Does anyone have the answer for question 18?

32.383 is  the cost of the textbook including the sales tax.

How does sales tax work?

The original price of the textbook = $32.50

Also, the discount percentage = 6%

Thus, the price of the textbook after discount = 32.50 - 6 % of 32.50

                                           = 32.50 - 6 * 3250/100

                                           = 32.50 - 1.95

                                            = 30.55

Now, the sales tax = 6 %

Hence, the cost of the textbook including sales tax

                                                                                = 30.55 + 6 % of 30.55

                                                                           = 30.55 + 6 * 30.55/100

                                                                        = 30.55 + 1.833

                                                                        = 32.383

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For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

Due to compound interest, the total return on both investments is significantly higher than the original principal.

Step-by-step explanation:

Both accounts model compound interest growth. Compound interest is a type of growth in which the interest earned on an investment is added to the principal, so that the interest earned in the future is based on a higher principal. In both of the accounts you described, the interest is compounded at a specific frequency (quarterly in Account A and monthly in Account B) over a number of years. This means that the interest earned on the investment is added to the principal at regular intervals, and the interest earned in the future is based on the new, higher principal.

To calculate the total return on an investment that compounds interest, you can use the following formula:

Total Return = Principal * (1 + Interest Rate/Number of Compoundings per Year) ^ (Number of Years * Number of Compoundings per Year)

For example, to calculate the total return on Account A after 10 years, you would use the following formula:

Total Return = $16,000 * (1 + 0.03/4) ^ (10 * 4) = $22,217.33

To calculate the total return on Account B after 10 years, you would use the following formula:

Total Return = $16,000 * (1 + 0.03/12) ^ (10 * 12) = $22,303.47

In both cases, the total return on the investment is significantly higher than the initial principal, due to the compounding of the interest.

Answer:

x=2; the extraneous root x=42.

All the details are in the attached picture, the answer is marked with red colour.

The solution set is {2, 42} & the extraneous root is 42

If there are two roots in an equation, and one of them does not properly satisfy the equation, then the root is called extraneous root of that equation.

Given equation is,

\(2+\sqrt{2x-3}=\sqrt{x+7}\)

Squaring both sides we get,

\(2^{2} +2(2)(\sqrt{2x-3} )+(\sqrt{2x-3}) ^{2} = (\sqrt{x+7}) ^{2}\)

⇒ \(4+4\sqrt{2x-3} +2x-3=x+7\\\)

⇒ \(4\sqrt{2x-3} =6-x\)

Again, squaring both sides we get,

⇒ \((4\sqrt{2x-3}) ^{2} =(6-x)^{2}\)

⇒ \(16(2x-3)=6^{2} -12x+x^{2}\)

⇒ \(32x-48=36-12x+x^{2}\)

⇒ \(x^{2} -44x+84=0\)

⇒ \(x^{2} -42x-2x+84=0\)

⇒ \((x-42)(x-2)=0\)

So, x = 2 & 42

Here extraneous root is 42.

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Answer:

Let x=Width

Length = 7x-22 (22m less the 7 times width)

A=L*w

A=(7x_22)x

7805=7x^2-22x

7x^2-22x-7805=0

(7x-223) (7x+223)=0

7x-223=0

7x=223

x=223%7

x=35

Now,

Length =7x-22

=7(35)-22

=223

therefore,length =223

If the area of the rectangle is 7805 square meters, The length of the rectangle will be 223 units

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that, A rectangle has a length of 22 meters less than 7 times its width. If the area of the rectangle is 7805 square meters,

Suppose the width of the rectangle is x.

Length = 7x-22 (22m less the 7 times width)

A=L*w

A=(7x_22)x

7805=7x²-22x

7x²-22x-7805=0

(7x-223) (7x+223)=0

7x-223=0

7x=223

x=223/7

x=35

As a result

Length =7x-22

=7(35)-22

=223 units.

Thus, if the area of the rectangle is 7805 square meters, The length of the rectangle will be 223 units

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Answer:

The Answer for 12 x 20 is 240 if this helps there was not much info you gave me to do this sorry if this is not your question or answer

Step-by-step explanation:

Mark Me Brainliest Please

We will have the following:

Since we can see that the line intercepts the parabola in two places we can determine then that the number of solutions for this particular system is 2.

The measures of the angles are Z = 146 degrees, X and W = 34 degrees and B = 119 degrees

Question 4

From the question, we have

<Y = 146 degrees

Because the lines XY and WZ are equal, it means that

<Z = 146

So, we have

X = W = (180 - 146)

Evaluate

X = W = 34

Question 6

Here, we have

Sum of the angles = 180 degrees

This gives

9x + 2 + 5x - 4 = 180

Evaluate the like terms

14x = 182

Divide by 14

x = 13

So, we have

B = 9 * 13 + 2

B = 119 degrees

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Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

4

Step-by-step explanation:

The current price per share is $32.59

The annual net earnings per share is $9.06

Therefore the PE ratio can be calculated as follows

= $32.59/$9.06

= 3.59

= 4 (to the nearest whole number)

Hence the PE ratio is 4

The radix for the number to convert is 16 so it's hexadecimal. There's, I believe a typo as there no "." in base 16. Base 2 is binary and so the answer would be \(1010010111011111\)

Answer:

y=-1/2x+6

Step-by-step explanation:

slope: -5/10 = -1/2

y=mx+b

y=-1/2x+b

substitute points to find b: 8=-1/2(-4)+b

8=2+b

6=b

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Answer:

Step-by-step explanation:

First, let us substitute x and y values: -7 = -2(-5) + 4

Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).

Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:

14 + b = -7

by simplifying, we can conclude that b = -21

Finally, we can plug in the b-value into our original equation:

y = -2x + 4 - 21

After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).

Answer:

B,D,E

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

The coordinates for the point J are (-5, 6).

The radius 12 represents the center of the circle from each band member to the edge of the circle.

The domain of the circle is -17 ≤ x ≤ 7.

The range of the circle is -6 ≤ y ≤ 18.

In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided above, we have the following equation of a circle:

x² + y² + 10x - 12y - 83 = 0

x² + 10x + y² - 12y = 83

x² + 10x + (10/2)² + y² - 12y + (-12/2)² = 83 + (10/2)² + (-12/2)²

x² + 10x + 25 + y² - 12y + 36 = 83 + 25 + 36

(x + 5)² + (y - 6)² = 144

(x + 5)² + (y - 6)² = 12²

Therefore, the center (h, k) is (-5, 6) and the radius is equal to 12 units.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-17, 7] or -17 ≤ x ≤ 7.

Range = [-6, 18] or -6 ≤ y ≤ 18.

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Answer:

544w + 11%

Step-by-step explanation:

544 is the number he started with, so if he increases 11% by w (the amount of weeks) then you will get your anwser based on the number of weeks he increases

Answer:

4/18

Step-by-step explanation:

Theres a total of 18 shirts and a total of 4 red shirts so it would give you a 4/18 ratio/chance of getting red.

Answer:

4:18

Step-by-step explanation:

8+4+6 is 18 and there are 4 red shirts

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Answer:

The answer is point A' (3, -2).

Applying the Angle Addition Postulate, the measure of angle BDC is calculated as: 57 degrees.

The Angle Addition Postulate establishes that when two angles are adjacent, the measure of the resulting angle formed by their combination is equal to the sum of their individual measures.

Therefore, according to the Angle Addition Postulate, we would have:

(-6x + 11) + (-7x + 15) = 104

Solve for x:

-6x + 11 - 7x + 15 = 104

-13x + 26 = 104

-13x = 104 - 26

-13x = 78

x = -6

Measure of angle BDC = -7x + 15

Plug in the value of x:

Measure of angle BDC = -7(-6) + 15 = 57°

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The representation that would be best for determining the two values that 50 % of the data will lie is C. Interquartile Range

The interquartile range (IQR) is a measure of the dispersion of a dataset. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. The interquartile range provides a measure of the spread of the middle 50% of the data, as opposed to the range which measures the spread of the entire dataset.

The interquartile range is useful because it is not affected by outliers or extreme values, unlike the range. It is therefore a more robust measure of dispersion and is often used in statistics and data analysis.

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Options for this question include: