A survey showed that 45% of a travel company's customers were planning an overseas vacation
the following year. Predict how many of the travel company's 13,400 travelers will vacation overseas
the following year.

The value of [tex]$\tan A$[/tex] in its simplest radical form is [tex]8/3$.[/tex]

What is radical form?

Radical form refers to a mathematical expression that includes radicals, which are symbols that indicate a root of a number.

To find the value of [tex]$\tan A$[/tex], we first need to determine the value of [tex]\cos A$.[/tex]

Using the Pythagorean identity, we have:

[tex]$$\sin^2 A + \cos^2 A = 1$$[/tex]

Substituting the given value of [tex]$\sin A$[/tex], we get:

[tex]$$\left(\frac{8}{\sqrt{73}}\right)^2 + \cos^2 A = 1$$[/tex]

Simplifying the left-hand side, we get:

[tex]$\frac{64}{73} + \cos^2 A = 1$$$$\cos^2 A = \frac{9}{73}$$$$\cos A = \frac{3}{\sqrt{73}}$$[/tex]

Since angle [tex]$A$[/tex] is in the first quadrant, both [tex]$\sin A$[/tex] and [tex]$\cos A$[/tex] are positive.

Therefore, we have:

[tex]$$\tan A = \frac{\sin A}{\cos A} = \frac{8/\sqrt{73}}{3/\sqrt{73}} = \frac{8}{3}$$[/tex]

So the value of [tex]$\tan A$[/tex] in its simplest form is [tex]8/3$.[/tex]

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Answer:

Refers to the attachment given below!

Step-by-step explanation:

Answer:

FH = 6.0

FG = 3.6

m<H = 31°

Step-by-step explanation:

sin Θ = opp/hyp

cos Θ = adj/hyp

sin 59° = FH/GH

sin 59° = FH/7

FH = 7 × sin 59°

FH = 6.0

cos 59° = FG/GH

cos 59° = FG/7

FG = 7 × cos 59°

FG = 3.6

m<F + m<G + m<H = 180°

90° + 59° + m<H = 180°

m<H = 31°

(a) The probability that at least two of the five points selected from the interval (0,1) are less than 1/3 is (161/243).  (b) The probability that exactly two of the points have the first decimal point as 3 is (3645/100000).

(a) The probability that at least two points out of five will be less than 1/3 can be found by subtracting the probabilities that no points and one point are less than 1/3 from 1.

Let us assume that each point is selected independently and at random.

P(no point less than 1/3) = (2/3)^5

P(one point less than 1/3) = 5C1(1/3)(2/3)^4 = (5/3)(2/3)^5

So the probability that at least two points are less than 1/3 is:

P(at least two points less than 1/3) = 1 - P(no point less than 1/3) - P(one point less than 1/3)

= 1 - (2/3)^5 - (5/3)(2/3)^5

= (161/243)

(b) To find the probability that the first decimal digit of exactly two of the five selected points is 3, we use a combination of counting and probability reasoning. There are five ways to choose two points out of five, which can each start with 3:

(0.3**, **.3**, **3.*, **.33, 33..)

The probability that the first decimal place of any point is 3 is 1/10, since there are 10 equally likely numbers in each of the five intervals. The probability that the first decimal point of each of the other three points is not 3 is 9/10.

Therefore, the probability of choosing two points from five where exactly the first decimal digit of both is 3 is:

P(exactly two points have first decimal digit of 3) = 5(1/10)^2(9/10)^3= (3645/100000)

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A card is drawn from a standard deck of 52 playing cards. the probability that the card will be a spade or a jack is 17/52 or 0.3269 (rounded to four decimal places).

The total number of playing cards in a deck is 52. Out of these 52 playing cards, there are 4 suits, and each of these suits includes 13 cards.

Hence, there are 4 types of cards, and each of these types includes 13 cards. Therefore, there are 52/4 = 13 cards per type.A card is drawn from the deck of 52 playing cards.

The probability that it will be a spade or a jack is given below:

The probability of a spade card is 13/52 or 1/4, since there are 13 spade cards in the deck of 52 playing cards.

The probability of a jack card is 4/52 or 1/13, since there are 4 jacks in the deck of 52 playing cards.

Therefore, the probability that the card will be a spade or a jack is (13/52) + (4/52) = 17/52 or 0.3269 (rounded to four decimal places).

Thus, the probability that the card will be a spade or a jack is 17/52 or 0.3269 .

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Answer:

  -1239/1961

Step-by-step explanation:

You want cos(A+B) given that tan(A) = 45/28 and cos(B) = 12/37.

Here, we'll use the tangent relations ...

The tangent of angle B can be found from ...

  tan(B)² = 1/cos(B)² -1

  tan(B)² = 1/(12/37)² -1 = 1225/144

  tan(B) = 35/12

Now the tangent of the angle sum is ...

  tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))

  = (45/28 +35/12)/(1 -(45/28)(35/12)) = (95/21)/(1 -75/16) = -1520/1239

Note that the tangent of this sum of two first-quadrant angles is negative. That means the result is a second-quadrant angle, so the cosine will also be negative.

  cos(A+B) = -1/√(tan(A+B)² +1)

  cos(A+B) = -1/√((1520/1239)² +1)

  cos(A+B) = -1239/1961

__

Additional comment

Some calculators maintain enough internal accuracy that you can obtain the answer directly from ...

  cos(arctan(45/28) +arccos(12/35))

The one shown in the attachment is not able to provide the ratio of integers equal to the floating point value it computes for this.

Answer:

To find the area, we will use formula of "area of circle" which is πr^2

Given:

Radius: 78cm

To find:

Area of circle: ?

Formula:

πr^2

Solution:

Area: π×r^2

: 3.14× 78^2

Area: 19,113cm

Answer:

19113cm is the area of circle

Hope you understand

Kindly mark the brainliest :)

Answer:

Matrix B is a 3 × 7 matrix.

Answer:

The secant function is defined as the reciprocal of the cosine function. So if `sec(theta) = √3`, then `cos(theta) = 1/√3`. Since `sin^2(theta) + cos^2(theta) = 1`, we can solve for `sin(theta)`:

`sin^2(theta) + cos^2(theta) = 1`

`sin^2(theta) + (1/√3)^2 = 1`

`sin^2(theta) + 1/3 = 1`

`sin^2(theta) = 2/3`

`sin(theta) = ±√(2/3)`.

Since it is given that `sin theta > 0`, we can conclude that `sin(theta) = √(2/3)`.

Now that we have the values of sine and cosine, we can find the remaining trigonometric functions:

`tan(theta) = sin(theta)/cos(theta)`

`= (√(2/3)) / (1/√3)`

`= √(6)/3`

`cot(theta) = cos(theta)/sin(theta)`

`= (1/√3)/(√(2/3))`

`= √6 / 6`

`csc theta = 1/sin theta`

`= 1/(√(2/3))`

`= √6 / √4`

So, in summary:

- sec theta = √3

- cos theta = 1 / √3

- sin theta = √(2 / 3)

- tan theta = √6 / 3

- cot theta = √6 / 6

- csc theta = √6 / √4

Is there anything else you would like to know?

The equation of the parabola in vertex form is: y = (1/4)x² - 5. We can calculate it in the following manner.

Since the parabola opens either up or down, its vertex form is given by:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola and "a" is a constant that determines the direction and shape of the parabola.

Using the given vertex (0, -5), we have:

h = 0 and k = -5

Substituting the vertex coordinates into the vertex form, we get:

y = a(x - 0)² - 5

y = ax² - 5

To determine the value of "a", we use the given point (–2, –4) on the parabola. Substituting these coordinates into the equation, we get:

-4 = a(-2)² - 5

-4 = 4a - 5

1 = 4a

a = 1/4

Substituting this value of "a" into the equation for the parabola, we get:

y = (1/4)x² - 5

Therefore, the equation of the parabola in vertex form is:

y = (1/4)x² - 5

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The match can be scheduled in 900 different ways.

Here, the number of players from each school = 3.

Let us assue that the players of the first school be A, B, and C.

And the players of the second school be X, Y, and Z.

Here, each player from the first school has to play twice with each player from the second school.

We can organize the schedule into six different rounds, i.e.,

R1 : AX BY CZ

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BY CX

So, the number of possible ways to do this would be : 6! = 720 ways.

Now, three rounds are played simultaneously in each round.

R1 : AX BZ CY

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BX CZ

R5 : AZ BY CX

R6 : AZ BY CX

And R1 : AX BY CZ

R2 : AX BY CZ

R3 : AY BZ CX

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BX CY

The total number of possible ways for the second case would be twice of  6! / (2! 2! 2!), which is equal to 90+ 90 = 180.

Therefore, the total number of ways in which the match can be scheduled is 720 + 180 = 900.

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The complete question is:

central high school is competing against northern high school in a backgammon match. each school has three players, and the contest rules require that each player play two games against each of the other school's players. the match takes place in six rounds, with three games played simultaneously in each round. in how many different ways can the match be scheduled?

Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.

The term "statistical data" refers to numerical data that is gathered from a sample or population in order to characterise or draw conclusions about a larger group. Observational studies, surveys, experiments, and other techniques can all be used to gather statistical data, as can data from already-existing records and databases. Many approaches and methodologies, including data visualisation, inferential statistics, and descriptive statistics, can be used to examine statistical data. Measures of central tendency (mean, median, mode), indicators of dispersion (standard deviation, range, interquartile range), and graphical representations are some examples of the key characteristics of a dataset that are summarised and described using descriptive statistics (histograms, box plots, scatter plots). A bigger population can be inferred from a sample of data using inferential statistics, on the other hand.

given

The stem-and-leaf plot that depicts the data set accurately is as follows:

Season Points for the 2021 Riverside Red Dragon Football

0 0 3

1 1 7 7 7 7

2 0 0 0 2 4 8 8

3 1 3

Key 1|1 = 11

This stem-and-leaf plot depicts the frequency distribution of the data set in an accurate manner.

Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.

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The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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The distance between the Eiffel tower and the location where the observer is standing is 2869.2929 meters.

Therefore, you are 2869.2929 meters away from the Eiffel tower.

The Eiffel Tower is 300m tall. If a person is standing at a certain location in Paris, the tower subtends an angle of 6 degrees. To calculate the distance from the Eiffel tower, trigonometry is used. Here's how you can calculate the distance between the Eiffel tower and the location you are standing in Paris;

Let AB be the height of the Eiffel Tower, which is 300 m.
Let AC be the distance between the observer and the base of the Eiffel Tower.
Let the angle of elevation at A be θ = 6 degrees.
Now, from the diagram, it is clear that;
Tan θ = AB/AC
Therefore, AC = AB/Tan θ
Substituting values, we get:
AC = 300/Tan 6 degrees
AC = 300/0.104528
AC = 2869.2929 meters.

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To make  a departure timetable:

The simplest: download a predefined template from Microsoft Excel.

To create a template: select A1:E2 > Merge and Center > click WEEKLY SCHEDULE > select Center Alignment.

Add borders and titles. Type the time in A3. In A4 and A5, enter time > fill cell > add days > save template.

1. Start Excel and open a new blank workbook.

2. Select the range A1:E2 and on the Home tab, select Merge and Center in the Alignment group.

3.

Type "WEEKLY SCHEDULE" in A1:E2, change the font size to 18, and select Center Alignment in the Alignment group.

4. Select cells F1:H2, on the Home tab, in the Font group, select the Border drop-down menu, and then select All Borders.

5. Enter “Daily Start Time” into F1, “Time Interval” into G1, and “Start Date” into H1.

Select the Select All icon (between 1 and A on the worksheet), then double-click the line dividing two columns to resize all cells to fit the contents.

6. Select cell A3 and enter "TIME".

7. Select cell A4 and enter the time you want the program to start.

To follow this example, enter "7:00".

8. In cell A5, enter the next interval to be listed in the plan. To follow this example, enter "7:30". Select A4:A5 and drag the fill handle down to fill the time increment for the rest of the day.

9. In cell B3, enter the day of the week you want the schedule to start. To follow this example, enter "SUNDAY".

10. Drag the fill handle to the right to automatically fill the calendar with the remaining days of the week.

11. Select row 3. Make the font bold and change the font size to 14.

12. Change the hour font size in column A to 12.

13. Choose the Select All icon or press Ctrl+A and choose Center from the Alignment group on the Home tab.

14. Select cells A1:H2. In the Font group on the Home tab, select the Fill Color drop-down list and choose a fill color for the selected cells.

15. Select the body of the program. Select the Border drop-down menu in the Font group and select All Borders.

16. Save the program that  we have made as time table.

Complete Question:

How can we help the park manager to draw a departure timetable in excel?

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Three-digit addition and subtraction with regrouping involves adding or subtracting numbers with three digits (numbers between 100 and 999) while carrying or borrowing values from one place value to another.

Addition is a basic arithmetic operation that involves combining two or more numbers or quantities to find the total amount or sum. It is often denoted by the symbol "+". For example, if we add 2 and 3, we get a sum of 5.

For example, let's say we want to add 357 and 468:

In this example, we first add the ones place (7 + 8 = 15), which gives us a sum of 5 and carry-over of 1. We then add the tens place (5 + 6 = 11) and add the carry-over from the ones place, which gives us a sum of 2 and carry-over of 1. Finally, we add the hundreds place (3 + 4 = 7) and add the carry-over from the tens place, which gives us a final sum of 825.

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Answer:

x = - 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

10(5x + 12) = 2(5x + 15)  Distribute the 10 and the 2

10(5x) + 10(12)  = 2(5x) + 2(15)

50x + 120 = 10x + 30  Subtract 10x from both sides

50x - 10x +120 = 10x - 10x + 30

40x + 120 = 30    Subtract 120 from both sides

40x + 120 - 120 = 30 - 120

40x = -90  Divide both sides by 40

[tex]\frac{40x}{40}[/tex] = [tex]\frac{-90}{40}[/tex]

x = [tex]\frac{-9}{4}[/tex] or - 2[tex]\frac{1}{4}[/tex]

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

The best unit of measure for the liquid in family-sized container of apple cider is the liter - True.

The metric unit of volume is known as the litre (international spelling) or liter (American English spelling) (SI symbols L and l,[1] with another symbol also used: ℓ). It is equivalent to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3). A litre or cubic decimetre fills a space of 10 cm × 10 cm × 10 cm (see figure) and is therefore equal to one-thousandth of a cubic metre. One litre of liquid water has a weight of almost precisely one kilogram, because the kilogram was initially defined in 1795 as the weight of one cubic decimetre of water at the temperature of melting ice (0 °C). However, subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.

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Answer:

Step-by-step explanation:

To find the volume of a figure, you need to multiply the length, width, and height of the figure.

The most expensive health insurance plan for someone who fills 7 prescriptions each month is Option B, which has a total monthly cost of $240.

To identify the most expensive health insurance plan, we need to calculate the total cost for each option per month. The total cost can be found by adding the monthly insurance premium to the product of the co-pay per prescription and the number of prescriptions per month.

From the calculations, Option B is the most expensive plan as it cost $240 per month.

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Answer:

B) x=12

Step-by-step explanation:

theres a 50/50 shot at getting heads, half of 24 is 12

I don't actually know but you could ask a professional.

Katie will pay $1.10 for shipping and handling.

The cost of shipping refers to the amount of money that is charged for the transportation of goods or products from one location to another.

To calculate how much Katie will pay for shipping and handling, we first need to find 10% of $11.

To do this, we multiply $11 by 0.10 (which is the decimal equivalent of 10%).

$11 x 0.10 = $1.10

Therefore, Katie will pay $1.10 for shipping and handling on top of the $11 she paid for the set of spoons.

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Answer:

h=

[tex] \frac{15}{4} [/tex]

Step-by-step explanation:

Divide both sides by 8:

[tex]2 - 7 + 4h = \frac{80}{8} [/tex]

Divide 80 by 8 to get 10:

[tex]2 - 7 + 4h = 10[/tex]

subtract 7 from 2 to get -5:

[tex] - 5 + 4h = 10[/tex]

add 5 to both sides:

[tex]4h = 10 + 5[/tex]

Add 10 and 5 to get 15:

[tex]4h = 15[/tex]

divide both sides by 4.:

[tex]h = \frac{15}{4} [/tex]

Hopefully this helps! :)

Answer: 0.09m > 56.60 + 0.07m, where m > 2830.

Step-by-step explanation:

Let's assume that Plan A costs more than Plan B for monthly phone use greater than some value m, where m is the number of minutes of phone use in a month.

For Plan A, the monthly cost can be expressed as:

Cost_A = 0 + 0.09m = 0.09m

For Plan B, the monthly cost can be expressed as:

Cost_B = 56.60 + 0.07m

To find the value of m for which Plan A costs more than Plan B, we need to set the two costs equal to each other and solve for m:

0.09m = 56.60 + 0.07m

0.02m = 56.60

m = 56.60 / 0.02

m = 2830

Therefore, for monthly phone use greater than 2830 minutes, Plan A will cost more than Plan B.

In mathematical notation, we can express this as:

0.09m > 56.60 + 0.07m, where m > 2830.

The proof involves showing that the bisecting line QS and the parallel sides QR and PS create pairs of congruent angles, which then proves that opposite sides are parallel. Therefore, PQRS is a parallelogram.

Proof:

Since QS bisects PR at T, we know that PT = RT and QT = TS.

Also, QR is parallel to PS. Therefore, angle QTS is congruent to angle RPT (alternate interior angles).

Using the same reasoning, we can show that angle PST is congruent to angle QRP (alternate interior angles).

Now, we have two pairs of congruent angles in the quadrilateral PQRS, which means that the opposite sides are parallel.

Therefore, PQRS is a parallelogram.

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This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.

If there are R125 in a box and half of the total is removed each day, it will take 10 days to reduce the total to 25 cents. This is because the total amount is being halved each day, and the amount remaining at the end of each day is the amount left at the start of the day, divided by two. This can be expressed mathematically using the formula[tex]R125/(2^t)[/tex] = 25, where t is the number of days.If we solve the equation for t, we get t = log2(R125/25). This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.To calculate this process over the 10 days, we can use the formula [tex]R125/(2^t)[/tex] for each day, where t is the day number. Starting at day 0, the amount remaining would be R125. At the end of day 1, the amount remaining would be R125/2 = R62.50. At the end of day 2, the amount remaining would be R62.50/2 = R31.25. This process continues until at the end of day 10, the amount remaining would be R0.25.

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In terms of journey times, Bus 14 is more reliable than Bus 47, as seen by its lower IQR and narrower range of travel times based on the line plot.

We must examine the data's variability to ascertain which bus is the most reliable. The interquartile range (IQR), which is the range of the middle 50% of the data, is one way to measure variability.

The line plot for Bus 47 reveals a range of trip times of 4 to 28 minutes, with an IQR of 8 minutes (from 10 to 18 minutes). This reflects a reasonable degree of consistency in journey times, as it shows that half of the students on Bus 47 have trip times that are within 8 minutes of one another.

With an IQR of six minutes, the line plot for Bus 14 reveals a travel time range of 8 to 28 minutes (from 14 to 20 minutes). This demonstrates that journey times on Bus 14 are more consistent than on Bus 47, with half of the students' travel times being within 6 minutes of one another.

We may also have a look at the data range, which is the range of numbers between the maximum and minimum. Bus 14 has a range of 20 minutes, while Bus 47 has a range of 24 minutes (from 4 to 28 minutes) (from 8 to 28 minutes). The conclusion that Bus 14 is more reliable is further supported by the suggestion that its range of travel times is lower.

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