Two control towers are located at points Q(500, 0) and R(500, 0), on a straight shore where the x-axis runs through (all distances are in meters). At the same moment, both towers sent a radio signal to a ship out at sea, each traveling at 300 m/µs. The ship received the signal from Q 3 µs (microseconds)before the message from R. Find the equation of the curve containing the possible location of the ship.

Answer:

$638.25

Step-by-step explanation:

I multiplied 17.25 times 37. The product was $638.25.

I was a bit confused when it said,"His overtime rate is 1 times his regular hourly rate." Since it is 1 times his hourly rate, it shouldn't affect the answer.

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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The number of hours it will take to travel 4000 km is 75 hours.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A bus travels 1 1/2 hours for 80km.

This can be written as,

1(1/2) hours = 80 km

3/2 hours = 80 km

Multiply 50 on both sides.

50 x 3/2 hours = 4000 km

75 hours = 4000 km

Thus,

It will take 75 hours to travel 4000 km.

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Answer:

y = kx

Step-by-step explantion:

We did this in math class and I know it is right! I hope this helps you! :)

a) Let x denote the quality rating and y denote the meal price.

b. From the above table, the marginal density function of x is 1.94

c. From the probability table, the marginal density function of y is 2.09

The probability distribution table for quality and meal price is obtained by dividing each and every frequency by the total frequency of 300 is attached in the image.

The probability distribution is obtained in the attached image below.

The expected value of x is,

1 x 0.28  + 2 x 0.50 + 3 x 0.22

= 1.94

To find the marginal density function of y

1 x 0.26  + 2 x 0.39 + 3 x 0.35

= 2.09

Given that var(x+y)=1.6691

var(x)=0.4964 and var(y)=0.6019

var(x+y) =1.6691

var(x) + var(y) +2* cov(x,y)=1.6691

0.4964+0.6019+ 2 *cov(x,y) =1.6691

1.0983+ 2 * cov(x,y) =1.6691

2 * cov(x,y) =1.6691-1.0983

2* cov(x,y)=0.5708

cov(x,y) =(0.5708)/2

cov(x,y)= 0.2854

Thus, the covariance of x and y is, 0.2854.

Here, the covariance of x and y is positive.

Thus, the relationship between quality and meal price is positive.

If the quality of the meal increases then the meal price also increases.

Yes, the expected result is positive because if the quality of the meal is good then meal price increases.

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Answer:

sin(t)

Step-by-step explanation:

tan(t)/sec(t) = tan(t) * 1/sec(t) = sin(t)/cos(t) * cos(t) = sin(t)

Answer:

$33.75; 25+1.75x

Step-by-step explanation:

a) cost = membership fee + cost of pizzas

= 25 + 1.75*5

= 25 + 8.75

= ($) 33.75

b) cost = 25 + 1.75x

Answer:

The slope is 7/4 and the y intercept is -10

Step-by-step explanation:

y=7/4x-10

This equation is written is slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 7/4 and the y intercept is -10

Step-by-step explanation:

we have 2 probabilities :

1. that a driver is wearing their safety belts : 0.68

2. that the driver is NOT wearing the safety belts :

1-0.68 = 0.32

A.

3 drivers are wearing it, 2 are not is a combination of

0.68³×0.32²

and how many combinations of these 5 probabilities can we have (e.g. the first 3 are wearing them, or the last 3 are wearing them, or ...) ?

that is 5 over 3 combinations :

5! / (3! × (5-3)!) = 5! / (3! × 2!) = 5×4/2 = 5×2 = 10

so, we have

10×0.68³×0.32² = 0.321978368

B

I am not sure I understand the question.

I assume this means from the 5 drivers they pull over the first 4 don't wear the seat belts, and only the fifth does.

so that is then

0.32⁴×0.68

and only one combination is possible. so, the result is just the product of these probabilities :

0.32⁴×0.68 = 0.0071303168

Substitute 5 for x in the equation x+y=4 to obtain the value of y.

So solution of the equations is (5,-1).

Given the equation of a quadratic function in the form:

Equation: y = x² - 6x + 7

where a = 1, b = -6, and c = 7.

Vertex form of a quadratic function:

where (h, k) is the vertex.

To find (h, k):

Vertex = (3, -2)

ANSWER

Vertex form of the quadratic equation:

Answer:

C

Step-by-step explanation:

For these types of problems, its important that we focus on the base as well as the lengths of the base and any other given lengths.

Here, the net has a base that forms a square with side lengths of 8mm.

So automatically, we can eliminate choices a and d as both have a base that is a triangle rather than a square.

We've also noticed that the base has a length of 8mm

If we look at B and C closely, we can tell that B has base lengths of 10mm while C has base lengths of 8mm.

So C is the correct answer choice.

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Answer:

133 Students

Step-by-step explanation:

Let the number of student in a van=v

Let the number of student in a bus=b

The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students.

Therefore: 12v+14b=796

General High rented and filled 14 vans and 12 buses with 738 students.

Therefore: 14v+12b=738

We solve the two resulting equations simultaneously

12v+14b=796

14v+12b=738

Multiply equation 1 by 12 and equation 2 by 14 to eliminate b

144v+168b=9552

196v+168b=10332

Subtract

-52v=-780

Divide both sides by -52

v=15

We substitute v=15 to obtain b in any of the equations

12v+14b=796

12(15)+14b=796

14b=796-180

14b=616

Divide both sides by 14

b=44

Therefore a bus contains 44 Students and a Van contains 15 students.

Number of Students who would fill 2 buses and 3 vans

=2b+3v

=2(44)+3(15)

=133 Students

Answer:

300+ 80+6

Step-by-step explanation:

i think i not sure

The solution is

The amount of 5 % Boric acid solution is = 31.5 mL

The amount of 15 % Boric acid solution is = 13.5 mL

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of 5 % Boric acid solution needed for the mix = x

Let the amount of 15 % Boric acid solution needed for the mix = y

Now , the total amount of solution is = 45 mL

So , the equation will be

x + y = 45   be equation (1)

And the mix is 60 milliliters of a 3 % Boric acid solution

So , the equation will be

The Boric acid in x + the Boric acid in y = 8 % of 45

Substituting the values in the equation , we get

0.05x + 0.15y = 0.08 x 45

On simplifying the equation , we get

0.05x + 0.15y = 3.6

Multiply by 100 on both sides of the equation , we get

5x + 15y = 360   be equation (2)

Multiply equation (1) by 5 , we get

5x + 5y = 225   be equation (3)

Subtracting equation (3) from equation (2) , we get

10y = 360 - 225

10y = 135

Divide by 10 on both sides of the equation , we get

y = 13.5 mL

Substitute the value of y in equation (1) , we get

x + y = 45

x + 13.5 = 45

Subtracting 13.5 on both sides of the equation , we get

x = 31.5 mL

Hence , the amount of 5 % Boric acid solution needed is 31.5 mL and the amount of 15 % Boric acid solution needed is 13.5 mL

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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The probability that someone who tests positive for HIV does not actually have HIV is 89.3% rounded to the nearest tenth of a percent.

what is percentage ?
Percentage is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred", so when we say "50 percent", we mean 50 out of 100, or 50/100. Percentages are often used to represent ratios and proportions in everyday life and in many fields of study, including mathematics, science, economics, and finance.

To convert a fraction or decimal to a percentage, we multiply it by 100. For example, 0.75 is equivalent to 75 percent, because 0.75 times 100 equals 75. Conversely, to convert a percentage to a fraction or decimal, we divide it by 100. For example, 50 percent is equivalent to 0.5 or 1/2, because 50 divided by 100 equals 0.5.

According to the question:

Based on the information provided, we can create the following table of possibilities:

Actual HIV Status                     HIV Positive    HIV Negative

Infected (1.1 million)                   1.07M              0.03M

Not Infected (298.9 million)     8.97M            290.93M

From this table, we can see that of the 1.1 million people living with HIV, 97% will test positive for HIV, which is 1.07 million people. The remaining 3% will test negative, which is 0.03 million people.

Of the 298.9 million people not living with HIV, 97% will test negative for HIV, which is 290.93 million people. The remaining 3% will test positive, which is 8.97 million people.

So, out of the total population of 300 million people, 1.07 million will test positive for HIV, but only 1.07/(1.07+8.97) = 10.7% of them actually have HIV. Therefore, if someone tests positive for HIV, the probability they don't actually have HIV is 100% - 10.7% = 89.3%.

Therefore, the probability that someone who tests positive for HIV does not actually have HIV is 89.3% rounded to the nearest tenth of a percent.

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Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

<95141404393>

Answer:

the value of m will be 20

EXPLANATION

Given the function f(x) = x^2 + 12x + 27

The expression in vertex form is as follows:

where a is the leading coefficient --> a=1

We need to compute h and k wich are the coordinates of the vertex (h,k)

The coordinates of the vertex are given by the following expression:

where b=12:

As x_v=-6 the expression of the function in standard form would be:

Removing the parentheses:

The only option that display this vertex form is the second one, hence that is the solution:

Answer:

400 apple pies

Step-by-step explanation:

To solve for the number of apple pies baked by her, let's solve using equations and solving them by substitution method.

\(\textcolor{steelblue}{\text{\textcircled{1} Define the variables}}\)

Let the number of apple pies and chicken pies baked be a and c pies respectively.

\(\textcolor{steelblue}{\text{\textcircled{2} Form equations}}\)

Total pies baked= 560

a +c= 560 -----(1)

Total pies sold= ½(560)

\( \frac{60}{100} \text{a} \: + \frac{25}{100} \text{b} = 280\)

0.6a +0.25b= 280 -----(2)

\(\textcolor{steelblue}{\text{\textcircled{3} Solve by substitution}}\)

Since we are only interested in the value of a, we should eliminate the term c by making c the subject of equation. This ensures that after substitution, the equation will be in terms of a only.

From (1):

c= 560 -a -----(3)

Substitute (3) into (2):

0.6a +0.25(560 -a)= 280

Expand:

0.6a +140 -0.25a= 280

Simplify:

0.35a +140= 280

0.35a= 280 -140

0.35a= 140

Divide both sides by 0.35:

a= 140 ÷0.35

a= 400

\(\textcolor{steelblue}{\text{\textcircled{4} Concluding statement}}\)

Thus, she baked 400 apple pies.

Answer:

r = 5/12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-1/3 = r - 3/4

Step 2: Solve for r

Okay, here we have this:

Considering the provided system we obtain the following:

The option more helpful for solving the system is add one equation to the other because in this way we can cancel the term of the "y", if we solve the system we obtain the following:

Adding the equations:

Now, let's replacing in the first equation with x=3/2:

Finally we obtain that the solution to the system is x=3/2 and y=8.

The remainder from the division of the polynomial (13 + 21y + 10y²) ÷ (2y + 3) is 4

The division of a polynomial is typically denoted using the symbol " / " or the "long division" symbol. For example, to divide the polynomial f(x) by the polynomial g(x), we write:

f(x) / g(x)

The process of polynomial division involves finding the highest power of the divisor (g(x)) that can be multiplied by a term in the dividend (f(x)) to get a term that matches the highest power in the divisor. The resulting term is then subtracted from the dividend, and the process is repeated with the resulting polynomial until there is no remainder left.

The final result of polynomial division is the quotient polynomial, which consists of the coefficients of the terms that were successfully divided, and the remainder polynomial, which consists of any terms that could not be divided. The remainder is always of a lower degree than the divisor.

The division of the given polynomial is ;

(13 + 21y + 10y²) ÷ (2y + 3) = 5y + 3 + (4/2y + 3)

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Taking point (0,-2) of graph one and replacing in the equation;

2x+3y=6

2(0)+3(-2)=6

-6=6

So graph isn't the required graph.

Taking point (0,2) of graph 2;

2x+3y=6

2(0)+3(2)=6

6=6

So, graph 2 is the required graph.

Answer:

nice

Step-by-step explanation:

10) a. 130

Step-by-step explanation:

\(180 - 50 = 130\)

Answer:

12 girls

Step-by-step explanation:

30*(2/5)=12

The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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