Consider the function f(x) = Log(7). (a) Describe the image of the unit circle under f. (b) Describe the image of the positive imaginary axis under f. (c) Describe the image of the positive real axis under f.

Both events A and B have probabilities of 1/12, and they are independent events since the outcome on one die does not affect the outcome on the other die.

The event A consists of all outcomes in which the number of spots showing on the red die is three or less.

Since the red die has six equally likely outcomes (1, 2, 3, 4, 5, and 6), the probability of A is:

P(A) = the number of outcomes in A / the total number of possible outcomes.

Out of the six possible outcomes on the red die, three of them are three or less: 1, 2, and 3.

Therefore, the number of outcomes in A is three.

Since there are six equally likely outcomes for the green die as well, the total number of possible outcomes is 6 x 6 = 36.

Therefore, we have:

P(A) = 3/36 = 1/12.

The event B consists of all outcomes in which the number of spots showing on the green die is more than three.

There are also three outcomes on the green die that satisfy this condition: 4, 5, and 6.

Thus, we have:

P(B) = 3/36 = 1/12.

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t=46°

u=134°

v=23°

w=23°

Answer:

Solution given;

v=w [base angle of triangle]

<SPQ+<SRQ=180°[sum of opposite angle of a cyclic quadrilateral is 180°]

81+v+53+w=180°

134°+v+v=180°

2v=180°-134°

v=46/2

v=23°

w=v=23°

In triangle ∆ PQR

v+w+u=180°[sum of interior angle of a triangle]

23+23+u=180°

u=180°-46°

u=134°

again

In triangle ∆ PSR

t+81+53=180°

t=180°-134°

t=46°

Answer:

t and u are supplementary as opposite angles of a cyclic quadrilateral.

v and w are equal as opposite angles to equal sides.

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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Answer:

a) red

b) red

c) the blue one is y=1/2x+1

Step-by-step explanation:

Answer:

-8/5

Step-by-step explanation:

hope it helps!

Answer:

14

Step-by-step explanation:

Substitute -2 for x in the two places where x occurs:

              8

(-2)^2 - ------- + 6    =    4 + 4 + 6  =  14

              -2

Answer:

6.1

Step-by-step explanation:

Add all, then divide by 8

Tell me if it works

\(\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b }},\:\quad \:a\ge 0,\:b\ge 0\)

\(\dfrac{\sqrt{6}}{\sqrt{27}}=\sqrt{\dfrac{6}{27}}\)

\(=\sqrt{\dfrac{6}{27}}\)

\(\mathrm{ Cancel \ \ \dfrac{6}{27} \ \ \ ; \ \ \dfrac{2}{9} }\)

\(=\sqrt{\dfrac{2}{9}}\)

\(\mathrm{Apply\:the\:laws\:of\:exponents}:\quad \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b }},\:\quad \:a\ge 0,\:b\ge 0\)

\(=\sqrt{\dfrac{2}{9}}\)

\(\sqrt{9}=3\)

\(=\dfrac{\sqrt{2}}{3} \ \ === > \ \ \ Answer\)

\(\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)

Answer:

\(y = \frac{1}{2}x - 7\)

Step-by-step explanation:

Slope-intercept form: y = mx + b

slope = m = 1/2

b = y-intercept = b

x = (x  , y) = -4

y = (x , y) = -9

Plug in the corresponding numbers and variables into their corresponding variables:

y = mx + b

\(-9 = \frac{1}{2} * -4 + b\)

First, simplify. Multiply 1/2 with -4:

\(-9 = \frac{1}{2} * -4 + b\\ \\-9 = \frac{1 * -4}{2} + b\\\\-9= -\frac{4}{2} + b\\ -9 = -2 + b\)

Next, isolate the variable, b. Note the equal sign, what you do to one side, you do to the other. Add 2 to both sides of the equation:

\(-9 = -2 + b\\-9 (+2) = -2 (+2) + b\\b = -9 + 2\\b = -7\)

Next, plug in -7 for b in the given slope-intercept form.

\(y = mx + b\\y = \frac{1}{2} x -7\)

\(y = \frac{1}{2} x - 7\) is your answer.

-

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Answer:

Step-by-step explanation:

Use point-slope form and convert to slope-intercept:

Angle-Angle (AA) similarity postulate,  if two angles of one triangle are congruent to two angles of another, then the triangles are similar.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

As per the diagram,

Triangles RPQ & RST are similar since

∠P = ∠S & ∠Q = ∠T

Side - side - side (SSS) similarity theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Triangles RPQ & RST are similar since

RP/RS = RQ/RT = ST/PQ

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==========================================================

Explanation:

We simply multiply the two values given to us

600*(1/12) = 600/12 = 50

We expect about 50 bulbs to be defective.

Note how if we had 50 bad bulbs, then 50/600 = (1*50)/(12*50) = 1/12 of the batch of 600 bulbs is defective.

Answer:

6.5

Step-by-step explanation:

We need to solve out for x , the given Equation is ,

\(: \implies\) x - 3x + 2 = -11

\(: \implies\) -2x = -11 -2

\(: \implies\) -2x = -13

\(: \implies\) x = -13/-2

\(: \implies\) x = 6.5

Answer:

x = 6.5

Step-by-step explanation:

\(x - 3x + 2 = - 11 \\ - 2x + 2 = - 11 \\ - 2x = - 11 - 2 \\ \frac{ - 2x}{ - 2} = \frac{ - 13}{ - 2} \\ x = + 6.5 \)

Answer:

4 people

Step-by-step explanation:

Answer:

105 were correct

Step-by-step explanation:

120 divided by 8 = 15.    15 questions were wrong.

15 times 7 = 105.

Hey there,

We have,

f(x) = x² + 11x + 30g(x) = x + 6

Now,

(f.g)(x) = f(g(x))

Substituting...

g(x) = x + 6f(g(x)) = f(x + 6)

Now,

f(x + 6)= (x + 6)² + 11(x + 6) + 30= x² + 12x + 36 + 11x + 66 + 30= x² + 23x + 132

So,The value is x² + 23x + 132

If f(x) and e(x) are graphed on the same set of axes, they would be reflections of each other over the line y = x.

What is Function ?

Function can be defined in which it relates an input to output.

a. To find the inverse of a function, we need to interchange x and y and solve for y. Therefore, we have:

x = 1 + √y + 5

Subtracting 1 from both sides, we get:

x - 1 = √y + 5

Subtracting 5 from both sides, we get:

x - 6 = √y

Squaring both sides, we get:

\((x - 6)^2 = y\)

Therefore, Eric's equation for his Fe(x) is:

\(e(x) = (x - 6)^2\)

b. If we push the two machines together and input -4 into f(x), we get:

f(-4) = 1 + √(-4) + 5

= 1 + 2i + 5

= 6 + 2i

Then, if we input this result into e(x), we get:

\(e(f(-4)) = (6 + 2i - 6)^2\)

= \((2i)^2\)

= -4

This happens because Eric's function e(x) is the inverse of Amanda's function f(x), so e(f(x)) = x for all values of x in the domain of f(x). In this case, -4 is in the domain of f(x), so e(f(-4)) = -4.

c. This is because the inverse function reverses the input and output values of the original function, so the graphs of the two functions must be reflections of each other over the line y = x.

Therefore, If f(x) and e(x) are graphed on the same set of axes, they would be reflections of each other over the line y = x.

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Divide total price by quantity:

15.60 / 6 = 2.60

Unit price = $2.60

Answer:

Hello!!

If a water bottle contains 500mL of water and your goal is to drink 4L of water each day then the water bottle is \(\frac{1}{8}\) of your daily goal.

Step-by-step explanation:

500mL = 0.5L

1000mL = 1L

1500mL = 1.5L

2000mL = 2L

2500mL = 2.5L

3000mL = 3L

3500mL = 3.5L

4000mL = 4L

Hope this helps!!

Answer:

The think the answer will be rotation

Answer:

your answer will be C. rotation

Step-by-step explanation:

hope it helps...

have a great day!

The expected value for the complete pairs of socks that make it out alive from the washing machine is calculated based on the probability of losing a sock and the number of pairs. The expected value for the complete pair of socks is 2.

Let's denote the random variable X as the number of complete pairs of socks that make it out alive. To calculate the expected value of X, we need to consider the probability of losing a sock and the total number of pairs.

In this case, there are 20 pairs of socks, which means there are a total of 40 socks. The washing machine eats four socks at random, which means there will be 36 socks remaining.

The probability of losing a sock can be calculated by dividing the number of socks lost by the total number of socks. In this scenario, four socks are lost out of 40 socks, so the probability of losing a sock is 4/40 = 1/10.

To calculate the expected value, we multiply the probability of losing a sock by the total number of pairs. In this case, the expected value is (1/10) * 20 = 2.

Therefore, the expected value for the number of complete pairs of socks that make it out alive from the washing machine is 2.

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Answer:

Just show basic multiplication skills that we learned in 3th grade i suppose since your teacher dosen't have a brain to figure this out

The quadratic equation that represents the solution is F: p(x) = x² - 49.

The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.

Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.

Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:

p(x) = (x + 7)(x - 7)

Solving the parentheses we have:

p(x) = x² - 7x + 7x - 49

Cancelling the same terms with opposite sign we have:

p(x) = x² - 49

Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.

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Step-by-step explanation:

Find differences in year (x)

x=2050-2015

x=35 years

Find total percentage

=2.5%×(x)

=2.5×35

=87.5%

Multiply percentage with initial number

=87.5%×380000

=33250000

Answer:

6km

Step-by-step explanation:

==>Given:

Map scale = 1 : 200,000

Distance on map between the park and the theatre = 3cm

==>Required:

Real life distance between the town and the theatre in km

==>Solution:

Note: the map scale given means 1cm on the map represents 200,000 cm in real life.

For a map distance of 3 cm between the town and the theatre, the real life distance would be:

3 × 200,000 = 600,000 cm

=>Convert to km

Thus, 100,000cm = 1km

Therefore, 600,000cm = 6km

Real life distance between the town and the theatre = 6km

Since it is translated 5 units down that means the y-intercept is -5, so the equation above is correct.

Step-by-step explanation:

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.... wrong answer

Answer:   4.3 miles

The decimal 4.3 is equivalent to the mixed number 4 & 3/10

=============================================================

Explanation:

Fractions are often a pain, so I find it helpful to convert to decimal form whenever possible.

1/2 = 0.5

21 & 1/2 = 21 + 1/2 = 21 + 0.5 = 21.5

21 & 1/2 miles = 21.5 miles

The object travels 21.5 miles in 5 hours. Divide the distance over the time value to get the speed (or rate). This is exactly identical to finding the number of miles traveled in one hour (since each hour the object travels the same amount of distance)

speed = distance/time = 21.5/5 = 4.3 mph

4.3 = 4 + 0.3 = 4 + 3/10 = 4 & 3/10

In my opinion, it is much easier to use decimals. Saying "the object traveled a distance of 4 & 3/10 miles" seems very clunky to me.

Therefore, each hour, the object travels 4.3 miles.

Answer: B

Step-by-step explanation:

On a coordinate plane, a triangle is shifted up is the area that shows only a vertical translation from the shaded figure onto the unshaded figure (Image attached).

Vertical translation is known to be a term that connote  the up or down movement that takes place in a graph of a function.

It is also called the movement or the shifting of the graph amidst the y-axis. Note that in vertical translation, all the point on the graph often moves k units vertically.

See full question below

Which shows only a vertical translation from the shaded figure onto the unshaded figure?

On a coordinate plane, a triangle is shifted up.

On a coordinate plane, a triangle is shifted to the left.

On a coordinate plane, a triangle is enlarged to form another triangle.

On a coordinate plane, a triangle is shifted up and to the left.

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Answer:

D) 48°

Step-by-step explanation:

Step 1:  First, we need to know the sum of the measures of the interior angles of the polygon.  We can determine the sum using the formula,

(n - 2) * 180, where n is the number of sides of the polygon.

Since this polygon has 4 sides, we plug in 4 for n:

Sum = (4-2) * 180

Sum = 2 * 180

Sum = 360°

Thus, we know that the sum of the measures of the interior angles of the polygon is 360°.

Step 2:  Now we can set the sum of four angles equal to 360 to solve for x:

127 + (5x + 3) + 88 + (10x + 7) = 360

215 + (5x + 3 + 10x + 7) = 360

215 + 15x + 10 = 360

225 + 15x = 360

15x = 135

x = 9

Step 3:  Now we can plug in 9 for x in the equation representing the measure of E to find the measure of E:

E = 5(9) + 3

E = 45 + 3

E = 48

Thus, the measure of E is 48°

Optional Step 4:

We can check that E = 48 by again making the sum of the angles = 360.  We already know the measures of angles J, E, and S so we can just plug in 9 for x in the expression representing angle J.  If we get 360 on both sides, we've correctly found the measure of E:

K + J + E + S = 360

(10(9) + 7) + (127 + 48 + 88) = 360

(90 + 7) + 263 = 360

97 + 263 = 360

360 = 360

Thus, we've correctly found the measure of E