Calculate a and b if
[tex] \sqrt{ \frac{ {7}^{2014} - {7}^{2012} }{12} } = a( {7}^{b} )[/tex]
and a is not a multiple of 7. ​

The measure of a length of 10cm on the scale is 1/6 units

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

Scale = 1 : 60

For a length of 10 cm, we have

Actual length = 10 cm

This means that

Scale ; 10 cm = 1 : 60

Express as fraction

So, we have

Scale/10 cm = 1/60

When evaluated we have

Scale = 1/6 units

Hence, the measure of a length of 10cm on the scale is 1/6 units

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The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * [tex]e^{rt}[/tex]

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * [tex]e^{0.02 * 4}[/tex]

Using a calculator, we can calculate:

A = $16,000 * [tex]e^{0.08}[/tex]

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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The sales tax on the computer is $69.93.

To calculate the sales tax on the computer, we need to multiply the price of the computer by the sales tax rate. Here's how you can do it:

Price of the computer: $999.00

Sales tax rate: 7% (which can be expressed as 0.07)

Sales tax = Price of the computer * Sales tax rate

Sales tax = $999.00 * 0.07

To find the sales tax in dollars and cents, we can perform the calculation:

Sales tax = $999.00 * 0.07

Sales tax = $69.93

Therefore, the sales tax on the computer is $69.93.

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Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.

To calculate Salina Grant's gross pay, we need to determine the pay for each range of chairs assembled and sum them up.

Let's break down the calculation based on the given differential piece rate scale:

1-25 chairs: $10 each

Salina assembled 25 chairs in this range, so the pay for this range is

25 * $10 = $250.

26-40 chairs: $13 each

Salina assembled 15 chairs in this range, so the pay for this range is

15 * $13 = $195.

Chairs over 40: $17.50 each

Salina assembled 47 chairs in total, and since she already assembled 25 chairs in the first range and 15 chairs in the second range, the number of chairs in this range is

47 - 25 - 15 = 7 chairs.

The pay for this range is

7 * $17.50 = $122.50.

Now, let's sum up the pay for each range to find Salina Grant's gross pay:

$250 + $195 + $122.50 = $567.50

Therefore, Salina Grant's gross pay for assembling 47 chairs in one week at Chairs and More is $567.50.

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Answer:

B) 16.47

Step-by-step explanation:

In order to find the mean of grouped data with intervals, we use the formula

(∑f * m) / (∑f)

Step 1:  First, we need to find the sum of the frequencies: ∑f = 2 + 3 + 8 + 4 = 17

Step 2:  Next, we need to find the midpoint (m) of each interval.  We do this by averaging the end points of each interval

m of first interval:  (9.5 + 12.5) / 2 = 11

m of second interval:  (12,5 + 15.5) / 2 = 14

m of third interval:  (15.5 + 18.5) / 2 = 17

m of fourth interval:  (18.5 + 21.5) / 2 = 20

Step 3:  Now, we multiply the frequency for each interval by its corresponding midpoint and add them together to find the sum

f * m for first interval: (2 * 11) = 22

f * m for second interval:  (3 * 14) = 42

f * m for third interval:  (8 * 17) = 136

f * m for fourth interval:  (4 * 20) = 80

Sum of f * m for each interval:  22 + 42 + 136 + 80 = 280

Step 4:  Finally, we divide the sum of f * m for each interval by the sum of f to find the mean:

280 / 17 = 16.47058824 = 16.47

The value of sinθ is √24/7 meanwhile the correct answer is not in the option provided or perhaps option (b) is meant to be √24/7 instead.

In the third quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) of the angle are negative.

Given that

cosθ = 5/7

we can determine the value of sinθ using the Pythagorean identity:

sin²θ + cos²θ = 1

sin²θ + (5/7)² = 1

sin²θ + 25/49 = 1

Now, let's solve for sinθ:

sin²θ = 1 - 25/49

sin²θ = 49/49 - 25/49

sin²θ = 24/49

Taking the square root of both sides, we find:

sinθ = √(24/49)

Simplifying further:

sinθ = √24 / √49

sinθ = √24 / 7

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Answer:

471.1 square units

Step-by-step explanation:

A regular nonagon is a 9-sided polygon with sides of equal length.

The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.

Therefore, the given diagram shows a regular nonagon with an apothem of 12 units.

The side length (s) of a regular polygon can be calculated using the apothem formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Given values:

Substitute the given values into the formula to create an expression for the side length (s):

[tex]12=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{9}\right)}[/tex]

[tex]12=\dfrac{s}{2 \tan\left(20^{\circ}\right)}[/tex]

[tex]s=24 \tan\left(20^{\circ}\right)[/tex]

The standard formula for an area of a regular polygon is:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

Substitute the found expression for s together with n = 9 and a = 12 into the formula and solve for A:

[tex]A=\dfrac{9 \cdot 24 \tan(20^{\circ}) \cdot 12}{2}[/tex]

[tex]A=1296\tan(20^{\circ})[/tex]

[tex]A=471.705423...[/tex]

[tex]A=471.7\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular nonagon with an apothem of 12 units is 471.1 square units, rounded to the nearest tenth.

The conversion of 3185 degrees to minutes and seconds is 19 minutes and 6.6 seconds

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

Degrees = 0.3185

By definition, there are 60 minutes in a degrees

So, we have

Minutes = 0.3185 * 60

Evaluate the product

Minutes = 19.11

The decimal part of the product above represents the number of seconds

So, we have

Minutes = 19

Seconds = .11 * 60

Evaluate

Seconds = 6.6

Hence, .3185 degrees is 19 minutes and 6.6 seconds

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Answer:

150

Step-by-step explanation:

To determine the number of possible combinations for the briefcase, we need to multiply the number of options for each wheel.

The first wheel has 10 digits, so there are 10 possibilities.

The second wheel has 5 digits, so there are 5 possibilities.

The third wheel has 3 digits, so there are 3 possibilities.

To calculate the total number of combinations, we multiply the possibilities for each wheel:

10 × 5 × 3 = 150

Therefore, there are 150 possible combinations for the briefcase.

Answer: 150

Step-by-step explanation:

I’m not completely sure, but this is going by my logic. The first one has ten digits and any of those ten digits could go with 1 digit from the 5 wheel, and 1 digit from the 3 wheel, so (I think) you have to multiply 10x5x3 to get the amount of possible combinations.

But, if this is wrong, please correct me! I love puzzles and just though this would be fun to try and figure out, I don’t want to spout out any mis or disinfo to anyone

But, in the case my answer’s right, hope this helped :D

Answer:

2.

Quarterly:

Monthly:

Continuously:

3.

Twice a year:

Eight times a year:

Continuously:

Step-by-step explanation:

The formula for compound interest is:

A = P(1+r/n)^nt

The formula for compounded continuously is:
A = Pe^rt

Where:

A = the future value of the investment

P = the principal balance

r = the annual interest rate (decimal)

n = number of times interest is compounded per year

t = the time in years

Using that we can plug the formula in for each question:

2.

Quarterly:

Monthly:

Continuously:

3.

Twice a year:

Eight times a year:

Continuously:

Step-by-step explanation:

sin Φ  = 5/6 = .8333

Arcsin ( sin Φ) =  arcsin (.8333)

Φ = 56.4 degrees

The area of the rectangular shaped kitchen floor is A = 96 feet²

Given data ,

The side length of each tile is 2ft, then the area of each tile is:

Area of a tile = side x side = 2ft x 2ft = 4 sq ft

Since there are 6 rows of tiles, each row has 4 tiles, therefore the total number of tiles is:

Total number of tiles = 6 x 4 = 24 tiles

So, the total area covered by the tiles is:

Total area covered by tiles = Area of a tile x Total number of tiles

= 4 sq ft/tile x 24 tiles

= 96 sq ft

Hence , the area of the kitchen floor is 96 feet²

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The radius of cylinder is 31.5 cm.

We have,

LSA of Cylinder. = 693 cm²

Height = 11 cm

We know the formula

Lateral Surface Area of Cylinder = 2πrh

So, LSA of cylinder = 639π

2πh= 693π

2rh = 693

r = 693 / 2h

r =693 / 2 x 11

t = 63/2

r = 31.5  cm

Thus, the radius of cylinder is 31.5 cm.

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The value of distance of two points shown in figure is,

⇒ d = √20

We have to given that;

Two points on graph are,

(0, 1) and (2, - 3)

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, The distance of two points shown in figure is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (2 - 0)² + (-3 - 1)²

⇒ d = √4 + 16

⇒ d = √20

Thus, The value of distance of two points shown in figure is,

⇒ d = √20

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The system of equations has infinitely many solutions, which corresponds to option (OB).

We can use the graphing function on a calculator to find the solution to the system of equations:

[tex]3y - 12x = 18\\\\2y - 8x = 12[/tex]

To do this, we can rearrange each equation to solve for y in terms of x:

[tex]3y = 12x + 18\\\\y =4x + 6[/tex]

For the second equation.

[tex]2y = 8x + 12\\\\y = 4x + 6[/tex]

We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.

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Answer:

1)

7+9-15 = add 7 and 9, then subtract 15

2)

15-(7+9) = The sum of 7 and 9 subtracted from 15

3)

15-(7+9) =  subtract 7 from 15, then add 9

Step-by-step explanation:

Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient

The area of the given figure is 133 m²

Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,

The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height

Therefore,

The area of the given figure = 9.5 x 14 = 133

Hence, the area of the given figure is 133 m²

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The angles in the parallel lines are solved

∠9 and ∠16 = alternative exterior angles

∠15 and ∠11 = supplementary angles

∠10 and ∠15 = alternate interior angles

∠12 and ∠15 = vertical angles

∠9 and ∠11 = corresponding angles

∠9 and ∠15 = none

∠13 and ∠14 = supplementary angles

∠14 and ∠11 = alternative interior angles

Given data ,

Let the two parallel lines be represented as a and b

where the transversal line is m

Now , from the given figure , we can deduct that

We can conclude some factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Now , the angles are

∠9 and ∠16 = alternative exterior angles

∠15 and ∠11 = supplementary angles

∠10 and ∠15 = alternate interior angles

∠12 and ∠15 = vertical angles

∠9 and ∠11 = corresponding angles

∠9 and ∠15 = none

∠13 and ∠14 = supplementary angles

∠14 and ∠11 = alternative interior angles

Hence , the angles are solved

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Table C shows the sample space for choosing 2 marbles from the bag with replacement. The probabity and there are 25 possible pairs.

The sample space for choosing 2 marbles from the bag with replacement consists of all possible pairs of marbles that can be chosen, where the order in which they are chosen does not matter.

Since there are 5 marbles in the bag and we are choosing 2 of them, there are 5 choices for the first marble and 5 choices for the second marble, for a total of [tex]5*5 = 25[/tex] possible pairs.

Table C shows the sample space for choosing 2 marbles from the bag with replacement. Each row and column in the table represents a different marble that can be chosen, and each cell represents a pair of marbles that can be chosen.

For example, the cell in row 2 and column 3 represents the pair of marbles consisting of the red marble and the clear marble. Tables A and B show the sample space for choosing 2 marbles from the bag without replacement. In this case, the order in which the marbles are chosen does matter, and each marble can only be chosen once.

Therefore, there are only 5 choices for the first marble, but only 4 choices for the second marble (since one marble has already been chosen), for a total of[tex]5 * 4 = 20[/tex] possible pairs.

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The complete question is:

A bag contains five green marbles, three blue marbles, two red marbles, and two yellow marbles. One marble is drawn out randomly.

a) Are the four different colour outcomes equally likely? Explain.

b) Find the probability of drawing each colour marble i.e., P(green), P(blue), P(red) and P(yellow)

c) Find the sum of their probabilities.

There are 4 variables in the expression 8d² + 2bc + 10ab

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

8d²+2bc+ 10ab

Express properly

So, we have

8d² + 2bc + 10ab

Consider an expression ax + by where the variable is a and b are constants

The variables in the expression are x and y

Using the above as a guide, we have the following:

The variables in the expression 8d² + 2bc + 10ab are a, b, c and d

This means that there are 4 variables in the expression

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After rotating the triangle counterclockwise by 270 degrees, the new coordinates of the vertices would be (3, -1), (-4, 2), and (3, 5).

To rotate a point counterclockwise around the origin by 270 degrees, we can use the following transformation rules:

[tex]New_x = -y[/tex]

[tex]New_y = x[/tex]

Let's apply these rules to each vertex of the triangle and find the new coordinates:

For the first vertex (-3, 1):

[tex]New_x = -1[/tex]

[tex]New_y = -(-3) = 3[/tex]

So, the new coordinates for the first vertex after rotating counterclockwise by 270 degrees are (3, -1).

For the second vertex (2, 4):

[tex]New_x = -4[/tex]

[tex]New_y = 2[/tex]

The new coordinates for the second vertex after rotating counterclockwise by 270 degrees are (-4, 2).

For the third vertex (5, -3):

[tex]New_x = -(-3) = 3[/tex]

[tex]New_y = 5[/tex]

The new coordinates for the third vertex after rotating counterclockwise by 270 degrees are (3, 5).

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The correct matrix representation is;  [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,

Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(1, 3) and P₂(5, 2)

Thus, by the coordinates of the two vectors, we can represent the matrix  ;

[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Hence, Option A) is the correct answer.

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The values for the determinants of the matrices are:

|A| = -3

|B| = -2

|AB|= -6

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

If the matrix Z is given as:

[tex]Z = \left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]

The determinant will be:

|Z| = (a * d) - (b * c)

Thus:

|A| = (-1 * 3) - (0 * 0) = -3

|B| = (2 * (-1)) - (0 * 0) = -2

AB = A * B

[tex]AB = \left[\begin{array}{ccc}-1&0\\0&3\end{array}\right] * \left[\begin{array}{ccc}-2&0\\0&-1\end{array}\right][/tex]  

Calculations for the product (multiply each row by each column):

[-1 * (-2)] + [0 * 0] = 2

[-1 * 0] + [0 * (-1)] = 0

[0 *  (-2)] + [3 * 0] = 0

[0 * 0] + [3 * (-1)] = -3

[tex]AB = \left[\begin{array}{ccc}2&0\\0&-3\end{array}\right][/tex]

Thus,

|AB| = (2 * (-3)) - (0 * 0) = -6

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Answer:

  16000

Step-by-step explanation:

You want to know the number of panels produced at plant B if that was 6000 more panels than at plant A, and the total number of defective panels was 820. The defect rate at plant A is 5%, and at plant B is 2%.

Let b represent the number of panels produced at plant B. Then the number produced at plant A is (b-6000). The total number of defects is ...

  0.05(b -6000) +0.02b = 820

Simplifying the equation, we have ...

  0.07b -300 = 820

  0.07b = 1120

  b = 16000

Plant B produced 16000 panels.

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Answer: 127

Step-by-step explanation:

360 - 70 - 36 = 254

254/2 = 127

D = 127

Answer:

When the cab travels 0 miles, the total fee will be $10.00.

Step-by-step explanation:

We Know

2 miles = $13.00

5 miles = $17.50

3 miles = 17.50 - 13.00 = $4.50

1 mile = 4.50 / 3 = $1.50

So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.

What does the y-intercept mean in this situation?

It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).

So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.

The formula for the surface area of a cylinder SA= 2mth + 2rr² is 525 cm².

To find the surface area of the cylindrical can, we need to use the formula:

SA = 2π[tex]r^2[/tex]+ 2πrh

where r is the radius of the circular base of the can, h is the height of the can, and π is a mathematical constant approximately equal to 3.14.

From the given dimensions, we know that the radius of the can is 4 cm. However, we do not have the height of the can. Therefore, we cannot accurately calculate the surface area of the can.

Based on the answer choices provided, we can approximate the surface area of the can by using the given value of r = 4 cm and an estimated value for the height.

For example, if we assume the height of the can is approximately 10 cm, then we can use the formula to calculate the surface area:

SA = 2π([tex]4^2[/tex]) + 2π(4)(10)

SA = 100.48 + 251.2

SA ≈ 351.68 [tex]cm^2[/tex]

     ≈525 cm²

This value is closest to the fourth answer choice of 350 [tex]cm^2[/tex]. However, it is important to note that this answer is an approximation based on estimated values, and may not be entirely accurate.The  correct answer is 525 cm².

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Answer:

24

Step-by-step explanation:

For this problem, substitute the value -3 for x and solve. It would look like this:

[tex]4(-3)^2+2(-3)-6[/tex]

Using the order of operations (PEMDAS) we solve the exponent first.

[tex]-3^2=9[/tex]

Then solve the multiplication parts.

[tex]4(9)+2(-3)-6\\4*9=36[/tex]and        [tex]2*(-3)=-6[/tex]

Finally subtract to get the answer.

[tex]36-6-6=24[/tex]

The angle formed by the cable between chairs B and J, and then

continue chair G is

75 degrees

The angle is determined with the knowledge of the total angle in a circle which is 360 degrees. Also, intercepted arc = 2 * inscribed angle

Assuming each chair is equal distance apart, then they will subtend equal angle.

The number of chairs for A to L is 12

angle per chair = 360 / 12 = 30 degrees

number of chairs from B to G = 5 and angle intercepted arc = 30 * 5 = 150 degrees

Inscribed angle = 1/2 * intercepted arc

Inscribed angle = 1/2 * 150

Inscribed angle = 75 degrees

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