Michelle is now 50 miles ahead of John.
Michelle is traveling at a constant rate. John is traveling in the same direction, at a rate 10 miles per hour faster than Michelle. In how many hours will John catch up to Michelle?
A. 6
B. 5
C. 2
D. 0
E. John can't catch up to Michelle

Therefore, the height of the balloon is 88.6 feet.

Height typically refers to the vertical measurement of a person or object, usually from the ground or base to the highest point. It is a common physical characteristic used to describe the distance between the bottom and top of something, such as a building, tree, or person. Height is usually measured in units such as feet or meters, and it can vary greatly depending on the object or individual being measured. For humans, height can be influenced by factors such as genetics, nutrition, and environmental factors.

by the question.

denote the height of the balloon as "h" and the distance from the observer to the point on the street directly beneath the balloon as "x". We can then use the tangent function to set up the following equations:

[tex]tan (53 °) = h / x[/tex]

tan (29°) = (h - b) / x (where "b" is the radius of the balloon)

We can solve for "x" in the first equation by multiplying both sides by "x" and then dividing by tan (53°):

[tex]x = h / tan (53°)[/tex]

We can then substitute this expression for "x" into the second equation:

[tex]tan (29°) = (h - b) / (h / tan(53°))[/tex]

We can simplify this equation by multiplying both sides by (h / tan(53°)):

[tex]tan (29°) * (h / tan (53°)) = h - b[/tex]

We can then solve for "h" by adding "b" to both sides and simplifying:

[tex]h = b + tan (29°) * (h / tan (53°))\\h - (tan (29°) / tan (53°)) * h = b\\h * (1 - tan (29°) / tan (53°)) = b\\h = b / (1 - tan (29°) / tan (53°))[/tex]

We just need to know the radius of the balloon to compute "h". Since we are given the angles of elevation to the top and bottom of the balloon, we can use the tangent function again to find the height of the lower part of the balloon:

tan (53°) = (h - b) / x

We can solve for "b" by multiplying both sides by "x" and then subtracting "h" from both sides:

[tex]b = x * tan(53°) - h[/tex]

We can substitute the expression we found for "x" earlier:

[tex]b = (h / tan(53°)) * tan(53°) - h\\b = h * (1 - 1 / tan(53°))[/tex]

Now we have an expression for "b" in terms of "h", which we can substitute into our expression for "h":

[tex]h = (h * (1 - 1 / tan(53°))) / (1 - tan(29°) / tan(53°))[/tex]

Multiplying both sides by the denominator:

[tex]h * (1 - tan(29°) / tan(53°)) = h - h / tan(53°)\\h * (tan(53°) - tan(29°)) / tan(53°) = h / tan(53°)[/tex]

Multiplying both sides by tan (53°) and simplifying:

[tex]h * (tan(53°) - tan(29°)) = h\\h = 60 * (tan(53°) - tan(29°))\\h = 88.6 feet[/tex]

To learn more about height:

https://brainly.com/question/10726356

#SPJ

Answer:

its prob a

Step-by-step explanation:

I think for sure its A

The sum of the first 97 terms of the arithmetic progression is 153761.

What is arithmetic progression?

Arithmetic progression (AP) is a sequence of numbers in which each term is obtained by adding a constant value (known as the common difference) to the previous term. In other words, an arithmetic progression is a sequence of numbers where each term is a fixed distance apart.

To find the sum of the first 97 terms of an arithmetic progression with the nth term given as 2 + n/3, we use the formula:

S_n = n/2 [2a + (n-1)d]

We first find the first term, a, by substituting n = 1 into the nth term equation to get a = 7/3. Then, we find the common difference, d, by subtracting the (n-1)th term from the nth term, which gives us d = n/3.

Substituting these values into the S_n formula, we get:

S_97 = 97/2 [2(7/3) + (97-1)(97/3)]

Simplifying this expression, we get:

S_97 = 47(14 + 96 × 97/3)

S_97 = 47(3263)

S_97 = 153761

Therefore, the sum of the first 97 terms of the arithmetic progression is 153761.

To learn more about arithmetic progression visit:

https://brainly.com/question/16954227

#SPJ1

Answer:

To find the constant of proportionality, you need to have two variables that are directly proportional to each other. This means that as one variable increases, the other variable increases in proportion to it.

Once you have identified two variables that are directly proportional, you can find the constant of proportionality by dividing one variable by the other.

For example, if you have two variables, x and y, and you know that they are directly proportional, you can write the equation:

y = kx

where k is the constant of proportionality.

To find the value of k, you can pick any set of values for x and y that satisfy the equation and solve for k. For example, if x = 2 and y = 4, you can write:

4 = k(2)

Solving for k, you get:

k = 4/2 = 2

So the constant of proportionality in this case is 2. This means that y is always twice as large as x, no matter what values of x and y you choose, as long as they are proportional.

Answer:

a < 12

Step-by-step explanation:

500 - 25a > 200

500 - 200 > 25a

300 > 25a

divide both sides by 25

300/25 > 25a/25

12 > a

therefore, a < 12

0.33 is the approximate experimental probability of landing on B or C.

The actual outcome of an experiment, which may differ from the theoretical probability, is known as experimental probability.

Consider an experiment where 100 coin flips are performed. Theoretically, the odds are 50% heads and 50% tails. Your experiment's true results might be 47 heads and 53 tails.

We have this table

outcome  A     B     C      D

frequency 20  11     14   30

The values in the bottom row add to 20+11+14+30 = 75, so that matches up with the fact that the spinner was spun 75 times. Of those 75 spins, 11+14 = 25 landed on either B or C.

So 25/75 = 0.33 is the approximate experimental probability of landing on B or C.

Answer: Choice A) 0.33

Read more about experimental probability here:

https://brainly.com/question/8652467

#SPJ1

Answer:

55.5cm^2

Step-by-step explanation:

5×3=15

12-3=9

5+4=9

9×9=81

81÷2=40.5

40.5+15=55.5

answer: 55.5cm^2

The length of AC is 32.

A triangle is a geometric shape that consists of three straight sides and three angles. The three angles of a triangle always add up to 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles.

Since the triangles ABC and DBE are similar, we have:

AB/DB = BC/BE

Substituting the given values, we get:

AB/12 = BC/(BE + 4)

We also have another similar ratio:

AD/DB = AC/BE

Substituting the given values, we get:

24/12 = AC/(BE + 4)

Simplifying this equation, we get:

AC = 2(BE + 4)

Substituting this expression for AC into the first equation, we get:

AB/12 = BC/(BE + 4)

AB/(2(BE + 4)) = BC/(BE + 4)

Simplifying this equation, we get:

AB/2 = BC

Now we have two equations:

AB/2 = BC

AC = 2(BE + 4)

Substituting these expressions into the ratio AD/DB = AC/BE, we get:

24/12 = 2(BE + 4)/(AB/2)

Simplifying this equation, we get:

AB = 48/(BE + 4) * (BE/2 + 2)

Substituting the given value DE = 4, we get:

AB = 48/(BE + 4) * (BE/2 + DE/2)

AB = 24 * BE/(BE + 4)

Now we can substitute this expression for AB into the equation AB/2 = BC to get:

24 * BE/(BE + 4) / 2 = BC

12 * BE/(BE + 4) = BC

Substituting this expression for BC into the equation AC = 2(BE + 4), we get:

AC = 2(BE + 4) = 2 * 16 * (BE + 4)/(BE + 4) = 32

Therefore, the length of AC is 32.

To know more about equation visit:

https://brainly.com/question/19570938

#SPJ1

Answer:

The drone is not free. The final price of the drone is $31.08

Answer: A scatter plot shows the association between two variables. A scatter plot matrix shows all pairwise scatter plots for many variables. If the variables tend to increase and decrease together, the association is positive. If one variable tends to increase as the other decreases, the association is negative.

Step-by-step explanation:

Answer:

(6,6)

Step-by-step explanation:

The first equation crosses the y axis at 3 and the second equation crosses at zero.

For the first equation, if you start where the line crosses the y axis at 3 you would go up one and to the right 2.  That is what the slope is telling you 1/2.  Now that you have two points, you can draw the line.

The second equation goes through the orginin (0,0).  It's slope is 1.  You go up one and on to the right.  Connect these two points and you have the line.

The point (6,6) is where the two graphs cross.  

Helping in the name of Jesus.

Answer:

80 minutes

Step-by-step explanation:

80x3 is 240

240 mins=4 hrs

(i promise its right this time- i bet)

Answer:

c. 80 minutes

Step-by-step explanation:

Some problems give you too much information, and you need to choose only the information you need. The number of pages is not important. Here you only need the time, 4 hours, and the number of assignments, 3.

4 hours × 60 minutes / hour = 240 minutes

240 minutes / 3 assignments = 80 minutes/assignment

Answer: c. 80 minutes

Using expressions -3 - 5 = -8 and -3 - 3=0, we can say that the statement The difference of a negative value and a positive value is 0 is never true i.e. C.

What exactly are expressions?

In computer programming, an expression is a combination of one or more constants, variables, operators, and functions that are interpreted and evaluated by the computer to produce a value.

Expressions can be simple, such as a single variable or constant, or they can be more complex, involving multiple operators and functions.

For example, in the expression "2 + 3 * 4", the operators "+" and "*" are used to perform arithmetic operations, and the constants "2", "3", and "4" are operands that are used in those operations.

Now,

Example: -3 - 5 = -8, which is not equal to 0.

Example: 5 - 3 = 2, which is also not equal to 0.

However, even if the negative and positive values have the same absolute value, then their difference will not be 0. For example: -3 and 3 have a difference of -6.

Hence,

          the statement The difference of a negative value and a positive value is 0 is never true.

To know more about expressions visit the link

brainly.com/question/13947055

#SPJ1

Answer:

What is 2097 plus 3284

2097 + 3284

Step-by-step explanation:

You're welcome.

The reasοns for angles fοr each οf the given statements are respectively;

1) Substitutiοn

2) Definitiοn οf a Straight angle because a straight angle is 180°.

3) Cοngruent Angles have equal measures

We are given that;

m∠1 = 90°

m∠1 + m∠2 = m∠5

∠3 ≅ ∠4

Statement 1; 90° + m∠2 + m∠4 = 180°

Reasοn 1; Substitutiοn

Statement 2; m∠1 + m∠2 + m∠3 = 180°

Reasοn 2; Definitiοn οf a Straight angle because a straight angle is 180°.

Statement 3; m∠3 = m∠

Reasοn 3; Cοngruent Angles have equal measures

Thus, the missing reasοns fοr each οf the given statements are respectively;

1) Substitutiοn

2) Definitiοn οf a Straight angle because a straight angle is 180°.

3) Cοngruent Angles have equal measures

Learn more about angles at;

brainly.com/question/12852445

#SPJ1

Complete question:

ANS : 2√(3 × 43) + √(1254) - √(38)

Let's break down the expression step by step:

Expression: √(516) + √(1254) - √(38)

Step 1: Identify prime factors of each number in the Square roots.
- Prime factors of 516: 2^2 × 3 × 43
- Prime factors of 1254: 2 × 3^1 × 11 × 19
- Prime factors of 38: 2 × 19

Step 2: Simplify the square roots using prime factors.
- √(516) = √(2^2 × 3 × 43) = 2√(3 × 43)
- √(1254) = √(2 × 3 × 11 × 19) (This square root cannot be simplified further.)
- √(38) = √(2 × 19) (This square root cannot be simplified further.)

Step 3: Substitute simplified square roots back into the expression.
- 2√(3 × 43) + √(1254) - √(38)

Since we cannot simplify the square roots of 1254 and 38 further, and there are no common terms to combine, the given expression is already in its simplest form:

Answer: 2√(3 × 43) + √(1254) - √(38)

To Learn More About Square roots

https://brainly.com/question/1859113

SPJ11

As a result, the anticipated value in this circumstance is -$1,750, which probability suggests that if the architect decides to bid on the design of the new museum, she can expect to lose $1,750 on average.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

0.15 x $45,000 = $6,750.

Consider the following scenario in which the architect is not granted the contract:

The likelihood of not winning the bid is 0.85.

In this case, the payback is -$10,000 (a negative value since the architect would lose the $10,000 cost of creating blueprints and presenting a model).

In this case, the anticipated value is:

0.85 x (-$10,000) = -$8,500.

We sum the anticipated values of both situations to determine the overall expected value:

$6,750 + (-$8,500) = -$1,750.

As a result, the anticipated value in this circumstance is -$1,750, which suggests that if the architect decides to bid on the design of the new museum, she can expect to lose $1,750 on average.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

The only type of geometric shape that can have two side lengths of 14 ft and exactly one right angle is the isosceles right triangle. So, correct option is C.

Geometric figures are shapes that are defined by their geometric properties, such as size, shape, orientation, position, and other characteristics that are inherent to their structure. These shapes can be two-dimensional or three-dimensional and can be classified into different categories based on their properties. Here are some examples of geometric figures:

Points: A point is a basic element in geometry that has no size, shape, or dimension. It is usually represented by a dot and is used to describe the position of other geometric figures.

Lines: A line is a straight path that extends infinitely in both directions. It has no thickness or width and is usually represented by a straight line with arrows at both ends.

Segments: A segment is a part of a line that has two endpoints. It can be measured by its length.

Rays: A ray is a part of a line that has one endpoint and extends infinitely in one direction.

Angles: An angle is the space between two rays that share a common endpoint, called the vertex. It is usually measured in degrees or radians.

The geometric figures that could describe how the garden might look are quadrilaterals with one right angle. Some examples of such quadrilaterals are:

Out of these options, the only type of geometric shape that can have two side lengths of 14 ft and exactly one right angle is the isosceles right triangle. Therefore, the answer is:

C. Isosceles right triangle.

To know more about angles visit:

https://brainly.com/question/22673976

#SPJ1

The width of the walkway around the rectangular garden should be approximately 2.061 feet wide.

What is rectangle?

A rectangle is a type of quadrilateral with four sides and four right angles (90-degree angles). It is characterized by two pairs of parallel sides of equal length.

Let's represent the width of the brick walkway by "x" feet.

Then the dimensions of the entire rectangle including the brick walkway will be [tex]$(25+2x)$[/tex] feet by [tex]$(13+2x)$[/tex] feet.

The area of the rectangle with the walkway will be:

[tex]$$(25+2x)(13+2x)$$[/tex]

We know that the area of the walkway itself is 287 square feet. So we can set up the following equation:

[tex]$$(25+2x)(13+2x) - 25\cdot 13 = 287$$[/tex]

Simplifying and solving for x, we get:

[tex]$$4x^2 + 86x - 216 = 0$$[/tex]

Using the quadratic formula, we get:

[tex]$x = \frac{(-86 \pm \sqrt{86^2 - 4(4)(-216)})}{2(4)}$$[/tex]

[tex]$$x \approx 2.061 \text{ or } x \approx -26.311$$[/tex]

Since the width of the walkway cannot be negative, we reject the negative solution. Therefore, the width of the walkway should be approximately 2.061 feet wide (rounded to the nearest thousandth).

To learn more about rectangle visit:

https://brainly.com/question/2607596

#SPJ1

Answer: The ratio of their heights is 1/2 .

Let the radius of one cone be 'r'

and its height be 'h'

therefore, its perimeter of circular base will be 2 π r

and its volume will be given as  1 /3 π [tex]r^{2}[/tex] h

Let the radius of second cone be 'R'

and the height be 'H'

therefore its perimeter of circular base will be given as 2 π R

and its volume will be given as  1 /3 π [tex]R^{2}[/tex] H

ratio of their perimeters = 3 : 4

                         →         [tex]\frac{2 \pi r}{2 \pi R}[/tex]  =  [tex]\frac{3}{4}[/tex]

                          →         [tex]\frac{r}{R}[/tex]  =  [tex]\frac{3}{4}[/tex]

and ratio of their volume = 9 : 32

                          →      [tex]\frac{\frac{1}{3} \pi r^{2} h}{\frac{1}{3} \pi R^{2} H}[/tex]  =    [tex]\frac{9}{32}[/tex]

                          →      [tex](\frac{r}{R} )^{2}[/tex] * [tex]\frac{h}{H}[/tex] =  [tex]\frac{9}{32}[/tex]

now put the value of  [tex]\frac{r}{R}[/tex]  in the above equation we get

                          →        [tex](\frac{3}{4}) ^{2}[/tex]  *  [tex]\frac{h}{H}[/tex]  =  [tex]\frac{9}{32}[/tex]

solving it we will get

                    →        [tex]\frac{h}{H}[/tex] = [tex]\frac{1}{2}[/tex]  

therefore the ratio of their heights will be    [tex]\frac{1}{2}[/tex] .

To learn more about volume of cones

https://brainly.com/question/1082469

https://brainly.com/question/28109167

Therefore, the sample size was approximately 1360 Americans.

In statistics, a sample is a subset of a larger population. It is a representative selection of individuals or objects taken from the population of interest to be studied. Samples are often used in statistical analysis because it is usually impractical or impossible to collect data from the entire population.

Here,

The survey states that 20% of American households own 2 pets, and the survey was conducted on 1000 Americans. Since we are trying to identify the sample size, we can use the formula:

sample proportion = x / n

where x is the number of households that own 2 pets, and n is the sample size.

We are given that 20% of the sample own 2 pets, so we can write:

0.20 = x / n

Multiplying both sides by n, we get:

n * 0.20 = x

Simplifying, we get:

n = x / 0.20

We don't know the value of x, but we can estimate it using the proportion of households that own 2 pets in the entire population. According to a study by the American Pet Products Association, about 68% of American households own at least one pet, and about 40% of pet-owning households own two or more pets. Assuming that these percentages hold true for the survey sample as well, we can estimate that:

x = 0.40 * 0.68 * 1000

= 272

Substituting this value into the equation above, we get:

n = 272 / 0.20

= 1360

To know more about sample,

https://brainly.com/question/15659544

#SPJ1

a) the critical number x= N/A ,b) the absolute maximum is -16 at x= 5

c) the absolute maximum is -4 at x= 0.25

what is critical number?

The term "critical number" can have different meanings depending on the context in which it is used. Here are a few possible definitions:

In the given question,

To find the critical numbers of the function, we need to find where the derivative is either zero or undefined. Let's find the derivative of y with respect to x:

y' = 4/x²

The derivative is undefined at x = 0, but this point is not in the given interval, so we don't have to consider it. The derivative is zero when:

4/x² = 0

This equation has no real solutions, so there are no critical numbers in the interval (0.25, 5).

Since the function y = -4/x is decreasing on the interval (0.25, 5), the absolute maximum will occur at the left endpoint x = 0.25, and the absolute minimum will occur at the right endpoint x = 5. Therefore:

a) the critical number x= N/A

b) the absolute maximum is -16 at x= 5

c) the absolute maximum is -4 at x= 0.25

To know more about critical number , visit:

https://brainly.com/question/30000833

#SPJ1

Answer:

Muffins and Pretzels

Step-by-step explanation:

Muffins: 70/400 = 0.175 or 17.5

Pretzels: 70/400 = 0.175 or 17.5

17.5 is closest to 18%

So, the sections of the circle graph that represent 18% of the entire circle are muffins and pretzels, since they are closest to 18%

Create an equation representing the total number of seats in vehicles for the orchestra members.x*25 + y*12 = 111 Create an equation representing the total number of licensed drivers.x + y = 6

The local orchestra has been invited to play at a festival, and they need to figure out how to transport the 111 members. We can create a system of equations to find the smallest number of busses the orchestra can rent. We need to create an equation representing the number of vehicles needed and one representing the total number of seats in vehicles for the orchestra members. We also need an equation representing the total number of licensed drivers. The equation for the number of vehicles needed is x + y = 6, where x is the number of busses and y is the number of vans. The equation for the total number of seats in vehicles is x*25 + y*12 = 111. Solving these equations will give us the smallest number of busses the orchestra can rent.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ1

Step-by-step explanation:

Area of a rectangle = Height * width

     area =        5y     *      ( 7y-4)

                    = 35 y^2 - 20y   ( or  y ( 35y-20) )

Answer:

3y + 5.

Step-by-step explanation:

There are an infinity of expressions that are equivalent to this one. However, you may get the simplest equivalent by simplifying it. This is how you do it:

[tex]3 ( y + 4 ) - 7\\ \\(3)(y)+(3)(4)-7\\ \\3y+12-7\\ \\3y+5[/tex]

Final answer: 3y + 5.

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

Solving equations is a process that requires a lot of rewritting and simplifying, so you might be interested on checking out some examples of this topic here to improve your math simplifying skills!

Learn more about solving equations here:

brainly.com/question/30652933  

brainly.com/question/30596312  

brainly.com/question/28282032  

brainly.com/question/28306861  

brainly.com/question/28285756  

brainly.com/question/28306307  

brainly.com/question/30015231  

brainly.com/question/29888440

Using Laws of Indices, the given expression can be simplified as: 4

Some of the laws of Indices are:

1) Multiplying indices: This states that when multiplying indices with the same base, add the powers.

2) Dividing indices: This states that when dividing indices that have the same base, subtract the powers.

3) Brackets with indices: This states that when there is a power outside the bracket multiply the powers.

4) Power of 0: This states that any non-zero value raised to the power of 0 is equal to 1.

5) Negative and fractional indices: This states that when the index is negative, put it over 1 and flip (write its reciprocal) to make it positive.

When the index is a fraction, the denominator is the root of the number or letter, then raise the answer to the power of the numerator.

We are given the expression:

[tex]16^{\frac{1}{2} }[/tex]

Using law of fractional indices, we have:

[tex]16^{\frac{1}{2} } = \sqrt{16}[/tex]

= 4

Read more about Laws of Indices at: https://brainly.com/question/15361818

#SPJ1

The expression that is in simplest form is:

[tex]$1/3 + x^7$[/tex], [tex]$x^{-5} - y^{-4}$[/tex], [tex]$x^{-9} - y^{-1}$[/tex]

What is expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are grouped together in a meaningful way.

The expression that is in simplest form is:

[tex]$1/3 + x^7$[/tex], [tex]$x^{-5} - y^{-4}$[/tex], [tex]$x^{-9} - y^{-1}$[/tex]

This is because there are no common factors that can be factored out of either term. All the other expressions have terms that can be simplified or combined. For example:

[tex]$1/3 + x^7$[/tex] cannot be simplified any further.

[tex]$x^{-9} - 1/y$[/tex] can be written as [tex]$x^{-9} - y^{-1}$[/tex], but it is not simpler than the original expression.

[tex]$1/(x^3) - 1/(y^4)$[/tex] can be combined into a single fraction with a common denominator: [tex]$(y^4 - x^3)/(x^3y^4)$[/tex].

[tex]$x^3 + 1/y - t^6$[/tex] can be simplified to [tex]$x^3 + 1/y - 1$[/tex].

[tex]$x^{-5} - y^{-4}$[/tex] cannot be simplified any further, as noted earlier.

To learn more about expression visit:

https://brainly.com/question/1859113

#SPJ9

In circulation is 6% cumulative preferred stock for ABC Corporation. ABC distributed a 6% preferred dividend two years ago. ABC distributed a 4% preferred stock dividend last year. The minimum payout to preferred stockholders is 8%.

As per the given information, ABC Company has outstanding 6% cumulative preferred stock. This means that the preferred shareholders are entitled to receive a dividend at a fixed rate of 6% every year before any dividend is paid to the common shareholders.

The term "cumulative" implies that any unpaid dividends from previous years must be paid before any dividends can be paid to the common shareholders.

Now, we are given that two years ago, ABC paid a 6% preferred dividend. This means that the preferred shareholders received their full dividend payment for that year.

ABC distributed a 4% preferred stock dividend last year. This means that the preferred shareholders did not receive their full dividend payment for that year, and there is an unpaid amount of 2% (6% - 4%) from the previous year.

Since the preferred stock is cumulative, the unpaid dividends from the previous year must be paid before any dividend is paid to the common shareholders. Therefore, this year, ABC must pay the preferred shareholders their full dividend of 6% for the current year, as well as the unpaid amount of 2% from the previous year, totalling 8%.

To summarize, this year, ABC must pay the preferred shareholders a dividend of 8% before any dividend is paid to the common shareholders.

To learn more about cumulative preferred stock, refer:-

https://brainly.com/question/26113091

#SPJ1