chipo set out from a on a bearing of 130 to town b ,she then boardef a bus from town b another town c on a bearing of 030 directly east of a. calculate the bearing of town a from her new position​

The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Answer:

50(64+36)

Step-by-step explanation:

Answer:

50x8=  400x4=1,600

Step-by-step explanation:

Given: cost of CAYMAN sleep couch with VAT is R2 699

cost without VAT is R1 999

2.1  To calculate the original price of the couch excluding VAT, we can use the following formula:

Price including VAT / 1 + (VAT rate / 100) = Price excluding VAT

In this case, the VAT rate is 15% (since it is included in the original price), so the formula is:

R2,699 / 1 + (15 / 100) = R2,346.96

2.2  To calculate the expected price of the couch including VAT at the sale price, we can use the following formula:

Price excluding VAT * (1 + (VAT rate / 100)) = Price including VAT

In this case, the VAT rate is still 15% and the sale price is R1,999 (excluding VAT), so the formula is:

R1,999 * (1 + (15 / 100)) = R2,299

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The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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the probability that preparation is within 2 minutes of the mean time is 0.134.

An illustration of a probability distribution shows the anticipated results of potential values for a specific data generation procedure.

Axiomatic, theoretical and experimental are the three types of probability.

P(35-2<X<35+2)= P(33<X<37)= P(X<37)-P(X<32)

Using cumulative functi0n we get

P(35-2<X<35+2)= P(33<X<37)= P(X<37)-P(X<32)

=\(\frac{37-20}{50-20}-\frac{33-20}{50-20}\\ =0.567-0.433\\=0.134\)

Thus the probability that preparation is within 2 minutes of the mean time is 0.134.

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THIS ONE I CANT FIGURE OUT SORRY :C

The predicted number of employed graphic designers in 2023 can be calculated by applying the annual growth rate of 9% to the number of designers in 2012. Based on this calculation, it is estimated that there will be approximately 35,889 graphic designers employed in 2023.

1. Determine the initial number of graphic designers in 2012: The question states that there were 23,900 designs in the industry in 2012.

2. Calculate the annual growth rate: The question mentions that the graphic design industry has an annual growth rate of 9%. This growth rate represents an increase of 9% each year.

3. Calculate the growth in the number of graphic designers from 2012 to 2023: To find the growth in the number of graphic designers, multiply the initial number of designers (23,900) by the growth rate (9%) for each year. Repeat this process for each year from 2012 to 2023.

4. Add the growth in the number of designers to the initial number of designers: Sum up the growth in the number of designers for each year and add it to the initial number of designers in 2012.

5. Calculate the predicted number of employed graphic designers in 2023: The sum obtained in step 4 represents the estimated number of graphic designers employed in 2023.

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Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

The answer is 128 because 4·4·4+8·8=128

Answer:

Step by step explanation

Total length of pole = 21.3 m

Length of pole inside the ground = 0.2 m

Let length of pole outside the ground be X,

So, according to the Question,

\(x + 0.2 = 21.3\)

Move constant to R.H.S and change its sign

\(x = 21.3 - 0.2\)

Calculate the difference

\(x = 21.1 \: m\)

Hope this helps...

Good luck on your assignment...

Answer:

See below:

Step-by-step explanation:

So, for starters, g(x) is just a fancy way of saying that it is a function, it's basically used as \(y\) and you can usually use g(x) or y whenever you want unless its a special situation.

So we can replace g(x) with y as there aren't any other functions we need to deal with.

y = 3x + 2

y = 11

Now that its simplified, we can see its a simple problem

After combining, we get 11 = 3x + 2

After solving, we get x = 3

Answer:

what's the problem?....

The median is the average of the two middle values: (334 + 448) / 2 = 391.

the third quartile is 391 lb.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.

To find the first and third quartile, we need to first arrange the data in ascending order:

132, 183, 191, 237, 251, 277, 279, 334, 448, 599

The median of the entire data set is the value that separates the lower 50% of the data from the upper 50% of the data. In this case, the median is the average of the two middle values:

(251 + 277) / 2 = 264

Next, we need to find the median of the lower half of the data set (also known as the first quartile). We can see that the lower half of the data set is:

132, 183, 191, 237, 251

The median of this data set is the value that separates the lower 50% of this half of the data from the upper 50% of this half of the data. In this case, the median is the average of the two middle values:

(191 + 237) / 2 = 214

So the first quartile is 214 lb.

Finally, we need to find the median of the upper half of the data set (also known as the third quartile). We can see that the upper half of the data set is:

277, 279, 334, 448, 599

The median of this data set is the value that separates the lower 50% of this half of the data from the upper 50% of this half of the data. In this case, the median is the average of the two middle values:

(334 + 448) / 2 = 391

So the third quartile is 391 lb.

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Recall the half-angle identity for cosine,

cos²(θ/2) = (1 + cos(θ))/2

Since θ lies in quadrant I, we also have θ/2 in quadrant I, since

0 < θ < π/2   ⇒   0 < θ/2 < π/4

Then for this θ, we have

cos(θ/2) = + √((1 + cos(θ))/2)

Also recall the Pythagorean identity,

cos²(θ) + sin²(θ) = 1

Multiplying through both sides of this identity by cos²(θ) gives another form of it,

1 + tan²(θ) = sec²(θ)

Because θ belongs to quadrant I, we know cos(θ) > 0, so we also have sec(θ) = 1/cos(θ) > 0.

It follows that

sec(θ) = + √(1 + tan²(θ)) = √89/8

⇒   cos(θ) = 8/√89

and so

cos(θ/2) = + √((1 + 8/√89)/2) = √(1/2 + 4/√89)

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

Answer: D

Step-by-step explanation:

To find f(g(x)), you want to take g(x) and plug that into f(x). Since we are given f(x) and g(x), we can go ahead and do that.

f(g(x))=2(x-3)+4                  [distribute]

f(g(x))=2x-6+4                     [combine like terms]

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

Now, we know that f(g(x))=2x-2.

Answer:

sample space 2 inches outcome  1/52

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

You just do 6 / 1/4 = 24

The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

You will need to use the information in the table you are given. Subtract: (final velocity - initial velocity) and divide by (final time - initial time).

Leg-A:  

Speed = 15km/10min = 1.5 km/min

Leg-B:  

Speed = 20km/15min = (1 and 1/3) km/min

Leg-C  

Speed = 24km/12min = 2 km/min

Leg-D:  

Speed = 36km/9min = 4 km/min

Leg-E:  

Speed = 14km/14min = 1 km/min

The equation that represents a quadratic relationship is y = 4x^2. Option A.

A quadratic relationship is a mathematical relationship where the variable y is a function of the variable x raised to the power of 2. In other words, it is an equation in which the highest power of the variable is 2.

Let's analyze the given equations:

1. y = 4x^2: This equation represents a quadratic relationship because the variable x is raised to the power of 2. The term 4x^2 indicates that the relationship between x and y is quadratic.

2. y = 4x^4: This equation represents a quartic relationship, not a quadratic relationship. The variable x is raised to the power of 4, which indicates a higher degree relationship than quadratic.

3. y = 4x^3: This equation represents a cubic relationship, not a quadratic relationship. The variable x is raised to the power of 3, indicating a higher degree relationship.

4. y = 4: This equation represents a linear relationship, not a quadratic relationship. It is a constant equation where y is always equal to 4, regardless of the value of x. In a quadratic relationship, the variable x should have a power of 2. Option A.

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Answer:

The complete question seems to be:

A doctor sees between 7 and 12 patients each day.

On Mondays and Tuesdays, the appointment times are 15 minutes.

On Wednesdays and Thursdays, they are 30 minutes.

On Fridays, they are one hour long.

The doctor works for no more than 8 hours a day.

Here are some inequalities that represent this situation.

0.25 ≤ y ≤ 1

7 ≤ x ≤ 12

xy ≤ 8

What represents each variable?

7 ≤ x ≤ 12

We know that the doctor sees between 7 and 12 patients each day, and the smallest value of x is 7, and the largest is 12, then x must represent the number of patients that the doctors see in a given day.

0.25 ≤ y ≤ 1

now,

On Mondays and Tuesdays, each appointment is 15 minutes long.

An hour has 60 minutes.

Then 15 minutes = 15/60 hours = 0.25 hours.

On Wednesdays and Thursdays, they are 30 minutes.

30 minutes = 30/60 hours = 0.5 hours.

Then the possible value of the time for each appointment are {0.25, 0.5, 1}

Then the variable y must represent the time that each appointment takes.

xy ≤ 8

We know that:

x =  number of patients in a given day.

y = time that the appointment takes in a given day.

x*y = total number of hours that he works in that given day.

and we know that he works, at maximum, 8 hours.

then the inequality xy ≤ 8 has sense.

The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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Answer:

x = 1/12

1/12 = 0.833

Step-by-step explanation:

to find the value of x

4+ |2-3x| =7

8 - 12x = 7

-12x = 7-8

-12x = -1

x = 1/12

if we write 1/12 in simplest form so

1/12 = 0.833

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Answer:

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

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

The reflection of the point (–4, 6) across both axes is (b) (4, -6)

From the question, we have the following parameters that can be used in our computation:

Point = (-4, 6)

The rule of reflections across both axes is

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

Using the above as a guide, we have the following:

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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