Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C. I, II, and III D. I, only

Answer: The probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Jennifer wants to visit 4 different cities A,B,C and D on her vacation.

If she visits in an order , total such orders will be [tex]4![/tex] = 4 x 2 x 3 x 1 =24.

Since probability = [tex]\dfrac{\text{Favourable outcomes}}{\text{total outcomes}}[/tex]

In this case favorable outcomes ( ABCD ,  DCBA)=  2

Total outcomes = 24

Required probability = [tex]\dfrac{2}{24}=\dfrac{1}{12}[/tex]

Hence, the probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

Answer:

[tex]\boxed{44}[/tex]

Step-by-step explanation:

[tex][-5+(-7)]^2-(7+3)^2[/tex]

Resolving Parenthesis

[tex](-5-7)^2-(10)^2\\(-12)^2-100\\144-100[/tex]

=> 44

Answer:

[tex]\boxed{44}[/tex]

Step-by-step explanation:

[tex][-5+(-7)]^2-(7+3)^2[/tex]

Solve for brackets first.

[tex][-12]^2-(10)^2[/tex]

Solve the exponent or power.

[tex]144-100[/tex]

Subtract the numbers.

[tex]=44[/tex]

Step-by-step explanation:

since PQRT is a rhombus,

URQ=TPU

y=180-90-24=66

x=180-32-90-24=34

4/5 recommend, so about 4/5(120) = 96 doctors recommend the brand.

Answer:

Step-by-step explanation:

                +2d+30    +2d+30

                    ÷(-15)      ÷(-15)

my mistake it's actually d= -30/19 sometimes I forget you put them in fractions

Answer:

Step-by-step explanation:

Hello!

a)

You have three triangles and you have to find the ratio of the adjacent sides to the angle 23.1º

Remember, considering a specific angle ∠, "the adjacent sides" are those that make contact with the angle and the "opponent side" is the one that is in the opposite side of the angle and the hypotenuse is the longest side of the right triangle, always opposed to the right angle.

First triangle, the adjacent sides, are

JL= 20.17m (hypotenuse)

JK= 18.55m

Ratio: [tex]\frac{JK}{JL}= \frac{18.55}{20.17}= 0.9196= 0.92[/tex]

Second triangle, adjacent sides:

PR= 141.19m (hypotenuse)

PQ= 129.85m

Ratio: [tex]\frac{PQ}{PR} = \frac{129.85}{141.19}= 0.9196= 0.92[/tex]

Third triangle, adjacent sides:

XZ= 181.53m (hypotenuse)

XY= 166.95m

Ratio: [tex]\frac{XY}{XZ} = \frac{166.95}{181.53} = 0.9196= 0.92[/tex]

b)

Using the calculator you have to calculate the trigonometric ratios of 23.1º:

sin(23.1º)= 0.392= 0.39

cos(23.1º)= 0.9198= 0.92

tan(23.1º)= 0.426= 0.43

c)

To calculate the trigonometrical ratios manually you have to do as follows:

Consider the angle A

[tex]sinA= \frac{opposite}{hypotenuse}[/tex]

[tex]cosA= \frac{adjacent}{hypotenuse}[/tex]

[tex]tanA= \frac{opposite}{adjacent}[/tex]

In item a) you calculated the ratios of the adjacent sides of the angle by the hypotenuse, this is equal to the cosine of the given angle.

I hope this helps!

Answer:  243 cm²

Step-by-step explanation:  If the diameter is 18, the radius is 9. Each square is  9×9, so 81 cm² for each.   Multiply:  81×3 = 243

Or take the length times width  to get area  27×9= 243

Answer:

It decreases from 45° to 40°

Step-by-step explanation:

The secant angle GBJ is half the difference of the measure of its intercepted arcs, that is

∠ B = [tex]\frac{1}{2}[/tex] (CDF - GHJ) = [tex]\frac{1}{2}[/tex](130 - 40)° = [tex]\frac{1}{2}[/tex] × 90° = 45°

If arc GHJ is now 50°, then

∠ B = [tex]\frac{1}{2}[/tex](130 - 50)° = [tex]\frac{1}{2}[/tex] × 80° = 40°

That is ∠ B decreases from 45° to 40°

Answer:

$3750 and $4250

Step-by-step explanation:

x + 500 = y

.045x + .035y = 317.50

.045x + .035(x + 500) = 317.50

.045x + .035x + 17.5 = 317.50

.08x = 300.00

x = 3750

y = 4250

Answer:

Add equations A + B to eliminate y

Then add equations A and C to eliminate y

Step-by-step explanation:

Since all the equations have y with a coefficient of 2, I would eliminate y

Add equations A + B to eliminate y

Then add equations A and C to eliminate y

Answer:

the 3rd choice

Answer:

151200 possible combinations

Step-by-step explanation:

There are 10 digits 0 - 9  ( 0,1,2,3,4,5,6,7,8,9)

There are 10 choices for the first digit

10

There are 9 choices for the second digit

9

There are 8 choices for the third digit

8

and so on  since we can only use each digit once

10 *9*8 *7 *6*5

151200 possible combinations

Answer:

Step-by-step explanation:

[tex]x^2+y^2=250\\\\x^2-2xy+y^2+2xy=250\\\\(x-y)^2=250-2xy\\\\(x-y)^2=250-2\cdot117\\\\ (x-y)^2=16\\\\x-y=4\qquad\qquad\vee\qquad \qquad x-y=-4\\\\x=4+y \qquad\qquad \vee\qquad\qquad x=-4+y\\\\(y+4)y=117\qquad\vee\qquad\quad (y-4)y=117\\\\y^2+4y-117=0\qquad\vee\qquad y^2-4y-117=0\\\\y=\dfrac{-4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\qquad\vee\qquad y=\dfrac{4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\\\\y=\dfrac{-4\pm\sqrt{16+468}}{2}\qquad\ \ \vee\qquad y=\dfrac{4\pm\sqrt{16+468}}{2}[/tex]

[tex]y_1=\dfrac{-4-22}{2}\ ,\quad y_2=\dfrac{-4+22}{2}\ ,\quad y_3=\dfrac{4-22}{2}\ ,\quad y_4=\dfrac{4+22}{2}\\\\y_1=-13\ ,\qquad y_2=9\ ,\qquad\quad\qquad\ y_3=-9\ ,\qquad y_4=13\\\\x_{1,2}=4+y_{1,2}\qquad\qquad\qquad\qquad\qquad x_{3,4}=-4+y_{3,4}\\\\x_1=-9\ ,\qquad x_2=13\ ,\qquad\quad\qquad x_3=-13\ ,\qquad x_4=9[/tex]

Answer:

Step-by-step explanation:

Let's call the "positive real number" X.

Basically, the question is  a riddle asking for the "solution" to 14x+240=x²

Figure that out, and

The answer is 24.

The correct answer is 24.

Answer:

23/30

Step-by-step explanation:

x/y

(3 5/6)/(3 3/4)

((3*6)+5/6)/((3*4)+ 3/4)

(18+5/6)/(12+3/4)

(23/6)/(15/4)

(23/6)*(4/15)

(23*3)/(6*15)

(69/90)

23/30

Answer:

1 1/45

Step-by-step explanation:

Answer:

Average speed for the entire trip, both ways, is

                (Total distance) divided by (total time) .

We don't know the distance from his house to the gift store,

and we don't know how long it took him to get back.

We'll need to calculate these.

-- On the trip TO the store, it took him 50 minutes, at 6 mph.

-- 50 minutes is 5/6 of an hour.

-- Traveling at 6 mph for 5/6 of an hour, he covered 5 miles.

-- The gift store is 5 miles from his house.

-- The total trip both ways was 10 miles.

-- On the way BACK home from the store, he moved at 12 mph.

-- Going 5 miles at 12 mph, it takes  (5/12 hour) = 25 minutes.

Now we have everything we need.

Distance:

        Going:       5 miles

        Returning:  5 miles

        Total         10 miles

Time:

        Going:        50 minutes

        Returning:   25 minutes

        Total:          75 minutes  =  1.25 hours  

        Average speed for the whole trip =

                      (total distance) / (total time)

                  =      (10 miles)  /  (1.25 hours)

                  =       (10 / 1.25)  miles/hours

                  =          8 miles per hour

Step-by-step explanation:

Answer:

Third option is the right choice.

Step-by-step explanation:

[tex]y=a(b)^x[/tex]   where "b", is the common ratio.

The common ratio for third table is constant for all the terms.

Best Regards!

Answer:

C. 97.5 yd

Step-by-step explanation:

The distance between Marsha, the ball and the tee for the fourth hole, forms a triangle.

Thus, the distance between Marsha's ball and the hole can be calculated using the Cosine formula below:

c² = a² + b² - 2abcos(C)

Where,

c = distance between Marsha's ball and the hole = ?

a = distance between the tee for the fourth hole and the tee = 300 yd

b = distance between tee and the hole = 255 yd

C = 18°

c² = 300² + 255² - 2(300)(255)cos(18)

c² = 90000 + 65025 - 153000 × 0.951

c² = 155025 - 145503

c² = 9522

c = √9522 ≈ 97.5

c = distance between Marsha’s ball and the hole = 97.5 yd (nearest tenth)

Answer:

Option B.

Step-by-step explanation:

According to the question, the data provided is as follows

[tex]H_o : p_1 - p_2 = 0\ (p_1 = p_2)\\\\ H_\alpha : p_1 - p_2 < 0\ (p_1 < p_2)[/tex]

Based on the above information,

The type ii error is the error in which there is an acceptance of a non rejection with respect to the wrong null hypothesis. The type I error refers to the error in which there is a rejection of a correct null hypothesis and the type II refers that error in which it explains the failure of rejection with respect to null hypothesis that in real also it is wrong  

So , the type II error is option B as we dont create any difference also the proportion is very less

Answer:

48%

Step-by-step explanation:

The total number of votes casted = 1524 votes = 100%

Let a = votes of first place candidate

b = votes of second place candidate

c = votes of third place candidate

The second place candidate had 140 votes less than the winner

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

a + b + c = 1524 votes....... Equation 5

If a = b + 140 and c = b - 395

The number of votes by b(second place candidate ) =

b + 140 + b + b - 395 = 1524 votes

3b = 1524 + 395 - 140

3b = 1779

b = 1779/3

b = 593 votes.

Therefore, the second place candidate had 593 votes.

Now we can calculate how many votes, the other candidates had.

The second place candidate had 140 votes less than the winner

Votes for the winner( first place candidate)

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Since b = 593

a = 593 + 140

a = 733 votes

Votes for the last place candidate

Since, Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

b = 593

c = 593 - 395

c = 198

From the above calculation,

a = votes of first place (winner) candidate = 733

b = votes of second place candidate = 593

c = votes of third(last) place candidate = 198

In the above question, we were asked to calculate the percentage of all the votes cast were received by the winner.

This is calculated as

= Voted received by winner/ Total number of votes casted × 100

= 733/1524 × 100

= 48.09711286%

Approximately to the nearest percent = 48%

Therefore, the percentage of all the votes cast were received by the winner = 48%

Answer:

[tex]\boxed{\sf \ \ \ x^2 + x -72 = 0 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

We need to use the distributive property which means that for a, b and c real numbers a(b+c)=ab+ac

So here we can write

[tex]x(x+1)=72\\<=> x*x+x*1=72\\<=> x^2 + x -72 = 0\\[/tex]

do not hesitate if you have any question

Answer:

x = 1, x = 2

Step-by-step explanation:

Given

f(x) = g(x) - 1, that is

x² - 2x - 1 = x - 1 - 2

x² - 2x - 1 = x - 3 ( subtract x - 3 from both sides )

x² - 3x + 2 = 0 ← in standard form

(x - 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

Answer:

Step-by-step explanation:

-2x + 3 = -x + 6

-x + 3 = 6

-x = 3

x = -3

y = 3 + 6

y = 9

(-3, 9)

Work Shown:

y = (4/5)x + 3

5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction

0 = 4x + 15 - 5y  ... subtract 5y from both sides

4x-5y+15 = 0 .... rearrange terms

The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.

Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.

Answer:

b

Step-by-step explanation:

you need to round 2.51 to 3 because it was the correct answer

Answer:

The 1st selection is appropriate.

_____

2nd: the rotation would need to be 90° CCW

3rd, 4th: rotation or double reflection will give the original orientation. This figure is reflected an odd number of times, so has its orientation reversed.

Hope it helps.. Mark brainliest

The sequence of transformations are reflection over the y-axis and then a rotation 90 clockwise about the origin.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, figure G is rotated 90° clockwise about the origin and then reflected over the x-axis, forming figure H.

Vertices of triangle G are (-3, 1), (-1, 2) and (-2, 5).

The reflection of point (x, y) across the y-axis is (-x, y).

On reflection over x-axis, we get coordinates as (3, 1), (1, 2) and (2, 5)

90° clockwise rotation: (x, y) becomes (y, -x)

On 90° clockwise rotation, we get coordinates as (1, -3), (2, -1) and (5, -2)

Triangle H has points (2, -1), (1, -3), (5, -2).

Hence, the sequence of transformations are reflection over the y-axis and then a rotation 90° clockwise about the origin.

Learn more about the rotation of 90° counterclockwise here:

brainly.com/question/1571997.

#SPJ6

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

[tex]tan(35)=\frac{12}{x}[/tex] Isolating x:

[tex]x=\frac{12}{tan(35)}[/tex] so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

[tex]tan(25)=\frac{12}{d+17.1377}[/tex] and simplifying a bit:

[tex]d+17.1377=\frac{12}{tan(25)}[/tex] and a bit more:

d + 17.1377 = 25.73408 so

d = 8.59, rounded

Answer:

Step-by-step explanation:

Given,

[tex] - \frac{2}{3} [/tex]

Now, let's find the value of 9x + 6

[tex]9x + 6[/tex]

plug the value of X

[tex] = 9 \times (- \frac{2}{3} ) + 6[/tex]

Multiplying a positive and negative equals a negative

[tex]( + ) \times ( - ) = ( - )[/tex]

[tex] = - 9 \times \frac{2}{3} + 6[/tex]

Reduce the number with Greatest Common Factor 3

[tex] = - 3 \times 2 + 6[/tex]

Multiply the numbers

[tex] = - 6 + 6[/tex]

The sum of two opposites equals 0

[tex] = 0[/tex]

Hope this helps..

best regards!!

Answer:

$60.00=Y× X

Step-by-step explanation:

You know she makes $60 but you need to figure out how many hours she works and how much an hour she makes working.