if there are 22 successful outcomes in a sample with a size of 50, what is the sample proportion?

See below for the solution to the inverse function and the rational equation

Create functions f(x) and g(x)

The functions are given as:

f(x) = x + a/b

g(x) = cx − d

Let a = 4 and b = 2.

So, we have:

f(x) = x + 4/2

Rewrite as:

y = x + 2

Swap x and y

x = y + 2

Make y the subject

y = x - 2

So, we have:

g(x) = x - 2

So, the functions are:

f(x) = x + a/b ⇒ f(x) = x + 4/2

g(x) = cx − d ⇒ g(x) = x - 2

Show that the functions are inverse functions

In (a), we have:

f(x) = x + 4/2

g(x)= x - 2

If the functions are inverse functions, then:

f(g(x)) = x

We have:

f(x) = x + 4/2

This gives

f(g(x)) = g(x) + 4/2

This gives

f(g(x)) = x - 2 + 4/2

Evaluate

f(g(x)) = x

Evaluate g(f(x))

In (a), we have:

f(x) = x + 4/2

g(x)= x - 2

We have:

g(x)= x - 2

This gives

g(f(x)) = f(x) - 2

This gives

g(f(x)) = x + 4/2 - 2

Evaluate

g(f(x)) = x

Graph the functions

See attachment for the graph

The table of values is:

x    f(x)    g(x)

0    2     -2

1     3      -1

2    4       0

3    5      1

4    6      2

Create the equations

The form of the equations is given as:

[tex]a\sqrt{x + b} + c= d[/tex]

So, we have:

[tex]\sqrt{4x + 5} + 1 = 0[/tex] --- has extraneous solution

[tex]2\sqrt{3x - 1} + 2 = 8[/tex] --- has no extraneous solution

The equation solution

Equation 1 with extraneous solution

[tex]\sqrt{4x + 5} + 1 = 0[/tex]

Subtract 1 from both sides

[tex]\sqrt{4x + 5} = -1[/tex]

Square both sides

4x + 5 = 1

Evaluate the like terms

4x = -4

Divide by 4

x = -1

Substitute x = -1 in [tex]\sqrt{4x + 5} + 1 = 0[/tex] to check

[tex]\sqrt{4(-1) + 5} + 1 = 0[/tex]

[tex]\sqrt{-4 + 5} + 1 = 0[/tex]

[tex]\sqrt{1} + 1 = 0[/tex]

Evaluate the root

[tex]1 + 1 = 0[/tex]

[tex]2= 0[/tex] --- false

Equation 2 without extraneous solution

[tex]2\sqrt{3x - 1} + 2 = 8[/tex]

Subtract 2 from both sides

[tex]2\sqrt{3x - 1} = 6[/tex]

Divide by 2

[tex]\sqrt{3x - 1} = 3[/tex]

Square both sides

3x - 1 = 9

Evaluate the like terms

3x = 10

Divide by 3

x = 10/3

Substitute x = x = 10/3 in [tex]2\sqrt{3x - 1} + 2 = 8[/tex] to check

[tex]2\sqrt{3 * \frac{10}{3} - 1} + 2 = 8[/tex]

[tex]2\sqrt{10 - 1} + 2 = 8[/tex]

[tex]2\sqrt{9} + 2 = 8[/tex]

Evaluate the root

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

[tex]8 = 8[/tex] --- true

Why the equations have (or do not have) an extraneous solution

The first equation has an extraneous solution because the solution is false for the original equation and the second does not have an extraneous solution because the solution is true for the original equation

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Answer:

See below.

Step-by-step explanation:

Sides: 15, 36, 41

True: 15 + 36 greater-than 41, so the side lengths will form a triangle.

True: 15 squared + 36 squared = 1,521

True: 41 squared = 1,681

True: Since a squared + b squared not-equals c squared, it will not be a right triangle.

Answer:

A) 15 + 36 greater-than 41, so the side lengths will form a triangle.

C) 15 squared + 36 squared = 1,521

D) 41 squared = 1,681

E) Since a squared + b squared not-equals c squared, it will not be a right triangle.

Proof:

Answer:

135°

Step-by-step explanation:

X is also 135°    as is S  , T  U , V, W and Y

Answer:

b)135°

Step-by-step explanation:

The value of an interior angle of 135° is appreciated

In a regular polygon all interior angles are equal

Angle x = 135°

Hope this helps

Answer

$30 minutes per hour

$0.5 per minute

Step-by-step explanation:

45/1.5=30

45/90=0.5

If the probability of observing at least one car on a highway during any 20-minute time interval is 609/625, then the probability of observing at least one car during any 5-minute time interval is 609/2500

Given The probability of observing at least one car on a highway during any 20 minute time interval is 609/625.

We have to find the probability of observing at least one car during any 5 minute time interval.

Probability is the likeliness of happening an event among all the events possible. It is calculated as number/ total number. Its value lies between 0 and 1.

Probability during 20 minutes interval=609/625

Probability during 1 minute interval=609/625*20

=609/12500

Probability during 5 minute interval=(609/12500)*5

=609/2500

Hence the probability of observing at least one car during any 5 minute time interval is 609/2500.

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Answer:

c) Oa^2 = c^2-b^2

Step-by-step explanation:

the formula of finding hypotenuse (c) is

c^2 = a^2 + b^2

that means c^2 - b^2 = a^2

a^2 = c^2 - b^2.

Hello:

Let's consider this problem in steps:

Let's gather some information:

Now let's apply our knowledge to solve the problem:

  [tex]\rm \hookrightarrow cos(cos^{-1}0.3) = 0.3[/tex]

Answer: 0.3

Hopefully that helps!

[tex]\frak{Hi!}[/tex]

                      [tex]\large\text{Related Concept-:}[/tex]

                     [tex]\boxed{\begin{minipage}{10cm} \sf{If\;you\;take\;the\;inverse\;cosine}\\ \;of\;a\;number,\;and\;then\;take\; its\;cosine,\;don't\;you\;get\;the\;number \\ you started with? \end{minipage}}[/tex]

The inverse cosine and the cosine are operations that undo each other.

This being said, let's solve our problem.

[tex]\bf{cos(cos^{-1}\;0.3)=0.3[/tex], based on what I said above

[tex]\cal{CALLIGRAPHY}[/tex]

The conditional and its converse that form a true biconditional is; Option A;  If x = 19, then 2x – 3 = 35.

A) If x = 19, then 2x – 3 = 35.

Thus, 2(19) - 3 = 35. Thus, this is a true biconditional.

B) If x = 3, then x²= 9.

This is not a true biconditional because x could also be -3.

C) If x² = 4, then x = 2

This is not a true biconditional because x could also be -2.

D) If x > 0, then |x| > 0.

This is not a true biconditional because x could also be negative which less than zero.

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The measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have shown the rhombus in the picture.

As we know the diagonals bisect at a 90-degree angle.

So angle 2 = 90 degree

angle 1 = angle 3

angle 1 = 54 degrees

angle 1 + angle 2 + angle 5 = 180

54 + 90 + angle 5 = 180

angle 5 = 36 degrees

angle 5 = angle 4 = 36 degrees

Thus, the measure of angles 1, 2, 4, and 5 are 54 degrees, 90 degrees, 36 degrees, and angle 36 degrees.

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If f(x) is an odd function, the greatest number of points that can lie in Quadrant II is 1

The given parameters are:

Function f(x) = Odd function

Points in quadrant IV

The number of points in the upper quadrants is:

Upper = 14/2

This gives

Upper = 7

The upper quadrants are I and II

This means that:

I + II = 7

So, we have:

6 + II = 7

Subtract 6 from both sides

II  = 1

Hence, the greatest number of points that can lie in Quadrant II is 1

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Answer:

135:147

Step-by-step explanation:

180/4=45

180-45=135

292-45=247

135:247

Answer:

Hence the expression [tex]$$(5x-y)(x-4)=5x^2-xy-20x+4y$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 5x & - & y \\ \times & {} & {} & {} & x & - & 4 \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}{} & {} & {} & - & 20x & + & 4y \\ 5{{x}^2} & - & xy & {} & {} & {} & {} \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}5{{x}^2} & - & xy & - & 20x & + & 4y \\ \end{matrix}$$[/tex]

To find the area of composite shapes, we can break the bigger shape down into small, simpler shapes, and find the sum of their areas.

For this triangle, we will need to know the formula to find the area of a triangle:

[tex]A=\dfrac{1}{2}bh[/tex]

The given shape can be seen as one large triangle with a little triangle cut out of it. To find the shaded region, we can:

[tex]A=\dfrac{1}{2}bh[/tex]

⇒ Plug in the values given for the base and height:

[tex]A=\dfrac{1}{2}(5)(2+4+6)\\\\A=\dfrac{1}{2}(5)(12)\\\\A=(5)(6)\\\\A=30 mm^2[/tex]

[tex]A=\dfrac{1}{2}bh[/tex]

⇒ Plug in the values given for the base and height:

[tex]A=\dfrac{1}{2}(3)(4)\\\\A=(3)(2)\\\\A=6mm^2[/tex]

[tex]30 mm^2-6mm^2\\=24mm^2[/tex]

The area of the shaded region is [tex]24mm^2[/tex].

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The length of QS can lie between 3 < QS < 13.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

As per the given law of triangle inequality, the sum of the two sides of the triangle is greater than the third side.

x + 8 > 5

x > -3

x + 5 > 8

x > 3

8 + 5 > x

13 > x

Hence, the length of QS can lie between 3 < QS < 13.

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Because the cosine and sine must be negative when evaluated in theta, the angle lies on the third quadrant.

We know that if:

Here we know that:

sec(θ) < 0

And we know that:

sec(θ)  = 1/cos(θ)

Then we have cos(θ) < 0

We also have that:

sec(θ)*csc(θ) > 0

Because sec(θ) < 0, we must have that csc(θ) < 0.

Remember: csc(θ) = 1/sen(θ)

Then sen(θ) < 0.

Then we have the two conditions:

sen(θ) < 0

cos(θ) < 0

The only quadrant where both are negative is the third quadrant, so that is the correct option.

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[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)

[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)

Answer:

4 units to the left and 2 units up.

Step-by-step explanation:

The distribution where the mean is most likely to be less than the median is the third histogram.

It should be noted that when the histogram shows the day is left skewed, it means the mean is less than the median.

If it right skewed, the mean is greater than the median.

When they're equal, the data is symmetric.

In this case, based on the information, the distribution where the mean is most likely to be less than the median is the third histogram.

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The equation which best models the data in the scatterplot is: D. y = -16743x² + 19.76x + 745.73.

By critically observing the scatter plot shown in the image attached below, we can logically deduce that it's data are best modelled by a quadratic equation (parabolic curve).

Mathematically, the equation of a quadratic equation (parabolic curve) is given by:

y = ax² + bx + c

Since the parabolic curve opens downward, we have:

a < 0, c > 0, x = 0 and y > 0;

y = -16743x² + 19.76x + 745.73.

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Answer:

D

Step-by-step explanation:

As you can observe from the pattern, the numerator gets multiplied by 4 every increase in the sequence.

So , clearly, the 5th term will be = [tex]\frac{64*4}{5} =\frac{256}{5}[/tex]

and the 6th term will be = [tex]\frac{256*4}{5} =\frac{1024}{5}[/tex]

Therefore , D will be the answer.

Answer:

Using a phone to drive people to web-based survey instruments is known as a hybrid survey.

Answer:

319

Step-by-step explanation:

i am really not sure but i believe so i hope it is the right answer

Answer:

1600 people

Step-by-step explanation:

This is a ratio problem. We can set up the proportion by letting x be the number of people who applied for admission:

[tex]\frac{4}{10}=\frac{640}{x}[/tex]

Since we know that 4 people get in for every 10 people that apply, we can set up an equation like the one above and solve for x by cross multiplying:

[tex]6400=4x\\x=1600[/tex]

This means that 1600 people applied for admission to the vocational school.

Suppose Z has a standard normal distribution with a mean of 0 and a standard deviation of 1. 27% of the possible Z values are smaller than  0.613.

The standard normal distribution, also known as the z-distribution, is a special normal distribution with a mean of 0 and a standard deviation of 1. The normal distribution can be standardized by converting its value to a z-score. The Z-score indicates how many standard deviations each value has from the mean.

The standard normal distribution (z distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. Each point (x) of the normal distribution can be converted to the standard normal distribution (z) using the equation z = (x-mean) / standard deviation.

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The attached figure represents the image of the triangle under the rotation

The coordinates of the triangle are given as:

P = (2, 1)

Q = (4, 1)

R = (4, -3)

The rule of 90 degrees rotation about the origin is:

(x, y) = (y, -x).

So, we have:

P' = (1, -2)

Q' = (1, -4)

R' = (-3, -4)

See attachment for the figure under the rotation

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According to multiplication you can use repeated addition to get the same product of the given equation.

Ex: 5x2= 2+2+2+2+2 ( 5 groups of 2)

Both will give you same answer (10).

Hence 2 x 3/4 = 3/4 + 3/4

Answer:

2 x 3/4 = 3/4 + 3/4

Step-by-step explanation:

Using a system of equations, it is found that since 20 child bikes and 6 adult bikes would require more testing than the allocated time, it is not possible to build this amount.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Each child bike requires 4 hours to build, as do each adult bike. The company has 100 hours of testing, hence:

4c + 4a = 100.

c + a = 25.

With 20 child bikes and 6 adult bikes in a week, we have that c = 20, a = 26, hence:

c + a = 26

20 child bikes and 6 adult bikes would require more testing than the allocated time, it is not possible to build this amount.

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The equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is D. -8≤a-h≤8.

From the information given, the estimate includes h hours of labor, where h>80 and the company's goal is for the estimate to be within 8 hours of the actual number of hours of labor.

Here, the equation that represents the relationship between the estimated number of hours of labor and the actual number of hours of labor is -8≤a-h≤8.

In conclusion, the correct option is D.

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The value of b and  c is 4 and 7.

Algebra is the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Algebra is divided into different sub-branches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra.

Elementary algebra: elementary algebra, branch of mathematics that deals with the general properties of numbers and the relations between them. Algebra is fundamental not only to all further mathematics and statistics but to the natural sciences, computer science, economics, and business.

From the given question,

[tex]\sqrt[4]{15^7}[/tex] This expression can also be written in the form of [tex]a^\frac{b}{c}[/tex]

We will convert [tex]\sqrt[4]{15^7}[/tex] to the required form:

[tex](15^\frac{7c}{4b} )\left \{ {{a=15^\frac{7c}{4b} } \atop {b=b} , c = c} \right.[/tex]

Hence,

From the above equation we get the value of b and c is 4 and 7.

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Answer:

c and d, because they both have 2 squares