Suppose a fair coin is tossed nine times. Replace the resulting sequence of H’s and 74 Chapter 2 Probability T’s with a binary sequence of 1’s and 0’s (1 for H, 0 for T). For how many sequences of tosses will the decimal corresponding to the observed set of heads and tails exceed 256?

Answer:

[tex]CD = 7.8[/tex]

Step-by-step explanation:

Given:

Δ DBC is a right angled triangle.

[tex]\angle B = 90\°\\\\\angle C = 59\°[/tex]

BC = 4

We need to find the value of CD

Solution:

Now we know that:

[tex]cos\ \theta = \frac{adjacent \ side}{hypotenuse}[/tex]

So we can say that;

[tex]Cos \angle C =\frac{BC}{CD}[/tex]

Substituting the given values we get;

[tex]Cos\ 59 = \frac{4}{CD}\\\\\\CD = \frac{4}{Cos\ 59} = 7.766[/tex]

Rounding to nearest tenth we get;

[tex]CD = 7.8[/tex]

Hence the Value of CD is 7.8.

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine tan m∠A, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan A = √32/2 = (√16 × √2)/2

Tan A = (4√2)/2

Tan A = 2√2

The value of tan A is in the simplest radical form  [tex]2\sqrt{2}[/tex].

The exact value of tanA in the simplest radical form.

The value of tan A is determined by using the formula;

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\[/tex]

Where Perpendicular = [tex]\sqrt{32}[/tex] and Base = 2

Substitute all the values in the formula;

[tex]\rm TanA = \dfrac{Perendicular}{Base}\\\\TanA = \dfrac{\sqrt{32}}{2}\\\\TanA = \dfrac{4}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\TanA = 2\sqrt{2}[/tex]

Hence, The value of tan A is [tex]2\sqrt{2}[/tex].

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The solution is in the attachment

The height of the rose after 10 weeks was approximately 7.714 inches. This is calculated by multiplying the original height of the rose (5.8 inches) by 1 1/3 (converted to a decimal as 1.33).

The subject of this question is Mathematics, and it involves performing multiplication to find the height of the rose after 10 weeks. Given that the height of the rose was 5.8 inches originally, and after 10 weeks, the height was 1 1/3 times the original height, we can calculate the new height as follows:

So, 5.8 inches * 1.33 = 7.714 inches.

Therefore, the height of the rose after 10 weeks was approximately 7.714 inches.

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Answer:

$4300.

Step-by-step explanation:

Let x represent amount of money invested in each account.

We have been given that equal amounts are invested in each of three accounts paying 7%, 9%, and 12.5%, one years combined interest income is $1,225.5.        

We will use simple interest formula to solve our given problem.

[tex]I=Prt[/tex], where,

I = Amount of interest after t years,

P = Principal amount,

r = Annual interest rate.

Since principal for each amount is equal and time is equal to 1 year, so we can represent our given information in an equation as:

[tex]1225.5=x(0.07+0.09+0.125)(1)[/tex]

[tex]1225.5=x(0.285)[/tex]

[tex]x=\frac{1225.5}{0.285}[/tex]

[tex]x=4300[/tex]

Therefore, an amount of $4300 is invested in each account.

Final answer:

The amount invested in each of the three accounts with different interest rates, which together yield a total interest income of $1,225.5, is $4,300 in each account.

Explanation:

To solve for the amount invested in each account, we need to set up an equation that represents the total interest income from the accounts.

Letting x represent the amount invested in each account, we can say that the interest from the first account at 7% is 0.07x, the second account at 9% is 0.09x, and the third account at 12.5% is 0.125x. The total interest income is the sum of these individual interests, which equals $1,225.5. Hence, the equation to solve is:

0.07x + 0.09x + 0.125x = 1,225.5

Combining like terms gives:

0.285x = 1,225.5

Dividing both sides by 0.285 gives us:

x = 1,225.5 / 0.285

x = 4,300

Therefore, the amount invested in each account is $4,300.

Answer:

The option x squared ( root index 4 start root x squared end root) is correct

Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]

Step-by-step explanation:

Given expression is [tex]\sqrt[4]{x^{10}}[/tex]

To find the equivalent expression to the given expression :

[tex]\sqrt[4]{x^{10}}[/tex]

[tex]=\sqrt[4]{x^{8+2}}[/tex]

[tex]=\sqrt[4]{x^8.x^2}[/tex] ( using the property [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=\sqrt[4]{x^{2\times 4}.x^2}[/tex]

[tex]=\sqrt[4]{(x^2)^4x^2}[/tex] ( using the peoperty [tex]a^{mn}=(a^m)^n[/tex] )

[tex]=\sqrt[4]{(x^2)^4}\times \sqrt[4]{x^2}[/tex] ( using the property [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex] )

[tex]=x^2\sqrt[4]{x^2}[/tex]

Therefore [tex]\sqrt[4]{x^{10}}=x^2\sqrt[4]{x^2}[/tex]

Therefore the equivalent expression to the given expression is [tex]x^2\sqrt[4]{x^2}[/tex]

The option "x squared (RootIndex 4 StartRoot x squared EndRoot)" is correct

That is [tex]x^2\sqrt[4]{x^2}[/tex] is correct

Answer:

the correct answer is A

Step-by-step explanation:

hope this helped

Answer:

y=1/3x-1

Step-by-step explanation:

A(0,-1)=(x1,y1) x1=0,y1=-1

B(3,0)=(x2,y2) x2=3, y2=0

m=(y2-y1)/(x2-x1)

m=(0-(-1))/(3-0)

m=1/3

y-y1=m(x-x1)

y-(-1)=1/3(x-0)

y+1=1/3*x

y=1/3*x-1

Answer:

Variability expected among these Proportions is given by Standard deviation = 0.125

Step-by-step explanation:

The probability of tossing heads is the same for a fair coin as the probability of tossing tails.

The probability of tossing heads is then 1 chance out of 2

P = 1/2 = 0.5

The standard deviation of the sample distribution of the sample proportion = √Pq/n

Standard deviation = √p(1-p)/n

= √0.5(1-0.5)/16

Standard deviation = 0.125

The variability among the proportions of heads obtained in the coin tosses is due to the random nature of the experiment. The law of large numbers explains that as the number of tosses increases, the observed relative frequencies of heads will approach the theoretical probability of 0.5.

The amount of variability that can be expected among the proportions of heads obtained by the students tossing a coin 16 times can be determined by understanding the concept of probability.

In a single coin toss, the probability of getting a head is 0.5. However, when the coin is tossed more times, the observed proportions of heads will vary from the theoretical probability of 0.5.  

The variability among these proportions is attributed to the random nature of the coin tosses and is due to the fact that the short-term results of an experiment do not necessarily match the theoretical probability. The law of large numbers states that as the number of repetitions of an experiment is increased, the observed relative frequencies of heads will tend to become closer to the theoretical probability of 0.5.

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Answer: the number of slices that each person will get is 4 4/9

Step-by-step explanation:

Antonio ordered 5 large pizzas, which have a total of 40 slices.

He invited 8 people to his party. If he plans to divide the pizza up equally among him and his friends, it means that the pizza would be divided among 9 people(Antonio and 8 friends = 9 people).

The number of slices that each of them will get would be

40/9 = 4 4/9 slices

x= -13 , y=11

Step-by-step explanation:

Using elimination method, make the x variable equal to eliminate the variable

-3x - y = -28

2x+ 3y=7

2(-3x-y =28)

3(2x+3y=7)

-6x - 2y =56

6x +9y=21

Apply addition

7y = 77

y=77/7 = 11

Use the value of y=11 in  

2x+ 3y=7

2x +3(11) =7

2x +33 =7

2x=7-33

2x= -26

x= -26/2 = -13

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Answer:

The answer to your question is letter C (x + 7)

Step-by-step explanation:

Expression

                             x² + 5x - 14

Factor the expression

- Find two number that multiplied give -14 and that added give 5

- Find the prime factors of -14

                       -14    2

                       -  7   7

                         -1

-From the prime factors, we notice that these numbers are + 7 and -2

-             x² + 7x - 2x - 14

- Factor the expression

              (x + 7)(x - 2)

Answer:

Zscore = 0.5

Step-by-step explanation:

If we assume a normal distribution, we mean that the diameters of each tomato follow a normal distribution. This is N~ (0,1).

By that, we mean that the mean (μ) = 0 and variance ([tex]\sigma^{2}[/tex]) = 1. Thus, since we are told that one tomato was in the 50th percentile. This implies the median. And is 0.5. And if the distribution is normal, the mean and median and mode should be equal.

Thus:

==> Z score = [tex]\frac{x-\mu}{\sigma}[/tex] = [tex]\frac{0.5 - \mu}{\sigma} = \frac{0.5-0}{1} = 0.5[/tex]

Answer:

Step-by-step explanation:

(2x+y)(3x²+y)=2x(3x²+y)+y(3x²+y)=6x³+2xy+3x²y+y²=6x³+3x²y+2xy+y²

Final answer:

The length of the rectangle increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially when the area is increasing at 8 square meters per hour and the width at 0.4 meters per hour.

Explanation:

To find how quickly the length of the rectangle increases, given that the area increases at a rate of 8 square meters per hour and the width increases by 40 centimeters (0.4 meters) per hour, we can use the area formula for a rectangle (Area = length × width). The rate of change of the area with respect to time (ΔA/Δt) can be related to the rates of change of the length and width with respect to time (ΔL/Δt and ΔW/Δt respectively) by the product rule for differentiation if we consider length and width as functions of time.

Initially, the area A is 10m × 7m = 70m². When the area is increasing at 8m²/h and the width is increasing at 0.4m/h, we can write the relation as follows:

ΔA/Δt = ΔL/Δt × W + L × ΔW/Δt

Substituting the given values and solving for the rate of change of the length (ΔL/Δt):

8 = ΔL/Δt × 7 + 10 × 0.4

8 = 7ΔL/Δt + 4

7ΔL/Δt = 4

ΔL/Δt = 4/7 m/h

Therefore, the length increases at a rate of 4/7 meters per hour (approximately 0.57 m/h) initially.

Answer:

The answer to your question is 25 girls

Step-by-step explanation:

Data

4 boys for every 5 girls

20 boys             ? number of girls

To solve this problem use proportions

Number of boys : Number of girls :: New number of boys : New number of

                                                                                                          girls

Substitution

                                       4 : 5 ::  20 : x

Solve for x

                                       x = (5 x 20) / 4

Simplification

                                      x = 100 / 4

Result

                                      x = 25

There are 25 girls                                

Answer:

Use math in healthcare career: In healthcare career one must translate medication orders into the right doses and number of pills to administer.

Step-by-step explanation:

Consider the provided information.

Math in healthcare career play significant role one should must know the units of the measurement for temperature, blood pressure, pulse rate, breathing rate etc.

In healthcare career one must translate medication orders into the right doses and number of pills to administer.

For example, If a doctor recommends a 100 gram of a drug every 6 hours and the hospital has 50 milligram pills, then you need to give two pills every 6 hours. Because 50 milligram times 2 is 100 milligram.

Math is vital in a healthcare career for tasks such as dosage calculations, interpreting vital signs, and handling medical billing. Proper math skills ensure accuracy and safety. Mastery in math will enhance your ability to provide effective patient care.

You asked how you will use math in your healthcare career. Math is essential in healthcare for various day-to-day operations. Here are some specific examples:

In conclusion, math is a vital skill in the healthcare field. Its applications range from dosage calculations to interpreting vital signs, and even handling billing. Mastery of math in your healthcare career will enable you to provide safe and effective patient care.

Answer:

He drive 1,400 miles last month all together.

So, option B) 1,400 is the correct answer.

Step-by-step explanation:

Given:

Alex has a truck. 42% of the miles he drove last month were for work.

If Alex drove 588 miles for work.

Now, to find miles he drive last month all together.

Let the miles he drive last month all together be [tex]x.[/tex]

42% of the miles he drove last month were for work.

Alex drove 588 miles for work.

Now, to get the miles he drive last month all together we put an equation:

[tex]42\%\ of\ x=588[/tex]

[tex]\frac{42}{100} \times x=588[/tex]

[tex]0.42\times x=588[/tex]

[tex]0.42x=588[/tex]

Dividing both sides by 588 we get:

[tex]x=1400\ miles.[/tex]

Therefore, he drive 1,400 miles last month all together.

So, option B)  1,400 is the correct answer.

Answer:

The answer is 1,400  

Step-by-step explanation: If you do 1,400x42%=588 So the answer is 1400!!!!!

Answer:

[tex]2\frac{2}{3}\text{ ft}^3\approx 2.67\text{ ft}^3[/tex]

Step-by-step explanation:

We have been given that Martha has 8 cubic feet of putting soil in the 3 flowerpots. She wants to put the same amount of soil in each pot.

To find the amount of soil in each pot, we need to divide total soil (8 cubic feet) by number of pots (3) as shown below:

[tex]\text{Amount of soil in each pot}=\frac{8\text{ ft}^3}{3}[/tex]

[tex]\text{Amount of soil in each pot}=2\frac{2}{3}\text{ ft}^3[/tex]

[tex]\text{Amount of soil in each pot}=2.6666\text{ ft}^3[/tex]

[tex]\text{Amount of soil in each pot}\approx 2.67\text{ ft}^3[/tex]

Therefore, Martha needs to put approximately 2.67 cubic feet of soil in each flower pot.

To determine the amount of soil Martha puts in each flowerpot, divide the total cubic feet of soil (8) by the number of flowerpots (3), which results in approximately 2.67 cubic feet of soil per pot.

The question pertains to the division of cubic feet of soil into equal amounts across three flowerpots. To find out how many cubic feet of soil Martha should put in each flower pot, we simply divide the total amount of soil by the number of flowerpots. In this case, Martha has 8 cubic feet of soil to distribute evenly into 3 pots.

The calculation would be as follows:

Therefore, Martha can put approximately 2.67 cubic feet of soil in each flower pot.

Answer:

52.814 degrees

Step-by-step explanation:

we know that

[tex]1^o=60'\\1'=60''[/tex]

we have

[tex]52^o48'51''[/tex]

[tex]52^o48'51''=52^o+48'+51''[/tex]

Convert 51'' to minutes

[tex]51''=\frac{51}{60}= 0.85'[/tex]

[tex]52^o48'51''=52^o+48'+0.85'=52^o+48.85'[/tex]

Convert 48.85' to degrees

[tex]48.85'=\frac{48.85}{60}= 0.814^o[/tex]

[tex]52^o+48.85'=52^o+0.814^o=52.814^0[/tex]

Final answer:

The angle measure 52°48'51'' is equivalent to 52.814 degrees in decimal form when you convert the minutes and seconds to a decimal and add them to the degree part.

Explanation:

The angle measure 52°48'51'' equivalent to in decimal degrees is calculated by converting minutes and seconds to a decimal form. One degree equals 60 minutes, and one minute equals 60 seconds. To convert, divide the number of minutes by 60 and the number of seconds by 3600, then add those amounts to the degrees to get the decimal degree.

Starting with the minutes: 48 minutes / 60 = 0.8 degrees.

Now converting the seconds: 51 seconds / 3600 = approx. 0.014167 degrees.

So, adding these together: 52 + 0.8 + 0.014167 = 52.814167 degrees, which rounded to the nearest thousandth of a degree is 52.814.

Answer: the value of the account at the end of 6 years is is $8577

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 6000

r = 6% = 6/100 = 0.06

n = 4 because it was compounded 4 times in a year.

t = 6 years

Therefore,.

A = 6000(1+0.06/4)^4 × 6

A = 6000(1+0.015)^24

A = 6000(1.015)^24

A = $8577

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

[tex]\angle ABE\cong \angle CDE[/tex]    ( right angles )

[tex]\angle AEB\cong \angle CED[/tex]  ( common angles )

By AA similarity postulate,

[tex]\triangle ABE\sim \triangle CDE[/tex]

∵ Corresponding sides of similar triangles are in same proportion,

[tex]\implies \frac{AB}{CD}=\frac{BE}{DE}[/tex]

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

[tex]\implies \frac{12}{4}=\frac{6+DE}{DE}[/tex]

[tex]12DE = 24 + 4DE[/tex]

[tex]8DE = 24[/tex]

[tex]DE=3[/tex]

Now, the speed of walking = 2 mph = [tex]\frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}[/tex]

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E  

[tex]= \frac{\text{Walked distance}}{\text{Walking speed}}[/tex]

[tex]=\frac{6}{2.933}[/tex]

= 2.045 hours

Hence, the change rate in the length of shadow

[tex]= \frac{\text{Length of shadow}}{\text{Time taken}}[/tex]

[tex]=\frac{3}{2.045}[/tex]

= 1.5 ft per sec.

Answer:

Step-by-step explanation:

7,300 = 5,500 + 300x

7,300 - 5,500 = 300x

1,800 = 300x

x = 6

Answer:

greater than or equal to 6

Step-by-step explanation:

i just took the plato test

Answer:

MA

Step-by-step explanation:

Answer:

[tex]m\angle H = 44.4\°[/tex].

Step-by-step explanation:

Given:

In Right Angle Triangle GIH

∠ I = 90°

GI = 7    ....Side opposite to angle H

GH = 10  .... Hypotenuse

To Find:

m∠H = ?

Solution:

In Right Angle Triangle ABC ,Sine Identity,

[tex]sin \ H = \frac{Oppsite\ side\ to\ \angle H}{Hypotenuse}[/tex]

Substituting the values we get;

[tex]sin\ H = \frac{7}{10} = 0.7[/tex]

Now taking [tex]sin^{-1}[/tex] we get;

[tex]\angle H = sin^{-1}\ 0.7 = 44.427[/tex]

rounding to nearest tenth we get.

[tex]m\angle H = 44.4\°[/tex].

Hence [tex]m\angle H = 44.4\°[/tex].

Answer / Step-by-step explanation:

Given the statement:

∃x∈D,(P(x)∧Q(x)) and (∃x∈D,P(x))∧(∃x∈D,Q(x)) ,

Then,

(a), The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement.

That is:

(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y))

Where  

(∃x∈D,P(x))∧(∃x∈D,Q(x)) = (∃x∈D,P(x))∧(∃y∈D,Q(y)) implies that P(x) is true for some element x in D and Q(y) is true for some element y in D. However, x and y are not necessary the same element and thus, we cannot be sure that  

P(x) ∧ Q(x) or P(y) ∧ Q(y) is true.

Moreover, if P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y,

Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement  

∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.

(b)

If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D, while x ≠ y, then Then, P(x) ∧ Q(x) is false and P(y) ∧ Q(y) is also false. Moreover, there is no other known element (z) such that P(z) ∧ Q(z) is true and thus the statement  

∃x∈D,(P(x)∧Q(x)) is false while the statement (∃x∈D,P(x))∧(∃x∈D,Q(x)) is true.

So in summary, we can say for:

(a) the statement does not contain the same truth value.

(b) The statement depicts there is such a choice in the first place.

In this exercise we have to use the knowledge of sets to identify which of the statements is true and false, thus we can state that:

A) the statement does not contain the same truth value.

B) The statement depicts there is such a choice in the first place.

Then, the first statement says that:

A)The variable used in a ∃ statement does not matter, thus, we can change the appearance of one of the variable used in the ∃ statement. That is:

[tex](\exists \ x \in D,P(x)) \wedge ( \exists \ x\in D,Q(x)) = (\exists \ x \in D,P(x)) \wedge (\exists \ y \in D,Q(y))[/tex]

Where the equation above implies that P(x) is true for some element x in D and Q(y) is true for some element y in D.

However, x and y are not necessary the same element and thus, we cannot be sure that   is true.

If P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x)[/tex] is false and [tex]P(y) \wedge Q(y)[/tex] is also false.  

B) If the statement P(x) is only true for x and no other element in the domain D, and if Q(y) is only true for y and no other element in the domain D. Then, [tex]P(x) \wedge Q(x) \ or \ P(y) \wedge Q(y)[/tex] is also false.

Moreover, there is no other known element (z) such that is true and thus the statement.

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Answer:

The answer to your question is right

Step-by-step explanation:

Acute is a triangle in which three internal angles are acute (less than 90°). The other angles measure  90°, so this option is incorrect.

Obtuse is a triangle that has one angle greater than 90°. This option is incorrect because of the angles of this triangle measure 30, 60, 90.

Equiangular is a triangle in which angles measures the same. This option is wrong because the angles have different values.

A Right triangle is a triangle that has an angle that measures 90°. This option is right.

Height  of the rock wall is 52.2 ft.

Step-by-step explanation:

These two triangles are similar, so using the similarity ratio, we can write as,

Δ HTV ~ Δ JSV

Now we can write the ratio as,

HT/TV = JS/SV

5.8/4 = x/36

Rearranging the equation to get x as,

x = 36 × 5.8 /4

 = 52.2 ft

Answer:

A group of students formed a circle during a game.The circumference of the circle was about 43.96 feet,and the diameter of the circle was 14 feet.Which expression best represents the value of π?

The expression which represents the value of π is option C from the attachment that is π = 43.96/14

Step-by-step explanation:

Given:

Circumference of the circle = 43.96 feet

Diameter f the circle = 14 feet

So,

We know that :

Circumference of the circle = [tex]2(\pi )r[/tex] or [tex](\pi)d[/tex]

Re-arranging the formula:

⇒ [tex](\pi)d = Circumference\ (C)[/tex]  

⇒ [tex](\pi )d =C[/tex]

⇒ [tex]\frac{\pi\times d}{d}=\frac{C}{d}[/tex]

⇒ [tex]\pi =\frac{C}{d}[/tex]

Plugging the numeric values:

⇒ [tex]\pi =\frac{43.96}{14}[/tex]

So the expression for π is 43.96/ 14,and option C is the correct choice.

The required expression for value of x is [tex]\frac{43.96}{14}[/tex].

Given that,

The circumference of the circle was about 43.96 feet,

And the diameter of the circle was 14 feet

We have to determine,

Which expression best represents the value of x.

According to the question,

Circumference of the circle = 43.96 feet

Diameter f the circle = 14 feet

Then,

Circumference of the circle = [tex]\pi \times d[/tex]

Let, [tex]\pi = x[/tex]

Circumference of the circle  [tex]= x d[/tex]

Circumference of the circle = 43.96 feet

Therefore,

[tex]= 43.96 = x\times 14\\\\= x = \frac{43.96}{14} \\\\[/tex]

Hence, The required expression for value of x is [tex]\frac{43.96}{14}[/tex].

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The measure of the angle R is [tex]m \angle R=69.4[/tex]

Explanation:

It is given that the lengths of the triangle are PQ = 8 and QR = 3

To find the angle of R using the opposite and adjacent side, we shall use the tangent formula.

[tex]\tan \theta=\frac{o p p}{a d j}[/tex]

where opp = 8 and adj = 3

Thus, substituting these values in the formula, we get,

[tex]\tan \theta=\frac{8}{3}[/tex]

Multiplying both sides by [tex]tan^{-1}[/tex], we get,

[tex]\theta=tan^{-1} (\frac{8}{3})[/tex]

Dividing, we get,

[tex]\theta=69.44[/tex]

Rounding off to the nearest tenth, we have,

[tex]\theta=69.4[/tex]

Thus, the measure of the angle R is [tex]m \angle R=69.4[/tex]

Answer:

5.28°

Step-by-step explanation:

Draw the triangle formed by the sledding run.  The hypotenuse is 300.  The height is 27.6.  The angle of depression is opposite of the height.

Using sine:

sin θ = 27.6 / 300

sin θ = 0.092

θ = 5.28°