6) What is the length of the diagonal of the rectangle?
A) 2.5 units
B) 4.5 units
C) 5 units
D) 7 units

Answer: 1840 pounds

Step-by-step explanation:4x4=16

460 x 4 = 1840

The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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Step-by-step explanation:

4= -8z - 7 +8z

4+7=Z

11=Z

sorry if I'm wrong in any of them

12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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Answer:

26/ 43

(Decimal: 0.604651)

Step-by-step explanation:

((2)(4)−3)2+1/ 3+ 100/ 5 (2)

Answer:

b = a² - 6

Step-by-step explanation:

a = \(\sqrt{b+6}\) ← square both sides to clear the radical

a² = b + 6 ( subtract 6 from both sides )

a² - 6 = b

Answer:

x less than or equal to 16.6

Step-by-step explanation:

50 divided by 3 is 16.6

since Jill wants 50 square feet as the maximum area x can be less than 16.6.

Answer:

The approximate value of the scale is 1:67

or the actual value without approximation is 1: 66 2/3 ( 66 while number , two over three)

Step-by-step explanation:

Here, we want to figure out the scale in inches of the drawing to the actual object.

The actual object is 500 ft by 700 ft

while the drawing is 90 inches by 126 inches

Mathematically, we know that 12 inches = 1 foot

So the actual object will be;

500(12) by 700(12)

= 6000 inches by 8400 inches

Now let’s make a division to get the scale;

6000/90 by 8400/126

we get 66.67 as answers on both ends

This is approximately equal to 67

So the scale we have here is 1:67

You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

So the answer is that you are 18 years old this year.

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You are 18 years old this year.

Let's call your age this year "x". Next year, your age will be "x + 1".

We know that the sum of the digits of "x" is three times bigger than the sum of the digits of "x + 1". Let's call the sum of the digits of "x" "s1", and the sum of the digits of "x + 1" "s2".

So we have the equation:

s1 = 3 * s2

If we add the digits of "x + 1", we get "s2 = a + b", where "a" and "b" are the digits of "x + 1".

Expanding the equation and substituting "s2":

s1 = 3 * (a + b)

Expanding the left side of the equation:

s1 = 3a + 3b

So the sum of the digits of "x" is three times the sum of the digits of "x + 1".

Now we need to find the values of "x" for which "s1" is three times bigger than "s2".

One possible solution is "x = 18", because:

"s1" = 1 + 8 = 9

"s2" = 1 + 9 = 10

9 = 3 * 10

So the answer is that you are 18 years old this year.

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The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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The segments AC, AE, and BC have the same length as AB.

Any of a thing's pieces that it naturally or artificially divides into. any portion of a figure that has been separated from it by a line or plane (often as a circle). A section of a straight line passes through two locations. A line segment, in geometry, is a portion of a straight line that is constrained by two clearly defined endpoints and contains every point on the line that is situated in between those endpoints.

Both circles A and B have the same radius AB, so the circles are congruent.

As all radii are congruent, then the segments congruent to AB are the radii of the two circles that are:

AC, B, AE, AD, BD

So, options A, B, and C are correct.

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We are given a regression model: test score = 800 - 8(student-teacher ratio)

If the student-teacher ratio drops by 2, then the new ratio is (old ratio - 2).

So, the new predicted test score is:

test score = 800 - 8(new ratio)

          = 800 - 8(old ratio + (-2))

          = 800 - 8(old ratio) - 8(-2)

          = 800 - 8(old ratio) + 16

Therefore, the predicted effect on the test score is an increase of 16 points.

So, the answer is (d) the test score will increase by 16 points.

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Answer:

15 for each side

Step-by-step explanation:

56-26 is 30, now 30 divided by 2 is 15. So for each side is 15 inches long.

PART A

We were told that the price of a T-shirt is $50

T shirt and backpack is $100

T shirt, backpack and sportsball is $125

If If Brennan's parents give him a $ 75 donation, let x represent the amount of money that he would still need to win the prize of a T -shirt , backpack , and sports ball. It means that

t + 75 = 125

Thus, the equation ito

The sine function graphed is defined as follows:

C. y = sin(x).

The standard definition of the sine function is given as follows:

y = Asin(Bx).

For which the parameters are given as follows:

(as the function crosses it's midline at the origin, it has no phase shift).

The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:

2A = 2

A = 1.

The period is of 2π/3 units, hence the coefficient B is given as follows:

B = 3.

Then the equation is:

y = sin(3x).

Meaning that option C is the correct option for this problem.

The graph is given by the image presented at the end of the answer.

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Answer:

-1

Step-by-step explanation:

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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The diameter is the length across the entire circle. This divides the circle into two equal parts and makes two equal-sized semicircles. The radius is the length from the center of the circle to the circumference. The diameter is always twice the size of the radius.

The equation to solve for the area of a circle is \(A =\) π \((d/2)^{2}\)

Substituting 5 and 3.14 into the equation gives us:

Solving for 5/2 gives us:

Therefore, \(A = 19.6m^{2}\)

Answer:

The area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

What is circle ?

A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, from a central point, called the center. A circle is the set of all points in a plane that are at a given distance from a given point, the center.

The area of a circle is given by the formula A = , where r is the radius of the circle. To find the area of a circle with a diameter of 5 m, we first need to find the radius. We can do this by dividing the diameter by 2:

r = 5 m / 2 = 2.5 m

Then we can substitute this value of r into the formula for the area of a circle:

A =  = π(2.5 m)^2 = 3.14 * 6.25 m^2 = 19.63 m²

So the area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².

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Step-by-step explanation:

Answer:y=1/3x+8

Step-by-step explanation:

Plug it into point slope form

y-6=1/3(x+6)

y-6=1/3x+2

+6. +6

y=1/3x+8

Since the coefficient of the squared term is positive (1), the parabola opens upwards. The direction of the parabola is upwards.

Given the vertex of a parabola, we can determine whether the parabola is facing upward or downward. In this case, the vertex is located at (1,2), and the y-intercept is located at (0,3).

To determine the direction of the parabola, we look at the coefficient of the squared term. If it's positive, then the parabola opens upwards, and if it's negative, then the parabola opens downwards. In this case, we can use the vertex form of a parabola which is given by:y = a(x - h)² + k

where (h, k) is the vertex. Substituting the given values, we get:

y = a(x - 1)² + 2

We also know that the y-intercept is located at (0, 3). So, substituting these values, we get:

3 = a(0 - 1)² + 23 = a + 23 - 2 = aa = 1

Therefore, the equation of the parabola is:

y = (x - 1)² + 2

Since the coefficient of the squared term is positive (1), the parabola opens upwards. Hence, the direction of the parabola is upwards.

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The solution is Option A.

The value of the 13th number from the equation A = ( -2/3 ) ( n - 1 ) is A = -8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( -2/3 ) ( n - 1 )   be equation (1)

On simplifying the equation , we get

The thirteenth number in the list is n = 13

So , when n = 13

A = ( -2/3 ) ( n - 1 )

A = ( -2/3 ) ( 13 - 1 )

On further simplification , we get

A = ( -2/3 ) ( 12 )

A = ( -2 ) x 4

So , the value of A = -8

Hence , the thirteenth number in the list is A = -8

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Answer:

x = 19 degrees

Step-by-step explanation:

180 - 114 = 66

180 - 66 = 114

Other triangle angle is 114 degrees

114 + 47 = 161

180 - 161 = 19

x = 19 degrees

Answer: Calculating a bowling score involves adding up the total number of pins knocked down over a series of frames. The basic scoring system in bowling is as follows:

- Each game is made up of 10 frames.

- In each frame, the bowler gets two chances to knock down all 10 pins.

- If the bowler knocks down all 10 pins on the first roll (called a strike), the frame is over, and the bowler is awarded 10 points plus the total number of pins knocked down on the next two rolls.

- If the bowler knocks down all 10 pins on the second roll (called a spare), the frame is over, and the bowler is awarded 10 points plus the total number of pins knocked down on the next roll.

- If the bowler does not knock down all 10 pins in a frame, the score for that frame is simply the total number of pins knocked down.

- To calculate the score for each frame, you add up the total number of pins knocked down in the two rolls. If the bowler gets a strike or a spare, you need to take into account the bonus points for the next rolls as described above.

To calculate the total score for the game, you add up the scores for all 10 frames, including any bonus points earned from strikes or spares.

For example, if a bowler knocked down 7 pins on the first roll, and 3 pins on the second roll (a spare) in the first frame, they would receive 10 points for that frame, plus the number of pins knocked down on the next roll (let's say 6). So the score for the first frame would be 10 + 6 = 16.

If in the second frame, the bowler gets a strike, then the score for that frame would be 10 plus the total number of pins knocked down on the next two rolls. Let's say they knock down 8 and 1 on the next two rolls. Then, the score for the second frame would be 10 + 8 + 1 = 19.

This process continues for all 10 frames, with bonus points being added for strikes and spares, until a total score for the game is obtained.

Step-by-step explanation:

If something is written in its simplest radical form, that means that you have already found all possible roots and eliminated any radicals from the denominator of a fraction. ... For example, if your fraction is 2/√7, multiply by √7/√7 to get 2√7/√49. This will simplify to 2√7/7.  hope this helps

Answer:

Square roots are the opposite of “squaring” a number, or multiplying it by itself. For example, three squared is nine (3 2 = 9), so the square root of nine is three. In symbols, this is √9 = 3. The “√” symbol tells you to take the square root of a number, and you can find this on most calculators.

Step-by-step explanation:

hope it helps

The closest percent markup cost to the bracelets Anna sells is 181%.

To determine the percent markup cost for the bracelets Anna sells, we need to calculate the difference between the selling price and the cost price, and then express it as a percentage of the cost price.

The selling price of the bracelets is $45, and the cost price is $16.

Markup = Selling Price - Cost Price

= $45 - $16

= $29

Now, to calculate the percent markup cost, we divide the markup by the cost price and multiply by 100:

Percent Markup Cost = (Markup / Cost Price) \(\times\) 100

= ($29 / $16) \(\times\) 100

= 181.25

Rounded to the nearest whole number, the percent markup cost is approximately 181%.

Therefore, the closest percent markup cost to the bracelets Anna sells is 181%.

This means that Anna is charging customers approximately 181% more than what it cost her to make the bracelets.

The markup cost represents the additional amount she adds to cover expenses, overhead, and to make a profit.

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Answer:

x = 5°

Step-by-step explanation:

5x + 21° + 20x + 34° = 180°

25x + 55° = 180°

25x = 180° - 55°

25x = 125°

x = 125°/25

x = 5°

Hope you got it dear !!!!

Geometric relationship is supplementary angles. Supplementary angles sum up to 180 degrees.

The value of x is 5.

Thus:

\((5x + 21) + (20x + 34) = 180^{\circ}\)  (angles on a straight line are supplementary)

\(5x + 21 + 20x + 34 = 180\)

\(25x +55 = 180\)

\(25x = 180 - 55\\\\25x = 125\)

\(x = 5\)

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Total 504 three digit numbers can be formed if no digit appear twice

What is Permutation?

The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.

Solution:

Total Numer of Digits = 9

Number of Characters in the number = 3

Total Numbers = 9P3 = 9! / 6!

9P3 = 504

Total 504 three digit numbers can be formed

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