From a balloon 777ft high, the angle of depression to the ranger headquarters is 78.4 degrees. How far is the headquarters from a point on the ground directly below the balloon. (Round to an appropriate number of significant digits)

a) The only outcome that satisfies both events X and Y is the letter C.

b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

c) The complement of event X is {D, E, F, G}.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The outcomes for each of the following events are:

(a) Event "X and Y": {C}

To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.

(b) Event "X or Y": {A, B, C, E, G}

The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

(c) The complement of event X: {D, E, F, G}

The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

Answer:

m=-1/6

Step-by-step explanation:

m=1-3/4+8=-2/12=-1/6

it's 8=8 meaning it is always true, and infinity.

Answer: all real num.

Step-by-step explanation:

4(a+2) = 8+4a

4a+8 = 8+4a

It can be all real number.

The interest amount is $622.85

The given parameters are:

The interest amount is calculated as:

I = P(1 + r/n)^(nt) - P

This gives

I = 1000 * (1 + 4.5%/1)^(1 * 11) - 1000

Evaluate the products and the quotient

I = 1000 * (1 + 0.045)^(11) - 1000

Evaluate the sum

I = 1000 * (1.045)^(11) - 1000

Solve

I = 622.85

Hence, the interest amount is $622.85

Read more about compound interest at:

https://brainly.com/question/24924853

#SPJ1

Answer:

After 3 min

Step-by-step explanation:

So becuase Tim is walking and Tim gave Alex a 50 meter head start so after 3 min they will tie each other.

Answer:

3.14

Step-by-step explanation:

Given that:

Mean weight (m) = 79 ounces

Population standard deviation (s) = 13.1

Sample size = 47

Maximal margin of error associated with 90% confidence interval.

The margin of error is given by:

Zcritical * (standard deviation / sqrt(sample size)

Z critical at 90% confidence interval = 1.645

Hence,

Zcritical * (standard deviation / sqrt(sample size)

1.645 * 13.1 / sqrt(47)

1.645 * (13.1 / 6.8556546)

1.645 * 1.9108313

Hence, the margin of error is :

3.1433174885

= 3.14

Answer:

\(\displaystyle d = 10\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (-2, 5)

Point (4, 13)

Step 2: Identify

x₁ = -2, y₁ = 5

x₂ = 4, y₂ = 13

Step 3: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

6.4 miles is your answer!

Step-by-step explanation:

Hope this helps and have a wonderful day!

Angle L's in the triangle LMN is,

⇒ L = 72.54°

We have to given that;

A triangle LMN is shown in figure.

And, The sides are,

Since, We know that;

A triangle is a three-sided polygon with three vertices, three angles that add up to 180 degrees, and three sides.

Since, We know that;

⇒ sin L = Opposite / Hypotenuse

And, cos L = Base / Hypotenuse

Two rays after combined into an angle have a single terminal. And, latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms.

Now, We can use trigonometry formula to find the value of angle l we get;

⇒ sin L = Opposite / Hypotenuse

⇒ sin L = LM / LN

⇒ sin L = 18/60

Taking arc sin both side, we get;

⇒ L = 72.54°

Therefore, The value of measure of angle L is triangle LMN is,

⇒ L = 72.54°

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

The percent of the total calories in each brownie comes from fat is 34%

Percentage is described as a number or ratio expressed as a fraction of 100.

It is often represented with the percent sign, "%"

Abbreviations like "pct" and "pc" are used to denoted it.

Percentage is a dimensionless number, that is, it has no unit of measurement.

From the information given, we have that;

207 calories of fat/606 calories in a brownie × 100/1

Divide the values, we get;

0. 34 × 100/1

Multiply the values

34%

Hence, the value is 34%

Learn about percentage on:

https://brainly.com/question/843074

#SPJ1

Answer:

Step-by-step explanation:

Xx to the power of 4+4 times x

Xx to the power of 8 times x

Xx to the power of 8 times x to the power of 1

Xx to the power of 8+1

Xx to the power of 9

Solving a quadratic equation we can see that the second bird catches the crab after 0.85 seconds.

The equation that describes the height of the crab is:

d = -t^2 + 10

The equation that represents the path of the second bird is:

d' = 5t + 5

The bird will be able to catch the crab when both are at the same height, this happens when:

-t^2 + 10 = 5t + 5

We need to solve this for t.

-t^2 + 10 - 5t - 5 = 0

-t^2 - 5t + 5 = 0

Using the quadratic formula we will get:

t = (5 ± √( (-5)^2 - 4*(-1)*5))/(2*-1)

t =  (5 ± 6.7)/(-2)

We only care for the positive solution, which is:

t = (5 - 6.7)/(-2)  = 0.85

So the bird catches the crab after 0.85 seconds.

Learn more about quadratic eqations:

https://brainly.com/question/1214333

#SPJ1

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

Answer:

the are is all the the lengths on the shape your using added

Step-by-step explanation:

a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.

b) An equation representing the situation is x = (125 - 80)/5.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The mathematical operations provide solutions to mathematical problems using operands.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

The total number of balloons that Andre has = 125

The number of balloons remaining after hanging some for the school party = 80

The difference (number of balloons used) = 45 (125 - 80)

The number of friends who hang the balloons = 5

The number of balloons hung by each friend of Andre = 9 (45/5)

Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.

Learn more about mathematical operations at https://brainly.com/question/30715366.

#SPJ1

Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

Learn more about dilations at:

https://brainly.com/question/3457976

#SPJ1

Answer:

$400

Step-by-step explanation:

Lets money that Anthea got be 2x

than Barry's money be 5x and Carol's be x

Barry got $200 more than Carol

This means that 5x is 200 more than x

5x = x + 200

4x = 200

x = 50

The sum of money is 2x + 5x + x

so this is 8x

8x = 50 * 8 = 400

Answer:

a) 0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.

b) The 75th percentile for the age of United States Presidents on the day of inauguration is 61.

c) 0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The age of United States Presidents on the day of their first inauguration follows a Normal distribution with mean 56 and standard deviation 7.3.

This means that \(\mu = 56, \sigma = 7.3\)

(a) (5 points) Compute the probability that a randomly selected President was less than 60 years old on the day of their first inauguration.

This is the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 56}{7.3}\)

\(Z = 0.55\)

\(Z = 0.55\) has a pvalue of 0.7088

0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.

(b) (5 points) Compute the 75th percentile for the age of United States Presidents on the day of inauguration.

This is X when Z has a pvalue of 0.75. So X when Z = 0.675.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.675 = \frac{X - 56}{7.3}\)

\(X - 56 = 0.675*7.3\)

\(X = 61\)

The 75th percentile for the age of United States Presidents on the day of inauguration is 61.

(c) (5 points) Compute the probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.

Now, by the Central Limit Theorem, we have that \(n = 4, s = \frac{7.3}{\sqrt{4}} = 3.65\)

This is the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{60 - 56}{3.65}\)

\(Z = 1.1\)

\(Z = 1.1\) has a pvalue of 0.8643

0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.

Answer:

I'm pretty sure the answer is 90

Step-by-step explanation:

27.7 rounded up is 28 and 2.8 rounded up is 3, and the product of those 2 numbers is 84 and 90 is the closest number so that should be the answer :)

Answer:

The answer is 90

Step-by-step explanation:

27.7 rounded up is 28 and 2.8 rounded up is 3 so 28 times 3 is 84 and the closest number to 84 is 90

Answer:

many solutions

Step-by-step explanation:

3×2k=????

3×5=??

6×k=??

6×4=??

then put all those together in a 2 step equation and then add 9 to the answer

The equation 3(2k-5)=6(k-4)+9 has infinitely many solutions.

Two or more expressions with an Equal sign is called as Equation.

3(2k-5)=6(k-4)+9

In the given equation k is the variable

Now apply distributive property to the RHS and LHS wherever it is required

6k-15=6k-24+9

6k-15=6k-15

Shift all terms to one side

6k-15-6k+15=0

0=0

Hence the equation 3(2k-5)=6(k-4)+9 has infinitely many solutions.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

Answer: 819.3

Step-by-step explanation:

Answer:

Exact form: 8193/10        Decimal form: 819.3        Mixed number form: 819 3/10

Step-by-step explanation:

I believe this is the answer idk... UwU

Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

For more question equation

https://brainly.com/question/17145398

#SPJ8

Answer:

3z(5z-3)

Step-by-step explanation:

first you choose the common items which in this case was 3z the you divide 15 by 3 and 9 by 3

Answer:

i think its 4x

Step-by-step explanation:

hope it helps

Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation: