A person of interest was identified by the police. Using three different telecommunication towers,
the police were able to gather the following information about the person's cell phone location.
• The person is 7 miles away from A(4,4.6).
• The person is 5 miles away from B(-3.5, - 3.8).
• The person is 6 miles away from C(-6, 5.5).
Use the information from towers A, B, and C to find the approximate location of the person of
interest.

We know that one gallon is equal to four quarts, then we have that:

Therefore we have that 24 miles per gallon is the same as 6 miles per quart.

Answer:

Summation of the non variable Expression within the quality sign

1/2 + 1-2x= -13/2

3/2-2x= -13/2

Step-by-step explanation:

1/2-1/3(6x-3)=-13/2

First step

Using the distributive property to simply

1/2-(6x/3)+(3/3)=-13/2

1/2 -2x +1 = -13/2

Second step

Summation of the non variable Expression within the quality sign

1/2 + 1-2x= -13/2

3/2-2x= -13/2

Third step

Isolating the variable Expression by using the addition property of equality

-2x = -13/2 - 3/2

-2x = -16/2

Fourth step

Isolating the variable by using the division property of equality

-2x = -16/2

X = -16/2 * -1/2

X = -16/-4

X= 4

Answer:

Simplify by combining like terms

Step-by-step explanation:

Answer:

509

Step-by-step explanation:

There are 4 prime factors of 6108

6108 ÷ 2 = 3054

3054 ÷ 2 = 1527

1527 ÷ 3 = 509

509 ÷ 509 = 1

Answer:

The percentage  is  %z \(= 41.9\)%    

Step-by-step explanation:

From the question we are told that

     The mean is  \(\mu = 63.5 \ g\)

     The  standard deviation is  \(\sigma = 12.2 \ g\)

      The  random number is  x  = 66 g

Given the the population is normally distributed

   The  probability is mathematically represented as

        \(P(X > 66 ) = P(\frac{X - \mu }{\sigma} > \frac{x - \mu }{\sigma } )\)  

Generally the z-score for this population is mathematically represented as

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

  So

      \(P(X > 66 ) = P(Z > \frac{66 - 63.5 }{12.2 } )\)  

      \(P(X > 66 ) = P(Z > 0.2049 )\)  

Now the z-value for 0.2049 from the standardized normal distribution table is  

     \(z = 0.41883\)

=>    \(P(X > 66 ) = 0.41883\)  

The  percentage  is

     % z     \(= 0.41883 * 100\)  

     %z   \(= 41.9\)%    

Answer:

123 Square Feet. Of Paint. Probably gonna take a little more than a sample-size quart, let me know how it turns out.

Step-by-step explanation:

You would need 11*15=165 square feet of paint. BUT

You need 42 less square feet, because there are 2, 7*3=21 square-foot windows.

165-42

Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

Answer:

Rectangular Prism

as Opposite sides are equal

Answer:

Mild or structural steel is a category of steel used in the manufacture of various forms of building materials.

Mild or structural steel is a category of steel used in the manufacture of various forms of building materials. Many forms of structural steel are in the form of elongated beams with profiles with specific cross sections. The shape, size, chemical composition, mechanical properties such as strength, storage methods, etc. of structural steel are regulated by standards in most developed countries.

Advantages:

Disadvantages:

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Answer:

The height of the flag was 3 feet.

Step-by-step explanation:

To solve this problem, we must first recall the formula for area of a rectangle to be:

Area = base * height

Next, we can substitute in the values that we were given in the problem.  We were told that the area was 27 square feet and the base was 9 feet.

27 = 9 * height

Now we can treat this equation that we have created similar to any other equation we would like to solve.  We must solve for the unknown, or the variable, which in this case is the height.  To do this, we should divide both sides by 9 to get the "height" variable by itself on the right side of the equation.  This is modeled below:

27/9 = (9 * height)/9

3 = height

Therefore, the height of the flag was 3 feet.

Hope this helps!

Answer:

The height is 3,

Step-by-step explanation:

First up, if we know the B in the B*H=A formula, we can divide the area by the base (27/9) and get the height, 3.

I too am learning this. The thing is you want to do a reverse order. For example, 2*3=6; so automatically we would know that 6/3=2.

Hope this has helped!

:)

Answer:

B. 30°

Step-by-step explanation:

By remote interior angle theorem:

100° = x + 70°

100° - 70° = x

30° = x

x = 30°

Answer:

The answer is 30

Step-by-step explanation:

A triangle equals 180, so to find out the value X, first you need the other corner. You know that one side of that line is 100, and it is a straight angle. So the other side is 80. 80 + 70 = 150. To get 180, you need to add 30 to that 150, therefore the answer is 30.

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Answer:

3

Step-by-step explanation:

Answer:

um I'm kinda confused right now

Answer: $16.60

Step-by-step explanation:

Price + Tax = 12.35+0.93

Total + tip = 13.28+3.32

total: 16.60

The total money did Carl pay for breakfast including the price of his meal, sales tax, and tip  $16.60

We have given that,

Carl went out for breakfast.

• The price of his meal was $12.35.

• The sales tax was 7.5% of the price of the meal.

• The tip was 25% of the price of the meal and the sales tax.

We have to determine the nearest cent, how much total money did Carl pay for breakfast including the price of his meal, sales tax, and tip.

Total money=price + tax

Price + Tax = 12.35+0.93

Total + tip = 13.28+3.32

Total money =16.60

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the food needed for 10 cats will be 80 pounds.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem. Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers

An animal shelter needs to buy 8 pounds of cat food for every cat

they have.

So per pound, it food needed for 10 cats will be 8*10 = 80 pounds.

Hence the food needed for 10 cats will be 80 pounds.

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Answer:

3/2

Step-by-step explanation:

Answer:

1 1/2 as a mixed number and 3/2 as a fraction

Step-by-step explanation:

The volume of the prism is 1323 feet³ (cubic feet).

Length= 21 feet.

Width= 9 feet.

Height= 7 feet.

The formula to calculate the volume of rectangular prisms is the following:

\(\sf V_{RP} =l*w*h\); where "l" is the length; "w" is the width, and "h" is the height of the prism.

Check the attached image to see where these values are measured from.

Substitute the variables in the formula by the values on step 1.

\(\sf V_{RP} =l*w*h=(21\ feet)*(9\ feet)*(7\ feet)=\boxed{\sf1323\ feet}.\)

The volume of the prism is 1323 feet³ (cubic feet).

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Answer:

The volume of the rectangular prism is 1323 cubic feet.

Step-by-step explanation:

Step 1: Write down the formula for the volume of a rectangular prism:

\(\qquad\Large\boxed{\rm{\:\:\:V = l \times w \times h\:\:\:}}\)

Step 2: Substitute the given values for the length, width, and height:

\(\qquad\Large\rm{V = 21\: ft \times 9\: ft \times 7\: ft}\)

Step 3: Multiply the numbers together:

\(\qquad\Large\rm\implies{V = 1323\: ft^3}\)

Step 4: Write the final answer with the appropriate units:

The volume of the rectangular prism is 1323 cubic feet.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer:

Can you give me an equation please and ill change this to the correct answer

Step-by-step explanation:

Answer:

x = 21, y = 15

Step-by-step explanation:

\((6x + 7) \degree + (3x - 16) \degree = 180 \degree \\ (exterior \: \angle s \: ) \\ \\ (9x - 9) \degree = 180 \degree \\ \\ 9x - 9 = 180 \\ \\ 9x = 180 + 9 \\ \\ 9x = 189 \\ \\ x = \frac{189}{9} \\ \\ x = 21 \\ \\ (11y - 32) \degree = (6x + 7) \degree \\ (vertical \: \angle s) \\ \\ (11y - 32) \degree = (6\times 21- 16) \degree \\ \\ (11y - 32) \degree = (126 + 7) \degree \\\\ (11y - 32) \degree = 133 \degree \\ \\ 11y - 32 = 133 \\ \\ 11y = 133 + 32 \\ \\ 11y = 165 \\ \\ y = \frac{165}{11} \\ \\ y = 15\)

1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.

2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.

When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.

Similar figures have the same shape, but they may have different sizes and be located in different positions.

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The area of the figure in this problem is given as follows:

A. 30 in².

The area of a triangle is given by half the multiplication of the base length by the height of the triangle.

Applying the Pythagorean Theorem, we can obtain the missing side length, as follows:

4² + x² = 6²

x² = 36 - 16

x² = 20

x = square root of 20

x = 4.47.

For a right triangle, one side is considered the height of the other, hence the sides are:

Hence the area of the triangle is then obtained as follows:

Area = 0.5 x 4 x 12.47

Area = 25 in².

Which is closest to 30 in².

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Answer:

j

Step-by-step explanation:

The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.

To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.

Let;

The rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.

To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.

h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|

Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.

D = depth of bowl

Using this relationship from the question given;

D = (1/3) * h

In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.

dD/dt = (1/3) * dh/dt

Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:

dD/dt = (1/3) * (7π)

Simplifying, we have:

dD/dt = (7/3)π cm³/s

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Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.

Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.

Therefore, we can write the volume of the box as

:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.

Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:

527 = constant × dh/dt

We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:

V = l × w × hV = 17 × 10 × hV = 170h

We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:

527 = constant × 6 cm

constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get

-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min

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1. selection of index number: during the construction of index number it is to be kept in mind that the selection of the index number should be correct accordingly.

2. selection of formula: while the construction of index numbers it is compulsory to select the correct formula for the given question.

3. selection of price: selection of prices should be done accordingly while constructing the index numbers.`

construction of index number is also available in two parts:

1. simple

2. weighted

1. simple: the simple method is classified into simple aggregative and simple relative.

2. weighted: the weighted method is classified into a weighted aggregative and weighted average.

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The sequence as shown is a geometric sequence.

We know that the geometric sequence is the kind of sequence in which there is the common ratio. We can tell that for the geometric sequence we have;

U(n) = Tr^n-1

Where T is the first term and then r is the common ration while n is the number of terms.

Given the fact that we have the terms in the sequence as 81, 27, 9, 3, 1. We can see that the common ratio of the sequence is given as;

r =  T2/T1 = 27/81

1/3

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Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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