Mathematics High School

Write the ratio in lowest terms: 4415 feet to 22245 feet

Answers

Answer 1

since they both end with 5 divide each number by 5

4415 = 883

22245/5 = 4449

there is no number that can go into 883 evenly

 so the lowest term

 would be 883/4449

Answer 2

The correct ratio in lowest terms is [tex]\(\frac{883}{4449}\)[/tex].

To find the ratio in lowest terms, we first write the ratio of the two given lengths:

[tex]\[ \frac{4415 \text{ feet}}{22245 \text{ feet}} \][/tex]

Next, we divide both the numerator and the denominator by their greatest common divisor (GCD) to simplify the ratio. The GCD of 4415 and 22245 can be found by using the Euclidean algorithm or by inspection.

We can start by dividing both numbers by 5:

[tex]\[ \frac{4415 \div 5}{22245 \div 5} = \frac{883}{4449} \][/tex]

Now, we check if 883 and 4449 have any common divisors other than 1. Since 883 is a prime number and does not divide evenly into 4449, we have found the simplest form of the ratio.

Thus, the ratio of 4415 feet to 22245 feet in lowest terms is [tex]\(\frac{883}{4449}\)[/tex].

Related Questions

What is the center and radius of the circle with equation x2 + y2 + 6x + 16y + 64 = 0?

Answers

Hello,
 
By making factors:
[tex]x^2+y^+2+6x+16y+64=0\\ x^2+6x+9+y^2+16y+64-9=0\\ (x+3)^2+(y+8)^2=9\\ radius=3 [/tex]


Please help me with math question

Answers

J is on -8, so it is 8 places to get to zero

 K is on 4

so you have 8 + 4 = 12 units


They are 12 units apart

Find the domain of f of x equals negative square root of the quantity two x plus four, plus 3?

Answers

You always find the domain of these by setting what's under the radical sign equal to 0 and solving for x.  In this case, 2x+4=0.  2x= -4 and x = -2.  If you graph it, you will see that it is true.  The negative sign out front means that the graph is "upside down" from its positive parent graph, and the "+3" means that it is moved up from the origin, but the domain is found by setting the radicand equal to 0 and solving for x.  Domain: [-2, infinity)

Find the 13th term of the sequence 8, -16, 32, -64, ...

A. 32768

B. -16384

C. -65536

D. None of these

Answers

The pattern is to multiply by -2 each time
8
-16
32
-64
128
-256
512
-1024
2048
-4096
8192
-16384
32768
Answer is A

This is a geometric sequence because dividing any term by the previous term results in a constant called the common ratio.  Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.

The common ratio,r, is -16/8=32/-16=-64/32=-2, and the first term, a, is 8

So the rule for this sequence is:

a(n)=8(-2)^(n-1), so the 13th term is:

a(13)=8(-2^12)

a(13)=32768


Person 1 can do a certain job in twenty-one minutes, and person 2 can do the same job in twenty-eight minutes. When completing the job together, which expression would be used to represent the amount of work done by person 1?
21
1/21
x/21
21x

Answers

The amount of work (or the rate) done by the first person is 1/21
r = 1/21

Answer:

[tex]\frac{1}{21}[/tex] would be used to represent the amount of work done by person 1.

Step-by-step explanation:

When someone does a work in x time,

Then, the work done by the person in one day = [tex]\frac{1}{x}[/tex]

Given,

Time taken by person 1 = 21 minutes

Thus, by the above statement,

The one day work of person 1 = [tex]\frac{1}{21}[/tex]

Hence, [tex]\frac{1}{21}[/tex] would be used to represent the amount of work done by person 1.

Second option is correct.

Choose the correct description of the graph of the compound inequality x - 3 less than or equal to 5

A- open circle on 8, shading to left
B- closed circle on 8, shading to left
C- open circle on 8, shading to right
D- closer circle on 8, shading to right

Answers

x - 3 < = 5
x < = 5 + 3
x < = 8

closed circle on 8 (it is closed because there is an equal sign in the problem)...and since it is less then, it will be shaded to the left.

Answer:

B- closed circle on 8, shading to left.

Step-by-step explanation:

We have been given an inequality [tex]x-3\leq 5[/tex]. We are asked to choose the correct description of the graph of the compound inequality.

Let us solve for x.

[tex]x-3+3\leq 5+3[/tex]

[tex]x\leq 8[/tex]

Since we have been given a less than or equal to sign, so we will have a solid dot at [tex]x=8[/tex].

Since the solutions for our given inequality are less than and equal to 8, so we will shade in all values of x that are to the left of 8.

Therefore, option B is the correct choice.

A gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches. how many square inches of wrapping paper are needed to wrap the box?

Answers

The surface area of the rectangular box is equal to 488 square inches.

What is surface area?

The area of the surface of the rectangular box is equal to the total surface area of the rectangular box.

Given that, a gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches.

The surface area will be calculated as,

SA = 2(6 x 14) + 2(6 x 8) + 2(14 x 8)

SA = 2(84) + 2(48) + 2(112)

SA = 168 + 96 + 224

SA = 488 square inches of paper to wrap the box.

Therefore, the surface area of the rectangular box is equal to 488 square inches.

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Final answer:

To find the square inches of wrapping paper needed for a gift box, calculate the surface area of the box by using its length, height, and width dimensions.

Explanation:

To calculate the square inches of wrapping paper needed to wrap the box, you need to find the surface area of the box.

Calculate the surface area of each side of the box: 2(length x width) + 2(width x height) + 2(length x height).

Plug in the given dimensions: 2(14 x 6) + 2(6 x 8) + 2(14 x 8).

Calculate the total: 2(84) + 2(48) + 2(112) = 168 + 96 + 224 = 488 square inches needed.

A club has 12 members. In how many ways can we select four members to go on a trip?

Answers

this is the number of combinations of 4 from 12

12C4   =        12!
                 ----------
                  4! 8!

=    12*11*10*9             11*5*9  =  495
      --------------     = 
        4*3*2*1

Find the next term in the sequence:
1/3,2/9,3/27,...

A. 4/36
B. 4/54
C. 4/81
D. 4/109

Answers

First, you would have to look for a pattern. As you can see, the numerators are increasing by one. In the denominator, the numbers are being multiplied by three.

Now, let's apply this rule to the last fraction. The denominator multiplied by three would be 81.

Therefore, the answer is C. 4/81

Pleaseeeeeeeeeee help what is circle b

Answers

ne S is the blue line, where does it contact circle B?

 it touches at Point K,

 so that would be the tangency.

 Answer Point K

convert 0.0000001 to a power of 10.

107
10−7
106
10−6

Answers

0.0000001 in scientific notation is: 10^-6. Please mark brainliest and have an amazing day.

Answer:

Its actually 10 to the power of -7.

Step-by-step explanation:

This is because it can be written as:

1/10000000

Because there is 7 0's it becomes -7

Therefore its 10 to the power of -7

When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and neither numerator determinant is zero, then the system _______.

A. has infinite solutions
B. is inconsistent
C. is dependent
D. is consistent

Answers

Final answer:

If the determinant of the coefficient matrix is zero and neither numerator determinant is zero when using Cramer's Rule to solve a system of equations, then the system is inconsistent, meaning there's no solution.

Explanation:

When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and neither numerator determinant is zero, then the system is inconsistent.

Cramer's Rule is a method applied in linear algebra to solve a system of linear equations. The rule states that the system is inconsistent if the determinant of the coefficient matrix is zero (meaning the equations do not intersect) but at least one of the numerator determinants are nonzero. This condition indicates that there's no solution to the system of equations.

On the contrary, if the determinant of the coefficient matrix is zero an all the numerator determinants are also zero, the system is said to be dependent, meaning it would have infinitely many solutions.

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need help: write the expression in a complete factored form: x²-9x+xy-9y

Answers

Factor this by grouping.  Group the first two terms together and then the second 2 terms together.  The idea here is that, after grouping, what you can pull out in both groups is the same.  Like this:
[tex]( x^{2} -9x)+(xy-9y)[/tex]
Now work on finding a common thing between the 2 groups:
[tex]x(x-9)+y(x-9)[/tex]
See, what you have in common there now is the (x-9) that you can factor out:
[tex](x-9)(x+y)[/tex]
And that is factored completely.

An and ac are opposite rays.all of the following are true except
A = A,B,C are collinear

B = A,B,C are coplanar

C = AB = AC

D = A is between B and C

Answers

All of the following are true except:

B = A, B, C are coplanar.

(I believe this should be the answer, but I'm not so sure.)

→It is given that, AB and AC are Opposite rays.

Means point ,A , B and C are collinear that is lying in the same line.

→Points are said to be Coplanar , if they lie in the same Plane.

Line segment Joining Points A, B and C lies on the same surface , so we can say that ,these points are Coplanar.

→As, AB and AC are rays , so point A will be in between C and B.

But, it can be sometimes true that,

  →AB=AC

So, Incorrect Statement is:

    AB=AC

#10 with explanation please

Answers

10. 4x = 1

x = 1/4

 since there is no y if you graph x = 1/4 you would get a straight vertical line at x = 1/4

 since it is a vertical line it is symmetric about the x axis ( it looks the same on both sides of the x axis)

The sum of 2 consecutive odd interferes is 92 find the numbers

Answers

92/2 = 46

46-1 =45

46+1 =47

45+47 = 92

 numbers are 45 & 47

If sin 42° =2/3, then cos 48°=

Answers

We know that:  sin Ф = cos(π/2 - Ф) ↔ sin Ф = cos(90° - Ф)
Then:

sin 42° = cos(90° - 42°) = cos 48°

IF sin 42° = 2/3, the cos 48° = 2/3
sinα=cos(90-α)  is a basic identity.

if sin42=2/3 then cos(90-42)=2/3 as well  (90-42=48)

The ordered pairs below represent a relation between x and y. (-3,-3), (-2,0), (-1,3), (0,6), (1,9), (2,12).
Could this set of ordered pairs have been generated by a liner function?
A. No, because the y-values decrease then increase
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it
C. No, because the distance between consecutive y-values is different than the distance between consecutive x-values
D. Yes, because the distance between x-values is inconstant

Answers

Notice that the first coordinates, -3, -2, -1, 0, 1, 2
are matched respectively to       -3,  0, 3, 6, 9, 12.

Thus, as the x-coordinate changes by 1, the y-coordinate changes by 3:

We can represent this change by the following picture:

         
                         |
                         |
            (2,12) _ |
                     |
                     |
         (1,9)  _ | 
                 |
                 |
     (0,6) _ |

                                                    
So, the points are on a straight line, because:

B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it

Where can the lines containing the altitudes of an obtuse triangle intersect.

Answers

The point, at which the lines containing the altitudes of a obtuse triangle intersect called orthocenter, is always outside the triangle.

Answer: The lines containing the altitudes of an obtuse triangle intersect at a point which lies outside the triangle called orthocenter.


Explanation:-

A line which passes through a vertex of the triangle and is perpendicular to the opposite side is called an altitude of the triangle.

The point where all three altitudes of the triangle intersect is called its orthocenter .

Orthocenter of acute triangle lies inside the triangle.Orthocenter of right triangle lies on the triangle.Orthocenter of obtuse triangle lies outside the triangle.

Identify the function as either a constant, direct variation, absolute value or greatest integer function f (x)=-4

Answers

Answer: Constant

No matter what the input x is, the output f(x) is going to be -4. Therefore, the output is constant. 

Note: f(x) can be interchanged with y. So we can say y = -4.

Which shows the graph of the solution set of 3y – 2x > –18? Mark this and return

Answers

When you are asked to graph an inequality, you would expect a graph with a shaded region. This is because the curve or line does not actually have those data points as the solution. It is the data points above or below the curve or line.

First, you disregard the inequality to graph the equation. Find the x- and y-intercepts, plot them, and connect these two dots by extending infinitely from both sides.

x-intercept: let y = 0
0 - 2x = -18
x = 9
y-intercept: let x = 0
3y- 0 = -18
y = -6.

The graph is shown in the picture. Next, you test the inequality by choosing a random data point that does not coincide with any of the data points passed by the line. Suppose, we choose the origin (0,0)

3y- 2x > -18
3(0) - 2(0) > -18
0 > 18

The inequality is true for (0,0), Thus, the shaded region must include this point. All of the region to the left bounded by the line is a solution. Note that the data points are hollow because they are not part of the solution because of the inequality '>'. If it were ≥, then those points would be solid.

What is the angle of rotation of the minute hand of a clock moving from 11:15 to 11:40? Include direction

Answers

25 minutes over 60 minutes (360 degrees is the whole round):

25/60*360= 150 degrees. Direction clockwise. In math clockwise is 'negative' so -150 degrees, and counterclockwise would be positive. But if you can say clockwise, the better


Follow the process of completing the square to solve 2x2 + 8x - 12 = 0. How will the left side of the equation factor in step 5?

A. (2x + 32)2

B. (4x + 8)2

C. (4x + 16)2

Answers

2x^2+8x-12=0
with form
ax^2+bx+c=0

move c to the other side
2x^2+8x=12

x^2 is multiplied -> divide equation by 2
x^2+4x=6

complete square:
divide b=4 by 2
4*1/2=2

square 2
2^2=4

add 4 to both sides
x^2+4x=6
x^2+4x+4=6+4
x^2+4x+4=10

transform to polynom
(x+2)^2=10

this left side is option B multiplied by a factor of 16 and therefore equal:
(4x + 8)^2
(4*4)x^2+(4*2*8)x+8*8
16x^2+64x+64
x^2+4+4

bonus: calculate root
x+2=+/-sqrt(10)
x=-2+/-sqrt(10)


so it is option B

Complete the square to solve [tex]2x^2 + 8x - 12 = 0[/tex].

Soooooooo, [tex](4x + 8)^2[/tex] is your answer. :)

Eight two-person teams are participating in a three-legged race. Find the number of orders in which all 8 teams can finish the race.

Answers

Each team needs two people for a 3-legged race.
Therefore, the number of orders (combinations) of 2 people at a time from 8 is
₈C₂ = 8!/(2!6!)
      = (8*7*6!)/(2*6!)
      = (8*7)/2
      = 56/2
      = 28

Answer: 28

Answer:

thx for points man

Step-by-step explanation:

The graph shows the location of Grant's, Hannah's, and Isobel's houses. Each unit on the graph represents 1 block. A coordinate plane graph is shown. Grants house is located at negative 4 comma 3. Hannahs house is located at 1 comma 3. Isobels house is located at 1 comma negative 4. If Grant walks from his house to Isobel's house, then on to Hannah's house along the path shown, how far will he have walked in blocks? Round your answer to the nearest tenth.

Answers

a^2 + b^2 = c^2
5^2 + 7^2 = c^2
25 + 49 = c^2
74 = c^2
sqrt 74 = c
8.6 = c

so grant's to Isabelle's is 8.6 blocks, then from there to hannah's house, which is 7 blocks....so he walks a total of 8.6 + 7 = 15.6 blocks




The total distance covered in the graph from Grant to Isobel's house and Isobel's house to Hannah's house is 15.06.

What is a graph?

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given coordinate has been drawn in the graph below,

The locus of the path from Grant's house to Isobel's house and then Hannah's house is making a right-angle triangle.

By Pythagoras' theorem,

Distance from Grant's house to Isobel's house ⇒

√(4² + 7²) = 8.06

The distance from Isobel's house to Hannah's house ⇒ 3 + | -4| = 7

Therefore, 8.06 + 7 = 15.06.

Hence "The total distance covered in the graph from Grant to Isobel's house and Isobel's house to Hannah's house is 15.06".

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A standard die is rolled. P(A)= the probability of rolling a three
P(B)= the probability of rolling a even number
What is P(A or B)

Answers

To find the probability of A or B, add the two probabilities (since they are mutually exclusive).

P(A)= 1/6 since 3 is one possibility out of 6
P(B)= 1/2 since there are 3 numbers that mke this true out of 6 and 3/6= 1/2

P(A or B)= 1/6+1/2
P(A or B)= 2/3

Final answer: 2/3

a country's population in 1995 was 175 million. In 2000 it was 181 million. Estimate the population in 2020 using exponential growth formula. Round you answer to the nearest million

Answers

First find the rate of growth
The formula is
P=Ae^rt
P 181 million
A 175 million
E constant
R rate of growth?
T time 2,000−1,995=5 years
Solve the formula for r
R=(log (p/A)÷log (e))÷t
R=(log(181÷175)÷log(e))÷5
R=0.0067

Now find the population in 2020
P=Ae^rt
P?
A 175 million
R 0.0067
T time 2,020−1,995=25 years
P=175×e^(0.0067×25)
P=207 million. .....answer

Janelle is at the movie theater and has $20 to spend.
She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99.
How many snacks, x, can Janelle buy?

Inequality: 20≥8 + 4.99x

Please answer, its urgent

Answers

Final answer:

After purchasing a movie ticket for $8, Janelle has $12 left to spend on snacks. Each snack costs $4.99, which means she can buy a maximum of 2 snacks.

Explanation:

Janelle started with $20 and has already spent $8 on a ticket, leaving her with $20 - $8 = $12 for snacks. Each snack costs $4.99. To determine how many snacks, represented by x, Janelle can buy, we can set up the inequality 12 ≥ 4.99x. Dividing both sides of the inequality by the cost of one snack (4.99) gives us x ≤ ≈ 2.4. Since Janelle cannot buy a fraction of a snack, she can buy a maximum of 2 snacks with her remaining $12.

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Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides.

Answers

The sum of the external angles of a polygon is always 360°

To find the measure of one angle, the formula is 360/n where n is the number of the sides of the polygon.

360/6 = 60°

The sum of all internal angles of a polygon can be find with the formula (n-2)*180° where n is the number of the sides. In this case 180(6-2) = 180*4 = 720°

To find one internal angle, follow this formula [180(n-2)] / n = [720/6] = 120°

Anyway, you can pick a vertex and from that vertex start to draw diagonals.

There will be some triangles, the sum of all internal angles of a triangle is 180°. In a polygon, the sum of all internal angles equals to the sum of all internal angles of all the triangles.

Hope I'm clear.
Final answer:

The interior angle of a regular hexagon is 120 degrees, and the exterior angle is 60 degrees.

Explanation:

To find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides, we will use the fact that the sum of interior angles of a polygon is given by (n-2)×180°, where 'n' is the number of sides of the polygon. Thus, a regular hexagon will have its interior angles sum to (6-2)×180° = 720°. Since all interior angles in a regular polygon are equal, each interior angle will be 720° ÷ 6 = 120°. The exterior angle of a regular polygon is calculated as 360° ÷ n. Therefore, an exterior angle of a regular hexagon will be 360° ÷ 6 = 60°.

So, the interior angle of a regular hexagon is 120°, and the exterior angle is 60°.

simplify the expression r^-3s^5t^2/r^2st^-2

Answers

Pertinent rules:

(a^b)/(a^c)=a^(b-c)  and a^(-b)=1/(a^b)

(r^-3s^5t^2)/(r^2st^-2)

r^(-3-2)s^(5-1)t^(2--2)

r^-5(s^4)t^4

(s^4t^4)/(r^5)
r^-3 * s^5 * t^2 / r^2 * s * t^-2
s^5 * t^2 * t^2 / r^3 * r^2 * s
s^4 * t^2 / r^5
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