interval based on n = 10 randomly selected observations would use a t*-value from the t-distribution with (n - 1 = 9) degrees of freedom.

b) A 99% confidence interval from an SRS of 20 observations would use a t*-value from the t-distribution with

Step-by-step explanation:

Answer:  14.25x is the expression

It represents the total combined cost everyone paid.

=======================================================

Explanation:

Add up the price of a ticket, a medium drink, and a large popcorn.

7.50+2.75+4.00 = 14.25

Each person spends $14.25 for those three items.

If x is the unknown number of people, then 14.25x represents the total amount spent by everyone combined.

Example: x = 10 people, so 14.25x = 14.25*10 = 142.50 dollars total is spent by everyone combined.

Answer:

here it is

Step-by-step explanation:

-3 represents the slope. Since its 3/1, this means which point on the slope is 3 to side and 1 either up or down. Since the slope is negative, it goes down.

The formula for a slope is y = mx + b. Since we don’t have the b, that means it is 0. B represents the y intercept or when the line crosses the y axis.

The range, given the cost of surfboard rentals, would be $ 140.

The interquartile range of the cost of surfboard rentals is $ 56.

There is an outlier which is the cost of 6 days of rentals which is $ 168.

To find the range, the formula is :

= Largest cost - Lowest cost

To find these costs, find the cost of the days of rentals :

1 day :                                  2 days                            3 days :

= 28 x 1                                = 28 x 2                         = 28 x 3

= $ 28                                   = $ 56                          = $ 84

6 days :

= 28 x 6

= $ 168

The range is therefore :

= 168 - 28

= $ 140

To find the Interquartile range, first find the First Quartile and the Third Quartile after ordering the costs:

Order of costs :

28, 28, 28, 56, 56, 56, 84, 84, 84, 168

First quartile position :

= 1 / 4 x ( n + 1 )

= 1 / 4 x ( 10 + 1 )

= 3 rd position which is $ 28

Third quartile position :

= 3 / 4 x ( n + 1 )

= 3 / 4 x ( 10 + 1 )

= 8 th position which is $ 84

The Interquartile range is :

= 84 - 28

= $ 56

The outlier is the cost of 6 days which is $ 168. This is a rental as it is much larger than other costs.

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The expression x^2 + 2x - a is divisible by x + 4 when a = 6x.

A long division polynomial is an algorithm for dividing polynomial by another polynomial of the same or a lower degree.

By using the long division method:

x + 4 | x^2 + 2x - a

-x^2 - 2x + 4x    

-------------------

      -a + 6x    

-x^2 - a + 6x    

-------------------

        2x - a

-x^2 - 2x + 4x    

-------------------

          0

The remainder is 0 a = 6x.

Hence, the expression x^2 + 2x - a is divisible by x + 4 when a = 6x.

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We can start by finding the expected value of X and Y separately: (X) = (0+0+1+1+2+1+0+1+0)/9 = 6/9 = 2/3, E(Y) = (0+0+1+1+2+0+1+0+0)/9 = 5/9

Next, we can expand (X+Y)^2: (X+Y)^2 = X^2 + 2XY + Y^2

Taking the expected value of both sides, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2)

To find E(XY), we can create a table of the possible values of X and Y, and their corresponding probabilities: [table in the attatchment]

So, we have:

E(XY) = 0*(3/9) + 0*(2/9) + 0*(1/9) + 0*(2/9) + 1*(1/9) + 2*(1/9) + 0*(1/9) + 2*(1/9) + 4*(1/9) = 1

Next, we need to find E(X^2) and E(Y^2): E(X^2) = (0^2+0^2+1^2+1^2+2^2+1^2+0^2+1^2+0^2)/9 = 8/9

E(Y^2) = (0^2+0^2+1^2+1^2+2^2+0^2+1^2+0^2+0^2)/9 = 5/9

Putting it all together, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2) = 8/9 + 2*1 + 5/9 = 23/9. Therefore, the answer is 23/9.

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Answer:

Technology improvements allow someone to look up jobs and be able to apply. This is much easier than going around yourself as it takes less time and effort. With technology we are capable of looking at ads of jobs and finding jobs in and around your area. Places such as indeed and linkedin have options for filters to allow you to adjust your search to salaries and areas that suit you.

Hope this helps, have a lovely day! :)

Hence, if i > j, then (AB)ij is a sum of products of zeros, and is therefore zero. This means that all the entries below the main diagonal in the matrix AB are zero. Therefore, AB is also an upper triangular matrix.

To show that if a and b are square, upper triangular matrices, then so is ab, we need to prove that all the entries below the main diagonal in the matrix ab are zero.

Let A and B be square, upper triangular matrices of size n x n.

Then the (i,j)th entry of AB is given by:

(AB)ij = Σk=1n AikBkj

For i > j, we have:

(AB)ij = Σk=1n AikBkj = Σk=1j AikBkj + Σk=j+1n AikBkj

Since A is upper triangular, we have Aik = 0 for k > i.

Therefore, the first sum above is non-zero only for k ≤ i. Since B is also upper triangular, we have Bkj = 0 for k > j.

Therefore, the second sum above is non-zero only for k > j.

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Answer: She lost 78% percent of her money.

450-100 is 350. This means that Kelly lost 350 dollars.

350/450 is 0.777777778. Rounded to the next whole number the percent is 78%. This means Kelly lost 78% of her money.

I hope this helped & Good Luck <3 !!

Answer:

The 2nd option

Step-by-step explanation:

You can substitute values to replace X and if it alines with the graph then you know that is the correct answer choice

No triangle can form with the given measurements.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

The given angles are 53° and 27°.

By using angle sum of property of a triangle, we get

53°+27°+x=180°

x=100°

It is not possible to draw a unique triangle with any 3 possible measurements of angles.

Therefore, no triangle can form with given measurements.

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The number  ways can make change for 70 cents using only​ nickels, dimes, and​ quarters is,

7 dimes, 0 nickels

6 dimes, 2 nickels

5 dimes, 4 nickels

4 dimes, 6 nickels

3 dimes, 8 nickels

2 dimes, 10 nickels

1 dime, 12 nickels

0 dimes, 14 nickels

In mathematics, Combination is a term which tells us how many ways there are for the selection of a few things without considering their order.

Formula for selection of a objects from the n objects,

N = ⁿCₐ

To find the number of ways to make change for 70 cents using only nickels, dimes, and quarters, we can use a combination of systematic listing and counting.

One approach is to consider the number of quarters used to make the change, which can be 0, 1, or 2, since using more than 2 quarters would exceed the total value of 70 cents.

Here are the possible combinations of coins to make change for 70 cents:

Using 0 quarters:

7 dimes, 0 nickels

6 dimes, 2 nickels

5 dimes, 4 nickels

4 dimes, 6 nickels

3 dimes, 8 nickels

2 dimes, 10 nickels

1 dime, 12 nickels

0 dimes, 14 nickels

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Answer:

p = 4.5

Step-by-step explanation:

0.5p - 3.45 = -1.2.

0.5p = -1.2 + 3.45

0.5p = 2.25

0.5p/0.5 = 2.25/0.5

p = 4.5

therefore p is equal to 4.5

The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as

[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]

The probability that the number of U.S. adults who oppose exactly 2 is given as,

P(2) = ⁶C₂ x (0.68)² x (1 - 0.68)⁴

P(2) = 0.0727

The probability that the number of U.S. adults who oppose less than four is given as,

P(x < 4) = ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ + ⁶C₂ x (0.68)² x (1 - 0.68)⁴ + ⁶C₃ x (0.68)³ x (1 - 0.68)³

P(x < 4) = 0.0137 + 0.0727 + 0.2061

P(x < 4) = 0.2925

The probability that the number of U.S. adults who oppose at least three is given as,

P (x ≥ 3) = 1 - ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ - ⁶C₂ x (0.68)² x (1 - 0.68)⁴

P (x ≥ 3) = 1 - 0.0137 - 0.0727

P (x ≥ 3) = 0.9136

The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.

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Answer:

Part A: PR ≈ 16.06

Part B: QR≈ 9.60

Step-by-step explanation:

Part A)

The length of rod PR can be found using the Pythagorean theorem.

In this case, rod PQ is one leg, rod QR is the other leg, and rod PR is the hypotenuse. So, we have: PQ^2 + QR^2 = PR^2

Substituting the given lengths, we have:

14^2 + 8^2 = PR^2

Solving for PR, we get:

PR^2 = 14^2 + 8^2 = 196 + 64 = 260

Taking the square root of both sides, we have:

PR = √260

PR ≈ 16.06

Part B)

If the length of rod PR is adjusted to 17 feet, we can use the Pythagorean theorem to find the new height QR.

PQ^2 + QR^2 = 17^2

Substituting the given length of PQ, we have:

14^2 + QR^2 = 17^2

Expanding both sides, we have:

196 + QR^2 = 289

Subtracting 196 from both sides, we have:

QR^2 = 289 - 196 = 93

Taking the square root of both sides, we have:

QR = √93

QR ≈ 9.60

Answer:

C

Step-by-step explanation:

Cause 13/17 is 0.76 so c is nearer to 1 about 0.76

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{13}{17}}\\\\\mathsf{\rightarrow 13\div17}\\\\\mathsf{\rightarrow 0.764705882352941}}\\\\\mathsf{\approx 0.764\approx 0.75\ (in\ this\ case)}}[/tex]

[tex]\huge\text{Therefore your answer should be:} \\\\\huge\boxed{\mathsf{Point\ C.}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The parametric equations for the tangent line to the curve

x = 26+27, t = 10+6t, z = 27+27t

In the given question points are given and we have to find the parametric equations for the tangent line to the curve.

given r(t) = <t³-1 , t²+1 , t³>

taking differentiation

r'(t) = <3t² , 2t , 3t² >

parameters corresponding to point at the point (26, 10, 27)

t²+1 = 10

=> t² = 9

=> t = √9

=>t=3

r'(t) at t = 3 is

r'(t) = <27, 6, 27 >

So the parametric equations for the tangent line to the curve

x = 26+27

t = 10+6t

z = 27+27t

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The complete question is :

Find the parametric equations for the tangent line to the curve

x = t³ - 1,

y = t² + 1,

z = t³

at the point (26, 10, 27). Use the variable t for your parameter.

The net number of ATP produced from eight molecules of glucose during glycolysis is 32 ATP molecules.

Glycolysis is a metabolic pathway that breaks down glucose into two molecules of pyruvate, which in turn produces ATP. Each molecule of glucose yields two molecules of ATP and two molecules of NADH. Each NADH molecule, in turn, produces three more ATP molecules when it is oxidized in the electron transport chain. Therefore, the total number of ATP produced from one molecule of glucose is four. When eight molecules of glucose undergo glycolysis, the total number of ATP produced is 4 x 8 = 32 ATP molecules. hence 32 ATP molecules produced during the process of glycolysis.

The complete question is : select the net number of ATP produced from 8 molecules of glucose during the process of glycolysis is

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Answer:

Step-by-step explanation:

To write the Taylor series for the function f(x) = e^(-x) about x = x0 = -1, we first need to find the k-th derivative of f(x) and evaluate it at x = -1.

f(x) = e^(-x)

f'(x) = -e^(-x)

f''(x) = e^(-x)

f'''(x) = -e^(-x)

f''''(x) = e^(-x)

...

The k-th derivative alternates between e^(-x) and -e^(-x), depending on the parity of k.

To evaluate the k-th derivative at x = -1, we substitute -1 into the k-th derivative expression and simplify:

f^k(-1) = (-1)^k * e^1

Now we can write the Taylor series using the formula:

f(x) = f(x0) + (x - x0) f'(x0) / 1! + (x - x0)^2 f''(x0) / 2! + (x - x0)^3 f'''(x0) / 3! + ...

Plugging in the values we obtained earlier, we have:

f(-x0) = e

f'(-x0) = -e

f''(-x0) = e

f'''(-x0) = -e

f''''(-x0) = e

...

Substituting these values into the formula, we get:

f(x) = e - (x + 1)e + (x + 1)^2 e / 2! - (x + 1)^3 e / 3! + (x + 1)^4 e / 4! - ...

Using sigma notation, we can write this as:

f(x) = ∑_{k=0}^∞ (-1)^k (x + 1)^k e / k!

where ∑_{k=0}^∞ represents the sum from k = 0 to infinity.