A guy wire attached to the top of a radio antenna

is bolted to the ground 48 m from the base of

the tower. If the wire makes an angle of 14°

with the ground. What is the length of the

guy wire? Round your answer to the nearest

hundredth of a meter.

1

Answer:

jason: 60mph

marie: 50mph

Step-by-step explanation:

let jason drive at x miles per hour

let marie drive at x-10 miles per hour

let jason drive for y hours

let marie drive for y+1 hours

distance = speed * time

for jason:

300 = x * y

for marie:

300 = (x-10) * (y+1) = x*y + x - 10y -10

300 = x*y

divide both sides by x to solve for y

300/x = y

plug this into the second equation

300 = (x-10) * (300/x+1) = 300 -3000/x +x -10

300 = 300 -3000/x +x -10

subtract 300 from both sides

0 = -3000/x + x - 10

multiply both sides by x to get rid of the denominator

0 = x^2 -10x -3000

factor

0 = x^2 - 60x +50x -3000

0 = x(x-60) + 50(x-60) = (x+50)(x-60)

x = 60 or -50

x cannot be negative so x = 60mph

marie = 60-10 = 50mph

Answer:

85

Step-by-step explanation:

So you know that there are 26 letters in the alphabet and 3 letters in the license plate, so that would be 26 multiplied by 3 to cover all of those letters.  The first letter can't be I or O, so you subtract 2 from the product.  26 times 3 is 78, minus 2 is 76. There are 10 single digits, but only one in the plate and it can't be 0.  This leaves 9 digits so you add that to the total number.  

76 + 9 = 85

I hope this helps!  :)

Sorry for my previous answer, I misread the question, but this is the correct answer now, hope this helped!

Answer:

129600 license plates

Step-by-step explanation:

This time, we will use an option of solving where we take the number of possibilities for one letter, then multiply it by the next, then multiply it by the next, then multiply it by the number of possibilities for the number. We would have 24 letters to start (not including I or O), then after we pick one, we need to remove it since we can't repeat letters. So just for our letters, we would get:

24 * 25(only the first digit can't have I or O) * 24

Then, we need to multiply that by 9 (since we are not including 0), giving us:

24 * 25 * 25 * 9 = 129600

Meaning, we can have 129600 different license plates.

Hope this helped!

The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Look up all the related responses.

The likelihood that an event will happen is quantified by probability. An event's likelihood is determined by how frequently it will occur over the long run. Probabilities are all digits that fall between 0 and 1, inclusive—that is, all digits that fall between 0 and 1.

Let the equation of Z score be:

z = (raw score - mean) / standard deviation

Given mean of 36 minutes and a standard deviation of 3 minutes.

If x = 32:

z = (32 - 36)/3 = -1.33

and x = 37:

z = (37 - 36)/3 = 0.33

P(-1.33 < z < 0.33) = P(z < 0.33) - P(z < -1.33)

= 0.6179 - 0.0198

= 0.5981

A consumer selected at random has a 59.81% chance of having to wait between 32 and 37 minutes.

The complete question is:

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 36 minutes and a standard deviation of 3 minutes. What is the probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes, to the nearest thousandth?

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All x-values that are within the scope of both f and g make up the domain of the (f g)(x). In this instance, f has a domain of {"x | x ≥ 0"} and g has a domain of "all real numbers"; as a result, (f - g)(x) has a domain of {"x | x ≥ 0"} as these values of x fall inside both f and g's domains.

A function's domain is the collection of all potential inputs. All x-values, or inputs, and all y-values, or outputs, make up a function's domain and range, respectively. When viewing a graph, the domain consists of all of the graph's values from left to right. The graph's whole range, from the bottom to the top, is the range.

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To solve x easily, shift the variables to one side, and shift all the other values including constants to the other side.

Solve for x means finding the value of x in an equation involving one variable that is x or with different variables like finding x in terms of y. Whatever the case is you are required to find  the value of x, for which the given equation holds true.

For example, if the equation is given as: 2x - 50 = 4

Now solve the tjis equation for x by keeping the term with variable x to one side, and shifting all the other values such as constants to the other side.

now

2x = 4 + 50

2x = 54

x = 54/2

x= 27

This is the required value of x which is obtained after solving the equation for x.

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Answer:

700 minutes

Step-by-step explanation:

Let y represent the cost and x represent the number of minutes of call time

We have the equation

99.95 = 0.10x + 29.95

Now let's solve

99.95 = 0.10x + 29.95

70 = 0.10x

x = 700 minutes

So, she was billed for 700 minutes

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The cost  of hiring a van for 5 days is $235.

In this question, we have been given an equation c = 10 + 45d that represents the cost in pounds of hiring a van for days.

here c = cost in pounds

d = number of days

We need to find the cost  of hiring a van for 5 days.

Substitute the value d = 5 in given equation.

c = 10 + 45d

c = 10 + (45 × 5)

c = 10 + 225

c = 235 dollars

Therefore, the cost for 5 days is 235 dollars

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An equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Given that, after 17 weeks, you have $570, and after 29 weeks, you have $822.

Here, (17, 570) and (29, 822)

Substitute (x₁, y₁)=(17, 570) and (x₂, y₂)=(29, 822) in m=(y₂-y₁)/(x₂-x₁)

= (822-570)/(29-17)

= 252/12

= 21

Substitute, m=21 and (x, y)=(17, 570) in y=mx+c, we get

570=21×17+c

570=357+c

c=213

Substitute, m=21 and c=213 in y=mx+c, we get

y=21x+213

Therefore, an equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.

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Answer:

perimeter = 10

area = 6.25

Step-by-step explanation:

Every square has four equal sides. If we know one side is 2.5, then all sides are 2.5.

2.5*4 = 10

To find the area of a square you multiply the height and length. Since all sides of a square are the same, you just multiply 2.5 with itself.

2.5*2.5=6.25

The equation indicates that the given equation's constant variable is 8.

In other words, you may claim that y directly depends on x or that y is directly proportional to x. The continuity equation or the constant variable variation in this function is m (or k). a direct variation's product of two variables or the result of two variables in such an inverse variation K is the constant of variation in the direct variation equations.

"X fluctuates directly as Y" denotes that as y rises, x also rises by the same amount. In other words, the ratio between y and x is constant and is:

                            x = k × y                

where k is the constant of variation.

Here,

it is given that y varies as  x,

if y=24 and x=3,

therefore,

y = kx

24 = 3k

∴ k = 8

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The option that is not involved in proving the converse of the Pythagorean theorem is D. substitution and contradiction

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

The converse of Pythagoras' Theorem states that a triangle must have a right angle if the square of one side equals the sum of the squares of the other two sides.

In this case, contradiction isn't involved. The correct option is D.

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The distance and bearing of the boat from its original location are about 183.33 miles, N71.97°E

A bearing is a description of the amount by which a north or south headed line is deflected in the eastern or western direction.

The initial direction in which the boat is traveling = Due east

The distance the boat travels in the direction due east = 130 miles

The distance the boat travels in the direction N38°E = 72 miles

Therefore;

The distance the boat has traveled from its original location is found using the law of cosines as follows;

The included angle between the 130 miles distance the boat travels east and the 72 miles distance the boat travels N38°E = 90° + 38° = 128°

Let d represent the distance of the boat from its original location, we get;

d² = 130² + 72² - 2 × 130 × 72 × cos(128°) ≈ 33609.1828181

d ≈ √(33609.1828181) ≈ 183.33

The distance of the boat from its original location is about 183.33 miles

Let the angle formed by the direction of the boat to its destination and the path the boat travels east, according to the law of sines, we get;

183.33/(sin(128°) ≈ 72/(sin(B))

(sin(B)) ≈ 72 × (sin(128°))/183.33

m∠B ≈ arcsin(72 × (sin(128°))/183.33) ≈ 18.03°

The bearing of the boat from its original location is; N(90° - 18.03°)E = N71.97°E

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The measure that would be most useful to determine if the people can safely use the elevator is B. Mean

The most useful measure to determine if the people can safely use the elevator would be the mean weight of the people, as it would give an idea of the average weight of the group and if it is below 4,500 pounds.

The mode is the most common value in a set of data and does not give information about the weight of the entire group. The interquartile range is a measure of the spread of the middle 50% of the data and does not give information about the average.

In conclusion, the correct option is B.

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Answer: 8

Step-by-step explanation:

Its a fish tank no fish can escape. So 10-2 because 2 fish died and that is 8.

So you have 8 fish.

Hope this helps

Option D) f(x) = |x|, is Correct.

What is parent function?

A parent function is a basic or fundamental function that serves as the starting point for a family or group of related functions. These functions can be obtained by applying a transformation to the parent function, such as shifting, stretching, or reflecting it.

The absolute value parent function is represented by the following function:

D. f(x) = |x|

The absolute value function is defined as |x| = x for x >= 0 and |x| = -x for x < 0. Graph of this function is a V-shape, and it's also known as "the absolute value of x" function. It is a reflection of the linear function f(x) = x across the x-axis and will always have a slope of 1 and a y-intercept of 0.

A. f(x) = x is a linear function, slope is 1 and y-intercept is 0, This is not absolute value function

B. f(x) = 2ˣ is the exponential function, and it is not an absolute value function

C. f(x) = x² is the quadratic function, it's a parabola opening upwards and not an absolute value function

D. f(x) = |x| is the absolute value function, V-shape and it's an example of the absolute value parent function.

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The amount of money in the account after 6 years is $68,847.56

To solve this problem, you can use the formula for compound interest,

where V is the final value of the account, P is the initial principal, r is the annual interest rate (expressed as a decimal), and t is the number of years the money is invested.

The formula for compound interest, V = Pe^(rt) is used to calculate the future value of an investment. It takes into account the effect of compounding, which means that interest is earned not only on the initial investment but also on the accumulated interest over time.

Plugging in the given values, we have

V = 51200e^(0.0546) = 51200e^0.324. e^0.324 is approximately 1.38, so the final value of the account is 512001.38 = $68,847.56

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An indirect proof is an argument that begins with the assumption that a conclusion is false, then uses logical reasoning to show that the assumption leads to a contradiction.

a fact or assertion that contradicts what someone else said or that differs from another fact or assertion to the point where one of them must be incorrect.

A situation or set of ideas that contradict one another is called a contradiction. A contradiction would be saying out loud that you support the environment while never remembering to empty the recycling. A statement that contains opposing ideas is frequently referred to as a "contradiction in terms."

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If triangle JKL is dilated by a scale factor of 3,cos(bº)=4/5.

Trigonometric By definition, ratios are the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

If you know the lengths of two of the triangle's sides, you can use trigonometric ratios to get the measurements of one (or both) of the acute angles.

tan(b)=P/B=3/4

sin(b)=P/H=3/5

cos(b)=B/H= To find

B=4, H=5

cos(b)=4/5

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Using the formula for the volume of cuboid that is the product of length, breadth and height, The answer is 7cm.

A cuboid is a three-dimensional shape with six rectangular faces, three of which are pairs of congruent squares and the other three are rectangles. It is also known as a rectangular prism. The opposite sides of a cuboid are parallel and equal in area. The length, width, and height of a cuboid are three of its measures of size.

The volume of a three-dimensional object is a measure of the amount of space it occupies. It is typically measured in units of cubic units, such as cubic centimeters (cm^3) or cubic meters (m^3). The formula for the volume of a cuboid is length x width x height. For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, its volume would be 5 x 3 x 2 = 30 cubic centimeters. In general, the volume of a three-dimensional object can be found by multiplying the area of its base by its height.

length = 2cm

breadth =3cm

volume = 42 cm³

volume = l*b*h

42 = 2*3*h

h= 42/6 =7cm

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Answer:

17

Step-by-step explanation:

5y - 8 = 9y - 28

-8 = 4y - 28

4y = 20

y = 5

9(5) - 28

45 - 28

17

The inequality that shows the maximum number of hours Penelope can rent is 35 + 4x ≤ 75

An equation shows how two or more numbers and variables are related to each other.

Let x represent the number of hours to rent

There is a fixed $35 fee and an hourly fee of $4. Hence:

Total cost = 4x + 35

Penelope has a budget of $75. hence:

35 + 4x ≤ 75

The inequality is 35 + 4x ≤ 75

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Answer:

-73

Step-by-step explanation:

So to begin you must find where you start on a graph. To do this you can go backwards from your first number and in this situation it would be 14.5 because the slope is -2.5x. I will use y as the answer.

y=-2.5x+14.5

From here you plug in how many terms are neeeded for the correct answer. In this situation there is 35 terms needed.

y=-2.5(35)+14.5

Solve this equation to get your answer.

y=-73

Answer:

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

Given sequence:

This is an AP with the common difference of:

The first term is a = 12.

Use the nth term equation to find the 35th term:

The ratio tells us how often one number is contained in another. In the class, there are six girls for every five boys. D is the right answer.

A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another. For instance, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) One-fourth are boys and three-fourths are girls.

The ratio tells us how often one number is contained in another.

Considering that 96 of the 176 junior students are female. Consequently, the class's gender distribution is,

96 girls are present.

80 boys out of 176, or 96 boys.

Currently, the junior class's gender distribution is as follows:

Girls to Boys in Ratio

96 girls and 80 boys.

Divide the numerator and denominator by 16 to simplify.

Boys/Girls: 6 to 5.

Therefore, the answer is option d) 6:5.

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a. 26%

sorry if wrong...

The equation of the linear function is A(t) = -975t + 15000

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

The table of values

From the table of values, we have:

A(t)         t

11,100   4

7200   8

3300   12

From the above table of values, we can see that

As t increase by 4, the value of A(t) decreases by 3900

This means that the table of values is a linear relation, and the slope is

slope = -3900/4

slope = -975

A linear equation is represented as

y = mx + c

Where

slope = m

So, we have

A(t) = -975t + c

Using the points on the table, we have

11000 = -975 * 4 + c

Evaluate

c = 15000

So, we have

A(t) = -975t + 15000

Hence, the equation is A(t) = -975t + 15000

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The ratio of yellow paint to mixed paint is 3/5.

A ratio is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is written as a/b or a: b. An equality of two ratios is a proportion. In order to write equivalent ratios, proportions are used, which aids in resolving the unknown quantities. As an illustration, a proportion is written as a: b = c: d.

Solution:-

Given,

Amount of yellow paint=3

Amount of blue paint=2

Ratio=yellow paint/total mixed paint

Ratio=3/(3+2)

Ratio=3/5

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Answer:

288

Step-by-step explanation:

32 x 9=288

There is a 60% chance that none of them will assault any of the others.

Only the likelihood that something will happen is included in probability. When we don't know how something will turn out, we could talk about the possibility of one or the likelihood of different outcomes. The scientific study of events that fit into a probability distribution is known as statistics.

It is based on the probability that something will happen. The fundamental principle of theoretical probability is the explanation of probability. For instance, when a coin is flipped, there is a 12% chance that it will land on its head.

Probability is a statistic that is used to show the possibility or likelihood that an event will happen. Probabilities can be expressed as fractions from 0 to 1 or as percentages from 0% to 100%.

  = 64/8 = 8

   =  8 - 2

    =  4

    =  64- 4

     = 60

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