Danny is in a 90 m high watchtower. Lily and Bryan are out searching for clues in regards to a route taken by an escaped prisoner. Lily radios to Danny that she has found some evidence and estimates that she is 350 m from the base of the watchtower. Danny radios this information to Bryan, who estimates that from his location, the angle of elevation to the top of the watchtower is 20°. Danny estimates that the angle from Bryan to the base of the watchtower to Lily is 85°.
a) To the nearest meter, how far is Bryan from the base of the watchtower?
b) To the nearest meter, how apart are Bryan and Lily?

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

B

Step-by-step explanation:

The area of the Sandbox is given as x^2 + 3x

You are also given that the width of the sandbox is x

The question is, what is the length

Formula

Area = L * w               Substitute the givens into the formula

x^2 + 3x = L * x          Use the distributive property to put brackets on left.

(x^2 + 3x) = L*x         Pull out the common factor on the left.

x(x + 3) = L * x            Divide both sides by x

x(x + 3)/x = L*x/x

x + 3 = L

On solving the provided question, we can say that - Probability of ace on 1st card and king on 2ndis 4/663

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1.

probability of drawing a specific second card depends on the identity of the first card.

\(P(ace on 1st card and king on 2nd) = 4/663\\ P(king on 1st card and ace on 2nd) = 4/663\)

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We can use the counting principle to determine the number of possible system configurations for an entertainment system with the given options for amplifiers, compact disc players, and speakers. The number of ways is  \(64\).

The counting principle states that if there are '\(a\)' ways to do one thing and '\(b\)' ways to do another thing, then there are '\(a*b\)' ways to do both things.

In this case: - There are \(2\) options for amplifiers. - There are \(4\) options for compact disc players. - There are \(8\) options for speaker models.

Using the counting principle, we can calculate the total number of possible system configurations by multiplying the number of choices for each component together:

Total system configurations \(=\) (Number of amplifier choices) \(*\) (Number of compact disc player choices) \(*\) (Number of speaker model choices)

Total system configurations \(=2\) (amplifiers) \(* 4\) (compact disc players) \(*8\)(speakers)

Total system configurations \(= 64\)

So, there are \(64\) possible system configurations that the customer can choose from when selecting an amplifier, a compact disc player, and a speaker model for their entertainment system.

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Answer:

Step-by-step explanation:

60+20=80

Answer:

Step-by-step explanation:

sorry but i,m not sure

The advantages of the parametric equations are the parametric equations are easier to enter into a calculator for graphing, the parametric equations show the direction in which the ellipse is drawn, and for a given value of the independent variable, the parametric equations yield exactly one point on the graph. Therefore, the correct option is B, D, and E.

The advantages of parametric equations are:

Parametric equations are easier to enter into a calculator for graphing because they separate the variables, allowing for easier input and manipulation in graphing calculators.

Parametric equations show the direction in which the ellipse is drawn because they represent the coordinates of a point on the ellipse as functions of a single parameter, which varies over a specified range. This parameterization allows us to trace the curve in a specific direction.

For a given value of the independent variable, parametric equations yield exactly one point on the graph because each value of the parameter corresponds to a unique point in the Cartesian plane. This makes it possible to represent a curve more precisely than with a single equation involving both variables.

Hence, the correct answer is option B, D, and E.

Note: The question is incomplete. The complete question probably is: What are the advantages of the parametric equations? Select all that apply. A) The parametric equations describe a three-dimensional figure. B) The parametric equations are easier to enter into a calculator for graphing. C) The parametric equations have a finite domain. D) The parametric equations show the direction in which the ellipse is drawn. E) For a given value of the independent variable, the parametric equations yield exactly one point on the graph.

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Answer:

Step-by-step explanation:

ac is Definition: Alternating Current (AC) is a type of electrical current, in which the direction of the flow of electrons switches back and forth at regular intervals or cycles. Current flowing in power lines and normal household electricity that comes from a wall outlet is alternating current.

Answer:

Step-by-step explanation:

5x - 6y = 27 .......... Equation 1

7x + 6y = 9 ………… Equation 2

To solve using elimination add the second equation to the first one to eliminate y

That's

5x - 6y + 7x + 6y = 27 + 9

12x + 6y - 6y = 36

12x = 36

Divide both sides by 12

x = 3

Substitute it into any of the equations

Using equation 2

That's

7(3) + 6y = 9

21 + 6y = 9

6y = - 12

Divide both sides by 6

y = - 2

The solutions are

x = 3

y = - 2

Hope this helps you

Answer:

The average cost per vet visit was $19.25.

Step-by-step explanation:

From the information given, you can find the average cost per visit by dividing the total amount paid for a year's worth of vet visits by the number of visits:

269.50/14= $19.25

According to this, the answer is that the average cost per vet visit was $19.25.

The weight of each bean bag is 0.71 lb.

The weight of the bean bags must sum up to 15lb. In order to determine the weight of each bean bag, divide the total weight of the bag by the total number of bean bags tossed.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Weight of each bag = total weight / total number of bags

Total number of bean bags = 13 + 8 = 21

15 lb / 21 = 0.71 lb

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Answer: im lazy too >:P

Step-by-step explanation: owo

Answer:

1 5/7

Step-by-step explanation:

I literally just took the test so yeah

Answer:

I think the answer is 2 3/7. because you are decreasing 1/7.

Step-by-step explanation:

Answer:

I Believe Its Eight Squares

There are 450 triangles, we can pick that do not form an equilateral triangles when 15 dots are evenly spaced on the circumference of a circle.

An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.

here, we have,

Let's calculate the total no. of possible triangles, it depends on the combination. To make a triangle, we have to choose 3 dots out of 15.

Here, we will use the combination rule to find out the possible triangles,

Thus, the total number of possible triangles = 15C3                                                                      = (15.14.13) / (1.2.3) = 455

Note that an equilateral triangle would be formed by connecting 3 equally spaced dots.

For an equilateral triangle, out of 15 dots, there would be 15 - 3 = 12 dots that will not be connected.

And 12/3 = 4 dots would be between any two connecting dots.

Taking 1st connecting dot, the second connecting dot would be

1 + 4 + 1 = 6th

Similarly, the third connecting dot would be 6 + 4 + 1 = 11th

So, the following connecting dots will form equilateral triangles: (1, 6, 11); (2, 7, 12); (3, 8, 13); (4, 9, 14); (5, 10, 15);

After applying the combination rule we found the total number of the possible triangle and there are 5 equilateral triangles:

So, there are 455 - 5 = 450 triangles that are not equilateral triangles.

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Complete question;

fifteen dots are evenly spaced on the circumference of a circle. how many combinations of three dots can we pick from these 15 that do not form an equilateral triangle?

5.23 × 10^(-6) kg/mm^3 is equal to 5.23 × 10^(-15) kg/m^3.

To convert 5.23 × 10^(-6) kg/mm^3 to kg/m^3, we need to multiply the given value by a conversion factor.

1 mm^3 is equal to (1/1000)^3 m^3, or 10^(-9) m^3.

Therefore, the conversion factor is 10^(-9) m^3/mm^3.

To convert kg/mm^3 to kg/m^3, we can multiply the given value by the conversion factor:

5.23 × 10^(-6) kg/mm^3 * 10^(-9) m^3/mm^3 = 5.23 × 10^(-15) kg/m^3.

what is factor?

In mathematics, a factor refers to a number or expression that divides another number or expression evenly without leaving a remainder. It is a key concept in multiplication and division.

Here are two common uses of the term "factor":

1. Factors of a Number: Factors of a number are the whole numbers that divide the given number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because these numbers divide 12 evenly.

2. Factoring in Algebra: Factoring in algebra involves expressing an algebraic expression or polynomial as a product of its factors. For example, the expression x^2 - 4 can be factored as (x - 2)(x + 2), where (x - 2) and (x + 2) are the factors of the expression.

Factors play an important role in various areas of mathematics, including number theory, algebra, and arithmetic. They are used to simplify expressions, solve equations, find common multiples and divisors, and analyze the properties of numbers and functions.

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Answer:

40x30= 1200, 20x15=300, 300/1200= 1/4.

Step-by-step explanation:

You can also visualize it. Imagine a field 40’ long and the boy cut the top 20’ of it but left 20’ of the bottom, he would have cut half of it at this point. Now it’s 30’ wide and he cut the left 15’ of what’s remaining but left the right 15’ uncut. So now there’s a 20’x15’ bottom right corner left uncut. There are 4 sections that are 20’x15’ and he left one out of four uncut, otherwise written as 1/4.

Answer:

m<1

Step-by-step explanation:

If the expression is in the form of \(ax^2+bx+c\), then the condition for having 2 different real roots is

\(b^2-4ac>0\cdots(i)\).

The given expression is \(x^2-2x+m\).

Here, a=1, b=-2 and c=m.

So, by using equation (i),

\((-2)^2-4(1)(m)>0\)

\(\Rightarrow 4-4m>0\)

\(\Rightarrow 4m<4\)

\(\Rightarrow m<4/4\)

\(\Rightarrow m<1\).

Hence, the condition for the expression \(x^2-2x+m\) to have two different real roots is m<1.

The frequency distribution table of the data is illustrated below.

The data we have been given represents the percentage of people who have completed 4 or more years of college education in different states. To create a frequency distribution, we need to first decide on the number of classes we want to use. In this case, we will use 7 classes.

Next, we need to determine the range of values for each class. To do this, we first find the minimum and maximum values in the data set, which are 18.9 and 37.9, respectively.

The range of values for each class will be (max value - min value) / number of classes, which in this case is (37.9 - 18.9) / 7 = 2.86.

We will start with the first class, which will include all values from 18.9 to 21.76 (the lower limit of the first class plus the range of values for each class). The next class will include values from 21.76 to 24.62, and so on, until we reach the final class which will include all values from 33.18 to 36.04 (the upper limit of the final class plus the range of values for each class).

To create the frequency distribution, we count the number of values in the data set that fall into each class. For example, the first class includes values between 18.9 and 21.76, and there are 2 values in the data set that fall into this range (21.4 and 20.0). We continue this process for each class until we have a table that shows the frequency of values in each class.

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Complete Question:

Percentage of People Who Completed 4 or More Years of College Listed by state are the percentages of the population who have completed 4 or more years of a college education. Construct a frequency distribution with 7 classes.

21.4,26.0,25.3,19.3,29.5,35.0,34.7,26.1,25.8,23.4,27.1,29.2,24.5,29.5,22.1,24,3,28.8,20,0,20.4,26.7,35.2,37.9,24.7,31.0,18.9,24.5,27.0

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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To find the area in the right tail more extreme than z = 0.77 in a standard normal distribution, we need to calculate the area to the right of z = 0.77.

Using a standard normal distribution table or a calculator, we can find the cumulative probability associated with z = 0.77. The cumulative probability represents the area to the left of the given z-score.

From the table, we find that the cumulative probability for z = 0.77 is approximately 0.7794.

To find the area in the right tail more extreme than z = 0.77, we subtract the cumulative probability from 1:

Area = 1 - 0.7794 = 0.2206

Therefore, the area in the right tail more extreme than z = 0.77 is approximately 0.221.

Similarly, to find the area in the left tail more extreme than z = -1.68 in a standard normal distribution, we need to calculate the area to the left of z = -1.68.

Using the standard normal distribution table or a calculator, we can find the cumulative probability associated with z = -1.68.

From the table, we find that the cumulative probability for z = -1.68 is approximately 0.0465.

To find the area in the left tail more extreme than z = -1.68, we simply use the cumulative probability:

Area = 0.0465

Therefore, the area in the left tail more extreme than z = -1.68 is approximately 0.047.

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Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Answer: Y = 4, X=4 (4,4)

Step-by-step explanation: You must multiply both equations so the leading coefficient cancels out. I’m multiplying both equations by both coefficients so I multiply the entire first equation by -2 so the first equation will be the negative coefficient and the second equation will be multiplied by positive 9 so the negative and positive equations cancel out.

STEPS IN MATH:

1. (9x-8y=4) -2 = -18x + 16y = -8

(2x-3y=-4)9 = 18x-27y= -36

2. ADD THESE EQUATIONS TOGETHER NOW

-18x+16y=-8

+ 18x-27y=-36

0-11y= -44

-11y=-44

DIVIDE -44 by -11y

The final answer is Y= 4

NOW pick an equation to plug in y to, any equation works

I chose the first one, so 9x-8(4)=4

9x-32=4

9x=36

x=4

Answer:

point form (4,4)

equation form  x= 4, y= 4

Step-by-step explanation:

a) When Lily's age is 20, and Raphael's age is divided by 3 then the expression of Lily's age in terms of h is h < 10.

b) Ethan's age is half of Raphael's age therefore, Ethan's age is half Raphael's age.

a) If Raphael is twice as old as his sister Lily, we can represent their ages as 2h and h, respectively, where h is Lily's age. The sum of their ages is less than 30, so we can write the equation:

2h + h < 30

Combining like terms, we get:

3h < 30

Dividing both sides by 3, we get:

h < 10

This is an expression of Lily's age in terms of h.

b) If Ethan's age is 16, and Raphael's age is twice Ethan's age, we can represent Raphael's age as 2 × 16 = 32.

Ethan's age is 16, which is half of Raphael's age of 32. Therefore, Ethan's age is half of Raphael's age.

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The question is -

Raphael is twice as old as his sister. The sum of their ages is less than 30.

a) Lily's age is 20, and Raphael's age is divided by 3. Write an expression in terms of h for Lily's age.

b) An expression for Ethan's age 16. Write a sentence to describe how Ethan's age compares with Raphael's age.

A rhombus is a quadrilateral that has four sides of equal length. A rhombus also has two diagonals, which are perpendicular bisectors of each other. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

To find the perimeter of a rhombus using diagonals, follow these steps:

Step 1: Obtain the length of each diagonal of the rhombus.

Step 2: Use the length of the diagonals to find the length of each side.

Step 3: Add the length of each side to find the perimeter of the rhombus.

The perimeter is the sum of all the sides of a figure. To get the perimeter of a rhombus using diagonals, the length of each diagonal has to be found first. The formula for finding the length of each side of a rhombus is:  where the diagonal is the measure of the diagonal of the rhombus.

To find the perimeter of a rhombus, add the length of all the sides of the rhombus. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

Therefore, the perimeter of a rhombus using diagonals can be found by following the above procedure and then using the formula to add all the sides of the rhombus.

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The calculated value of the expression 1/2(20+24) * 5) * 8 + (8 * 8) * 8 is  1392

Given that

1/2(20+24) * 5) * 8 + (8 * 8) * 8

The expression 1/2(20+24) * 5 evaluates the average of 20 and 24, which is 22, and then multiplies it by 5, giving 110.

Then, this value is multiplied by 8 to get 880.

The second part of the expression (8x8) * 8 simply involves multiplying 8 by 8 to get 64 and then multiplying this result by 8, which gives 512.

Finally, the two sub-expressions are added together to get the final result:

880 + 512 = 1392

Therefore, the value of the expression 1/2(20+24) * 5) * 8 + (8 * 8) * 8 is  1392

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A) the three inequalities that must be satisfied are:

B) Graph shaded and satisfying all conditions is attached.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.

It is most commonly used to compare the sizes of two numbers on a number line.

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Answer:

x=(3y-11)/5

3(y-2)= 5(x+1) by cross multiplication

5x+5=3y-6

5x=3y-6-5

5x=3y-11

We divide by 5 on both sides

Answer:

C orB looks like it

Step-by-step explanation: