HELP PLZ!

On a coordinate plane, the green triangle is rotated 90 degrees to form the blue triangle. Triangle Q R S is rotated 180 degrees to form triangle J K L. Use the graph to complete the statements. The green triangle is rotated degrees to form the blue triangle. Triangle QRS is rotated degrees to form the image triangle JKL.

HELP PLZ!On A Coordinate Plane, The Green Triangle Is Rotated 90 Degrees To Form The Blue Triangle. Triangle

Answers

Answer 1

Answer:

The green triangle is rotated  

✔ 90

degrees to form the blue triangle.

Triangle QRS is rotated  

✔ 180

degrees to form the image triangle JKL.

Step-by-step explanation:

have a nice day because I said so but mostly because you want to

Answer 2

The green triangle is rotated 90 degrees to form the blue triangle. And ΔQRS is rotated 180 degrees to form the image of ΔJKL.

What is coordinate plane?

" Coordinate plane is also known as cartesian plane in two dimensional , which is represented by intersection of two axis at 90°, the horizontal axis is known as x-axis and vertical axis is known as y-axis."

According to the given question,

Here all triangles are right angled triangle.

All triangles are perpendicular to the respective axis as per diagram.

Rotation of triangle on coordinate plane from one axis to another forms 90°.

Hence, we conclude that the green triangle is rotated 90 degrees to form the blue triangle. And ΔQRS is rotated 180 degrees to form the image of ΔJKL.

Learn about more coordinate plane here

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Related Questions

SOMEONE PLEASE HELP ME ASAP PLEASE!!!​

Answers

Hey there! :)

Answer:

4.

Step-by-step explanation:

Parallel lines contain the same slope. A line that is parallel to y = 4x + 2 has the same slope.

In this instance, a parallel line would contain a slope of m = 4.

Answer:

4

Step-by-step explanation:

Parallel lines have same slope.

How many distinct triangles can be drawn using three of the dots below as vertices?

Answers

Answer:

The number of distinct triangles that can be drawn using the dots = 6

Step-by-step explanation:

The parameters given are;

Two rows of three evenly spaced dots

To form a triangle, two dots will be selected from 1 row while the third dot will be selected from the other row

The number of ways of selecting the dots are therefore;

₃C₂ × ₃C₁ = 3 × 3 = 9 triangles

The same procedure can be done from the top row to give another 9 triangles

Which gives the total number of triangles = 18 triangles

The number of distinct triangles are found as follows;

Given that triangles obtained from the top row are similar to those of the bottom row, we reduce the range from which the distinct triangles can be found to 19 - 9 = 9 triangles

Of the 9 triangles formed by one dot on top and two dots on the bottom, the two adjacent dots of the three dots which are on the left and on the right of the lower row of dots, form the same three triangles with the three dots on the top row

Therefore, since there are 3 sets of two dots forming 9 triangles, each pair of dots can form 3 triangles, and as mentioned, 2 pairs of dots of the 3 pairs form the same triangles making the distinct triangle = 9 - 3 = 6.

HELP ASPAP!!!!! WILL MARK BRAINIEST standard deviation

Answers

Answer:

The standard deviation of the given data is 11.34.

Step-by-step explanation:

We have to find the standard deviation for the given data;

Grade on     No. of students          

 test (X)        with that score (f)        [tex]X \times f[/tex]       [tex]( X - \bar X)^{2}[/tex]        [tex]f \times ( X - \bar X)^{2}[/tex]

     50                  1                       50      1073.218      1073.2176

     57                 2                       114      663.578      1327.1552

     60                 4                       240       518.018     2072.0704

     65                 3                       195       315.418      946.2528

     72                 3                       216        115.778       347.3328

     75                12                       900        60.218       722.6112

     77                10                       770        33.178       331.776

     81                 6                       486        3.098       18.5856

     83                 6                       498        0.058        0.3456

     88                9                       792        27.458      247.1184

     90                12                      1080        52.418      629.0112

     92                12                       1104        85.378     1024.5312

     95                 2                        190        149.818      299.6352

     99                 4                        396        263.738     1054.9504

    100                 5                      500         297.218     1486.088    

   Total                  91                          7531                              11580.68    

Firstly, the mean of the above data is given by;

            Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X \times f}{\sum f}[/tex]

                             =  [tex]\frac{7531}{91}[/tex]  =  82.76

Now, the standard deviation of the data is given by;

          Standard deviation, S.D.  =  [tex]\sqrt{\frac{\sum f(X-\bar X)^{2} }{\sum f-1}}[/tex]

                                                     =  [tex]\sqrt{\frac{11580.68}{91-1}}[/tex]

                                                     =  11.34

Hence, the standard deviation of the given data is 11.34.

State how many imaginary and real zeros the function has.

f(x) = x4 + 12 x3 + 37x2 + 12x + 36

Answers

Answer:

Step-by-step explanation:

If you'd graph this function on a graphing calculator or graphing utility, you'd see quickly that the graph never touches or crosses the x-axis.  This tells us immediately that there are no real roots; all four roots are complex or imaginary.

Answer:

2 real roots and 2 imaginary roots

Step-by-step explanation:

The roots are x=i,-i,-6,-6.

WILL MARK BRAINIEST IF CORRECT FOR THE FIRST TO ANSWER!!! PLEASE HELP!!!


1. Create a data set with at least 5 values.
2. Write instructions that tell a friend how to find the mean absolute deviation of your data set.

Answers

Step-by-step explanation:

6,5,8,2,8,6,5,8,8

To find the mean you MUST add all of the numbers together

then divide by the number of numbers

this will be your mean

Then to find the absolute deviation you must find the absolute value of the numbers in this case they stay the same  since the absolute value is NEVER negative....

then you need to find the data value of the entire data set

then subtract the mean from that number!

Please help out ASAP :)

Answers

The correct answer is D

Using this coin and a number cube, which simulation would help you answer this question? A professor found that her students pass the final exam about 50% of the time. She gives the exam during the fall, spring, and summer terms. If she has 30 students during each term and you choose a student at random, what are the chances that the student passed the exam during the fall term.

Answers

Answer:

didnt understand the quedtion clearly

pls help i give brainliest when I can [ill be fair]

Answers

Answer:

A

Step-by-step explanation:

x= 1 2/3, y=4 2/3

y=4(1 2/3)-2.    y=4 2/3

y=1 2/3+3        y=4 2/3

and that make the answer going to be A. Also other answer didn't work so yet. Then, A should be the right answer!

Hope this help!

Answer:

A. x = [tex]\frac{5}{3}[/tex] or [tex]1\frac{2}{3}[/tex]  and y = [tex]\frac{14}{3}[/tex] or [tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

y = 4x - 2  ; y = x + 3

1. UNDERSTAND what you are given.

both equations solved for "y"when this is the case the easiest method is ALMOST ALWAYS SUBSTITUTION.

2. SUBSTITUTION METHOD means you replace one of the variables in terms of the other to start solving.

4x - 2 = x + 3 (write eq.)

3x - 2 = 3 (combine like terms: part 1)

3x = 5 (combine like terms: part 2)

x = [tex]\frac{5}{3}[/tex] or [tex]1\frac{2}{3}[/tex] (inverse operations: division)

3. PLUG IN VALUE FOR X to solve for y. Pick the simpler equation.

y = x + 3 (pick an original equation, either will work)

y  = [tex]\frac{5}{3}[/tex] + 3

y = [tex]\frac{5}{3}[/tex] + [tex]\frac{9}{3}[/tex]

y = [tex]\frac{14}{3}[/tex] or [tex]4\frac{2}{3}[/tex]

More explanations...

Find the missing side length in the attached image.

Answers

Answer:

24 units.

Step-by-step explanation:

we can use  concept of Thales intercept theorem in this problem

according to this theorem, if  there are n lines parallel to each then and two transverse line drawn such that they intersect the three parallel line given the problem, then the parallel line divides the transverse line equal proportion.

For this problem

For the line having length 45, one of the length is 25 units,

then other length will be 45-25 = 20 unit

Now using Thales intercept theorem

30/? = 25/20

30/? = 5/4

? = 30*4/5 = 24

Thus, missing side length will be 24 units.

(08.03)Solve the system of equations and choose the correct answer from the list of options. d + e = 1 −d + e = −5 Label the ordered pair as (d, e). (0, 0) (3, −2) (−2, 3) (−3, 0)

Answers

Answer:

(3, -2).

Step-by-step explanation:

d + e = 1

−d + e = −5    Adding the 2 equations:

0  + 2e = -4

e = -2.

Plug this into the first equation:

d + -2 = 1

d = 1 + 2

d = 3.

Check these results in the second equation:

-3 + -2 = -5    -  checks out.

-3+-2=-5 that’s correct

Find the are of ABC with the side lengths a=8 and b=12, and included angle C=84 degrees. Round your answer to the nearest tenth

Answers

Answer:

47.7 square units

Step-by-step explanation:

It is important to know that,

The area of any triangle with two given sides and an inclusive angle = 1/2(absinθ)

In the question above, we are given the following values:

Where : a = 8, b = 12, θ = C = 84°

Area of the Triangle ABC = 1/2 ×( 8 × 12 × sin 84)

Area of Triangle ABC = 47.737050978 square units

Approximately to the nearest tenth = 47.7 square units.

Therefore, the Area of triangle ABC to the nearest tenth = 47.7 square units.

A freight train is carrying goods across the country. The number of gallons of fuel it has used varies directly with the distance it has traveled. See the graph
below.

Answers

Answer:

0.125 miles per gallon.

Step-by-step explanation:

After 200 gallons used the freight train has traveled 25 miles. This means that we need to divide both sides by 200 to get a singular gallon's worth of miles traveled. 200/200 is 1, and 25/200 is 0.125.

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

Extra

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

IF it were how many gallons per mile, you would divide both answers by 25 resulting in 8 gallons per mile.

Which is the solution of the quadratic equation (4y - 3)2 = 72?
y
3 +/Z and y
y=
3-6/2
4
3+62
y=
and y=
-3 – 6/2
4
4
0
y=
9/2
4
and y= -3/2
4
9/2
4.
y=
3/2
and y=
4​

Answers

Answer:

Step-by-step explanation:

Let's solve (4y - 3)^2 = 72 for y.  To do this, take the square root of both sides.  This yields:

4y - 3 = ±√72 = ±√(36·2) = ±6√2

Then 4y = 3 ±6√2, or

       3 ± 6√2

y = ----------------

             4

The required solution of quadratic equation is y = (3±6√2)/4. Option A is correct.


Solution of the quadratic equation (4y - 3)2 = 72 to be determine.


What is quadratic equation?

Quadratic equation are the equation having maximum power 2.

Here,
(4y - 3)² = 72
4y-3 = ±√72
4y = ±√72 +3
y = (3 ± 6√2)/4


Thus, The required solution of quadratic equation is y = (3±6√2)/4.


Learn more about quadratic equation here:
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What is the value of Fraction 1 over 2x3 + 3.4y when x = 2 and y = 5?

18
20
21
37

Answers

Answer:

[tex]C. \[/tex]   [tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]

Step-by-step explanation:

Given

[tex]x = 2[/tex]

[tex]y = 5[/tex]

Required

[tex]\frac{1}{2}x^3 + 3.4y[/tex]

Substitute 2 for x and 5 for y;

The expression becomes

[tex]=\ \frac{1}{2} * 2^3 + 3.4 * 5[/tex]

Multiply 3.4 by 5

[tex]=\ \frac{1}{2} * 2^3 + 17[/tex]

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

[tex]2^3 = 2 * 2 * 2 = 8[/tex]

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

[tex]=\ \frac{1}{2} * 8 + 17[/tex]

[tex]=\ \frac{8}{2} + 17[/tex]

[tex]=\ 4 + 17[/tex]

[tex]=\ 21[/tex]

Hence;

[tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]

State whether the following is reasonable or not. Explain your answer. Josefina gave away 130% of her stamp collection.

Answers

Answer:

Hey there!

That wouldn't be possible.

130% of something is more than the total amount.

For example, if she had 100 stamps, and gave away 130%, she would have -30 stamps, which is unreasonable.

Hope this helps :)

Laura’s overall monthly living expenses are $1,600. How much money does she have at the end of the month to put into savings?

Answers

Step-by-step explanation:

The question has missing details nevertheless we can make head way with the information on ground.

Given that Laura's overall monthly living expenses are  $1,600

in order to calculate her savings for the month we need to know her income for the month, that is the overall sum she has at hand before incurring any expenses(this is the missing detail).

Say this overall amount is "x"

her saving for the month = [tex](x- 1600)[/tex]

PLEASEEE HELPP!!! BRINLIEST TO FIRST ANSWER!!
The dance team has 9 dancers to perform different roles in each performance. The probability that the team selects the same order as last performance is 1 divided by 362880 . -Explain where each the numerator and denominator come from. -What is the probability that the team puts the top hip hop dancer in the third position and top break dancer in the first position? Assume these are not the same people. -Create a question, related to the dancers, where you use the indirect method, n(A’), to solve.

Answers

Answer:

The probability that the team puts the top hip hop dancer in the third position and top break dancer in the first position is 1/72.

Step-by-step explanation:

It is provided that a dance team has 9 dancers to perform different roles in each performance.

The number of arrangements of the 9 dancers in the different roles is:

Number of order of performance = 9!

                                                       = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

                                                       = 362880

If the team selects the same order as last performance, then the possible number of arrangements is, 1.

The probability that the team selects the same order as last performance is:

[tex]=\frac{1}{362880}[/tex]

Now it is provided that the team puts the top hip hop dancer in the third position and top break dancer in the first position.

So of the 9 positions the 1st and 3rd are occupied.

There are a remaining 7 positions to be filled by 7 dancers.

That can happen in 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 ways.

Compute the probability that the team puts the top hip hop dancer in the third position and top break dancer in the first position as follows:

[tex]=\frac{5040}{362880}\\\\=\frac{1}{72}[/tex]

Thus, the probability is 1/72.

The graph of F(x) shown below resembles the graph of G(x) = x ^ 2 but it has been changed somewhat. Which of the following could be the equation of F(x)

Answers

Answer:

Option (A)

Step-by-step explanation:

Parent function of the function graphed is,

G(x) = x²

Graph shows the vertex of the given parabola is at (3, 3).

Vertex form of a parabola is,

F(x) = a(x - h)² + k

where (h, k) is the vertex.

By substituting the coordinates of the vertex in the equation,

F(x) = a(x - 3)² + 3

Since the given parabola is opening upwards, value of 'a' will be positive.

So the equation will be,

F(x) = 2(x - 3)² + 3

Therefore, from the given options, equation given in Option (A) matches the answer.

Answer:

A is the correct answer.

Step-by-step explanation:

2. Company A packages roofing nails in boxes that are normally distributed with a mean of 276 nails and a standard deviation of 5.8 nails. Company B packages roofing nails in boxes that are normally distributed with a mean of 252 nails and a standard deviation of 3.4 nails. Which company is more likely to produce a box of 260 roofing nails? Explain your answer using z-scores.

Answers

Answer:

Company B

Step-by-step explanation:

We would use z score formula

z = (x - μ) / σ

x = raw score

μ = mean

σ = Standard deviation

let x = 260 with the mean μ1 = 276 and standard deviation σ = 5.8

let x = 260 with the mean μ2 = 252 and standard deviation σ = 3.4

z1 = (x- μ1) / σ = (260- 276) / 5.8 = -2.7586206897

z2 = (x2 - μ) / σ = (260 -252) / 3.4= 2.3529411765

Comparing the two z scores, we can see that company B has the probability of producing 260 nails because it has a positive z score of approximately 2.35 compared to company A with a z score of -2.76.

It has been estimated that a student's final grade in a course decreases by 5 points for every 2 days absent from class . If student misses 4 days by now how many points will the students final grade decrease

Answers

Answer:

The students points will decrease 10 points in 4 days

Step-by-step explanation:

In 2 days he loses 5 points. So for 4 days all you have to do is double the amount of points because the amount of days have doubled

Can you please say if the point will be on the line?

Answers

Answer:

The point will be on the line.

Step-by-step explanation:

PLEASE HELP ME!!!
ABCD is a rectangle in the coordinate plane. Give possible coordinates for the vertices of rectangle ABCD.

How do you know that your vertices form a rectangle?

Answers

Answer:

(1,1) (2,1) (2,3) (1,3) They form a rectangle because there are two pairs of parallel sides.

:)

Sorry the question before didnt make sense.heres the full pic .

Answers

Answer:

No

Step-by-step explanation:

The question is:

Are 3/5 and 6/25 equivalent fractions?

Multiply the first fraction by 5/5:

3/5 * 5/5 = 15/25

3/5 is equivalent to 15/25

15/25 is not equal to 6/25.

Answer: No

What is the solution to the equation below? log 20xrise 3-2logx=4

Answers

Answer:

[tex]x = 500[/tex]

Step-by-step explanation:

Given

[tex]log20x^3 - 2logx = 4[/tex]

Required

Solve for x

[tex]log20x^3 - 2logx = 4[/tex]

Using law of logarithm which says;

[tex]nlogx = logx^n[/tex]

The expression becomes

[tex]log20x^3 - logx^2 = 4[/tex]

Also, using laws of logarithm which says:

[tex]loga - logb = log\frac{a}{b}[/tex]

The expression becomes

[tex]log(\frac{20x^3}{x^2}) = 4[/tex]

[tex]log(20x) = 4[/tex]

Also, using laws of logarithm which says

[tex]If\ loga = b\\then\ a = 10^b[/tex]

The expression becomes

[tex]20x = 10^4[/tex]

[tex]20x = 10000[/tex]

Divide through by 20

[tex]\frac{20x}{20} = \frac{10000}{20}[/tex]

[tex]x = \frac{10000}{20}[/tex]

[tex]x = 500[/tex]

Answer:

500

Step-by-step explanation:

The graph of the function F(x) = 2x^2-8 is changed. The new graph can be
represented by the function F(X)= -2x^2-4.

Which of the following describes the changes made to the graph of the
original function?

Answers

Answer:

The graph now opens in the opposite direction. The y intercept is shifted up 4.

Step-by-step explanation:

F(x) = 2x^2-8

F(X)= -2x^2-4

We know that the graph is reflected over the y-intercept becuase of the negative sign in the second equation ( F(X)= -2x^2-4)

We know that the intercept is shifted up four, because the number decreased from 8 to 4, and the graph is reflected.

Attacthed is both of the equations graphed to help you visualize this shift!

PRE CALC, help please

Answers

Answer:

option C is correct ...

Step-by-step explanation:

Because, x= -1 and x =3 are the solution of function.....
I think the answer is option c

Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles

Answers

Answer:

40 + 8pi

Step-by-step explanation:

1/2 circle = 1/2 pi r-squared = 1/2x4x4x pi = 8pi

triangle = 1/2bh = 1/2x8x10 = 40

total area = 40 + 8pi

What is the simplified form of?

Answers

Answer:

-2√7(-5.291503)

Step-by-step explanation:

combine like terms

Answer:

[tex] - 2 \sqrt{7} [/tex]

Step-by-step explanation:

[tex]3\sqrt{7} - 5\sqrt{7} = - 2 \sqrt{7} [/tex]

We subtract 3 and 5 and not the numbers under the radical.

The number under the radical can be changed if multiplied or divided.

3-5=-2 or

-5+3=-2

It's like having 5 dollar debt and then paying 3 dollars, you still have to pay those 2 dollars left.

Hope this helps ;) ❤❤❤

Marty says the probability of the high school team winning the hockey game is 35%.
Karim says the probability is 2/5. Who thinks the event is more likely, Marty or Karim?
Explain​

Answers

Answer:

Karim

Step-by-step explanation:

1. Turn 2/5 into a percentage by multiplying the numerator and denominators of 2/5 with 20 so the new fraction's denominator can be 100.

2. Your new fraction should be 40/100 also known as 40%.

3. Compare who's probability is more likely.

4. The answer will be (40%) Karim's.

Answer:

Karim

Step-by-step explanation:

35% is equivalent to 0.35, whereas 2/5 is equivalent to 0.40.  Karim is correct; 0.40 represents a greater probability than does 0.35.

Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 litres tin of paint in his store and decides to paint the tank (not the base). If he uses 250 ml to cover 1 , will he have enough paint to cover the tank with one layer of paint? [take π=3.142]

Answers

Answer:

Yes, he will have enough paint to cover the tank with one layer of paint.

Step-by-step explanation:

We are given that Tublu buys a cylindrical water tank of height 1.4 m and diameter 1.1 m to catch rainwater off his roof. He has a full 2 liters tin of paint in his store and decides to paint the tank (not the base).

He uses 250 ml to cover 1 [tex]\text{m}^{2}[/tex].

From the question, it is clear the area of the tank which needs to be painted is the lateral surface area (because the base is not included).

The lateral surface area of the cylinder = [tex]2\pi rh[/tex]

where, r = radius of the cylinder =  [tex]\frac{\text{Diameter}}{2}[/tex]  = [tex]\frac{1.1 }{2}[/tex] = 0.55 m

           h = height of the cylinder = 1.4 m

           [tex]\pi[/tex] = 3.142 (given)

So, the lateral surface area of a cylindrical water tank = [tex]2 \times 3.142 \times 0.55 \times 1.4[/tex]

                                                                                         = 4.84 [tex]\text{m}^{2}[/tex].

Now, it is given in the question that; Tublu uses 250 ml to cover 1 [tex]\text{m}^{2}[/tex] area, this means that;

To cover 4.84 [tex]\text{m}^{2}[/tex] area, he will use paint = [tex]4.84 \times 250[/tex] = 1210 ml

Since he has a full 2 liters tin of paint in his store which is equal to 2000 ml but he need only 1210 ml of paint.

This means that yes, he will have enough paint to cover the tank with one layer of paint.

Other Questions
Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12. He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week? If s=1/2 unit and A=12s^2, what is the value of A, in square unit? what is the relationship between variable x and variable y Please help its eighth math! Calculate the temperature atwhich the following reactionbecomes feasible:4HCI + O2 -> 2Cl2 + 2H2OEnthalpy: +280 kJ/molEntropy: +235 J/KmolA. 45.0 KB. 65.80 KC. 515.0 KD. 1191.49 KReset Selection plz answer question in screen shot 78. What color pigmentation is associated with pregnancy mask?brownblueb. yellowd. red n is an interger -15 SOMEONE PLSSS HELPP W MY SPANISH HW!!! ASAAPPPP!!! Which was NOT a response to the September 11 terrorist attacks on the United States? 1.Iraq denounced the events and disassociated itself from al-Qaeda. 2.World leaders pledged support to the United States during its recovery. 3.Citizens all over the country came together to support each other and the president. 4. The president requested and received congressional authorization for the use of military force. Read the following and fill in the blank from the choices given.In Macbeth, while Lady Macbeth plots to murder King Duncan,King Duncan suddenly arrives and apologizes to Lady Macbethfor intruding on the home of his dear friends and thanks LadyMacbeth for providing such a lovely place to stay. This is anexample of__________.A:overstatementB:dramatic irony plz helpurgent !!!!will give the brainliest !! Expand (x+3)(2x-4)(x-6) What single transformation maps ABC onto A'B'C'? A. rotation 90 clockwise about the origin B. rotation 90 counterclockwise about the origin C. reflection across the x-axis D. reflection across the line y = x What are the problems in this photo and how would it feel to be living their Fred can mow a lawn in 60 minutes. rocky can mow the same lawn in 40 minutes. how long does it take for both fred and rocky to mow the lawn if they are working together? express your answer as a reduced fraction. What were two beneficial effects of Jethro Tull's seed drill? Given the following function, find f(-5), f(0), and f(2).f(x) = - 3x-5f(-5) = Which of these factors is involved in earthquake formation?plates getting largerrocks breakingstress that decreasesfaults that remain stationary Which of the following is an incorrect statement? a If individual audit risk remains the same, detection risk bears an inverse relationship to inherent and control risk. b The greater the inherent and control risk the auditor believes exist the less detection risk that can be accepted. c The auditor might make separate or combined assessments of inherent risk and control risk. d Detection risk cannot be changed at the auditors discretion.