why must there be at least 2 lines on any given plane?​

Answer:

The size of the crowd that is 5 feet deep on both sides of the street along a 2-mile section of a parade route is 42,240 people

Step-by-step explanation:

The number of people that can fit comfortably in a 5 feet by 5 feet area = 10

Therefore;

The ratio of the number of people per unit area = 10/(5 × 5) = 10/25

The area, A, occupied by the crowd = 5 feet × 2 mile × 2

2 miles = 10,560 feet

∴ A = 5 feet × 10,560 feet × 2 = 105,600 ft²

We then have;

[tex]\dfrac{Number \ of \ people}{105,600} =\dfrac{10}{25}[/tex]

[tex]Number \ of \ people = {105,600} \times \dfrac{10}{25} = 42,240 \ people[/tex]

Answer:

factor of hundred is

100 - 1, 2,4,5,10,100

Answer:

x = 14

Step-by-step explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

7x - 3 is an exterior angle of the triangle, thus

7x - 3 = 4x - 2 + 41

7x - 3 = 4x + 39 ( subtract 4x from both sides )

3x - 3 = 39 ( add 3 to both sides )

3x = 42 ( divide both sides by 3 )

x = 14

Answer:

m<ABC=27°

m<DBC=56°

Step-by-step explanation:

(x+10)+(4x-12)=83

5x-2=83

5x=83+2

5x=85

x=17

m<ABC=(x+10)=(17+10)=27°

m<DBC=(4x-12)=(4*17-12)=56°

Answer:

[see below]

Step-by-step explanation:

Volume of a triangular prism is: [tex]V=\frac{1}{2}bhl[/tex]

We are given the base of 5, the length of 12, and the height of 8. All measurements are in meters.

[tex]V=\frac{1}{2}(5*12*8)\\\\V=\frac{1}{2}(480)\\\\V=240[/tex]

The volume of the prism should be 240 square meters.

Answer:

V = 240 m^3

Step-by-step explanation:

The volume of a triangular prism is

V = Bh  where B is the area of the base and h is the height

B = the area of the triangular base

B = 1/2 bh

B = 1/2 *5*12

B = 30 m^2

The volume is

V = 30 * 8

V = 240 m^3

Answer:

Step-by-step explanation:

m∠1+∠2=180

2x+40+2y+40=180

2x+2y=180-80

2x+2y=100

x+y=50

x=50-y

m∠1=m∠3

2x+40=x+2y

2x-x=2y-40

x=2y-40

2y-40=50-y

2y+y=50+40

3y=90

y=30

x=50-y=50-30=20

m∠1=2x+40=2×20+40=80°

m∠2=2y+40=2×30+40=60+40=100°

m∠3=x+2y=20+2×30=80°

Answer:

The answer is option C

Step-by-step explanation:

f(x) = x³ + 2x² + 3x + 4

To find f(-1) substitute the value of x that's

- 1 into f(x)

That's

We have the final answer as

Hope this helps you

Answer:

Amount per kilogram, undercharged or overcharged is 0.50

Step-by-step explanation:

Given:

cost of T-bone steaks per pound = $ 15.99

weight listed on package = 5.77 lb

Accuracy of the scale = 1/32 lb

To find:

Amount undercharged or overcharged

Solution:

Let x represent the weight of the package.

Then compute the error in the weight

| x - 5.77 | < 1 / 32

This makes an absolute value inequality

If an inequality is given in the form | x | < a then solution is in the form:

–a < x < a.

If an inequality is in the form | x | > a, then solution splits in the form:

x < –a or x > a.

compute the amount undercharged or overcharged:

First multiply the above inequality by cost of T-bone steaks per pound

15.99 |x - 5.77| < 15.99 (1 / 32)

15.99 |x - 5.77| < 15.99(0.03125)

15.99 |x - 5.77| < 0.4996875

15.99 |x - 5.77| < 0.50

Hence the amount undercharged or overcharged is $0.50

Answer:

See explanation

Step-by-step explanation:

The golden rule for solving equations is to

A. Simplify each side of the equation by removing parentheses and combining like terms

B. Add/Subtract to isolate the term with the variable on one side

C. Use multiplication/division to isolate the variable

Let's assume we have the equation [tex]2x + 3x + (5\cdot2) = 35[/tex]

The first thing we need to do is solve inside the parentheses and combine like terms. 2x and 3x are like terms, so:

[tex]2x + 3x + 10 = 35\\\\5x + 10 = 35[/tex]

Now we have to subtract/add to isolate the term with the variable. To do this, we can subtract 10 from both sides.

[tex]5x + 10 - 10 = 35-10\\\\5x = 25[/tex]

Now we divide to isolate x.

[tex]5x \div 5 = 25\div5\\\\x = 5[/tex]

Hope this helped!

Answer:

length = 15 cm

Width = 12 cm

Step-by-step explanation:

Let width = w cm

Length = w + 3

Perimeter of rectangle = 54 cm

2 * (length + width) = 54

2 * (w+3 + w) = 54   {Add like terms}

2 *(2w + 3) = 54

2*2w + 2 * 3 = 54

4w + 6   = 54

Subtract 6 form both sides

4w = 54 - 6

4w = 48

Divide both sides by 4

w = 48/4

w = 12 cm

Length = 12 + 3= 15 cm

Answer:

Length = 15cm

Step-by-step explanation:

let width be x

length = x+3

Perimeter = 2(l + b)

Perimeter = 54cm

equating:

2(x + x + 3) = 54

2(2x +3) = 54

4x + 6 = 54

4x = 54 - 6

4x = 48

x = 48/4 = 12

width = x = 12cm

length = x +3 = 12 + 3 = 15cm

Answer:

B

Step-by-step explanation:

The problem is simple because they use powers of 10. When something is multiplied by a power of ten, it is essentially moving the decimal point over for every power.

9.46x10^12= 9460000000000

4.0x10^13= 40000000000000

Although 4 itself is less than 9.46, since is is being multiplied by 10^13, it will be one decimal place bigger.

Answer:

we have 6 planes of symmetry

Answer:

[tex]x = -4, y =-8[/tex] is the solution to the system of equations.

Step-by-step explanation:

Given the system of equations as:

[tex]y= \dfrac{1}{2}x-6[/tex]

and

[tex]x =-4[/tex]

To find:

The solution to the system of equations = ?

Solution:

Here, we are given two equations and two variables i.e. [tex]x[/tex] and [tex]y[/tex].

So, we can solve the system of equations for the values of [tex]x[/tex] and [tex]y[/tex].

Let us first consider the 2nd equation.

[tex]x =-4[/tex] we already have the value of [tex]x[/tex].

Now, let us put the value of [tex]x[/tex] in the 1st equation to find the value of [tex]y[/tex].

[tex]y= \dfrac{1}{2}x-6[/tex]

[tex]\Rightarrow y= \dfrac{1}{2}\times (-4)-6\\\Rightarrow y= -\dfrac{1}{2}\times 4-6\\\Rightarrow y= -2-6\\\Rightarrow \bold{y =-8}[/tex]

So,  the solution to the system of equations is:

[tex]x = -4, y =-8[/tex]

Answer:

cow = 4

pig = 5

chicken = 9

horse = 3

horse + chicken - pig =7

Answer:

Step-by-step explanation:

[tex]16\:girls \\14\:boys\\\\Probability = \frac{Event}{Total \:possible\:outcome}\\\\ Event=16\\\\ Total\:possible\:outcome = 16+14=30\\\\P = \frac{16}{30}\\ \\Probability = \frac{8}{15}[/tex]

Answer:

r = 2q - 6

Step-by-step explanation:

10q - 5r = 30

-10q        -10q

-5r = -10q + 30

/-5     /-5     /-5             -10/-5 = 2        30/-5 = -6

r = 2q - 6

Answer:

17 bottles

Step-by-step explanation:

full case: 24

he added 7 bottles to fill a case

24-7=17

Answer: x+ 2x -3 = 12

Step-by-step explanation:

x represents Michael's laps. 2x -3 represents Braden's laps. Added together for a total of 12

One step further would be to combine the x terms, so the equation becomes 3x - 3 = 12

Answer:

if t is 2 then coefficient will be 3

if t is 3 then coefficient will be 2

Step-by-step explanation:

18 + ?t = 24

subtracting 18 from sides

18 + ?t - 18= 24 -18 = 6

=> ?t = 6 = 2*3

as value of both ? and t is not given thus both can take value of 2 and 3

hence,

if t is 2 then coefficient will be 3

if t is 3 then coefficient will be 2

Answer:

the answer is 123

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

If we see, the order is that:

if 1 green block increases, then 1 blue block will increase in the next.

Since, 1 green block increased, so 1 blue block will increase in the next.

So, the answer is C.

Answer:

The correct box plot is B  (Bottom left)

Step-by-step explanation:

I have attached the appropriate picture containing the box plots to this answer. In order to choose the most appropriate box plot, we have to find the median of the distribution and locate the box plot showing the correct median. This is done as follows:

To find the median, we will first arrange the distribution in ascending (or descending) order

Median = 52, 54, 56, 58, 60, 62, 64

Next, we will group the data into two halves, and choose the middle term, which is 58. this becomes the median.

From the diagram, box plots, A, B and C have their median as 58, in order to determine the correct plot, we will find the medians to the lower and upper halves of the distribution. This is done as follows:

Lower half: 52, 54, 56, 58

Median of lower half = (54 + 56) ÷ 2 = 55

upper half = 58, 60, 62, 64

Median of upper half = (60 + 62) ÷ 2 = 61

From the picture the plot with these three medians from lower half to upper half (55, 58, 61) is plot B (bottom left)

Note the medians are the lines that form the boundaries and at the middle of the box.

Answer:

The answer is B bottom left :

Answer:

square root of 25 because it equals 5

Step-by-step explanation:

Because the square root of the other they don’t replete or terminate.

square root of 22 is 4.6904157...

square root of 23 is 4.7958315...

square root of 24 is 4.8989794...

square root of 25 is 5

Answer:

The probability that the middle school student owns a skateboard or a bicycle is 0.61.

Step-by-step explanation:

We are given that the probability of a middle school student owning a skateboard is 0.58, of owning a bicycle is 0.48, and owning both is 0.45.

A middle school student is chosen at random.

Let the probability of student owning a skateboard = P(S) = 0.58

The probability of student owning a bicycle = P(B) = 0.48

The probability of student owning both = P(S [tex]\bigcap[/tex] B) = 0.45

Now, the probability that the middle school student owns a skateboard or a bicycle is given by = P(S [tex]\bigcup[/tex] B)

        P(S [tex]\bigcup[/tex] B) = P(S) + P(B) - P(S [tex]\bigcap[/tex] B)

                      = 0.58 + 0.48 - 0.45

                      = 0.61

Hence, the probability that the middle school student owns a skateboard or a bicycle is 0.61.

Answer:

[tex]\frac{227}{1000}[/tex]

Step-by-step explanation:

A rational number has the form

[tex]\frac{a}{b}[/tex] where a and b are integers

Given

0.227 ← with the 7 in the thousandths place value position, then

= [tex]\frac{227}{1000}[/tex]

Answer:

Method 1 (using the area of a whole circle and dividing by 4)

First work out the area of the whole circle by substituting the radius of 8cm into the formula for the area of the circle:

A = π ×r²

= π ×8²

= 64π (leave the answer as an exact solution as this need to be divided by 4).

So all you need to do now is divide the answer by 4:

Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² to 3 significant figures.

Method 2 (using ¼ πr²)

Substitute r = 8 directly into the formula A = ¼ πr².

A = ¼ πr².

A = ¼ × π × 8².

A = 50.3 cm²

As you can see it gives exactly the same answer as method 1.

Answer:

64pi / 4 = 16pi, or 50.27

Step-by-step explanation:

We use the area formula:

π * r^2 = Area

Substitute in 8 for r to get 64pi

Then all you have to do is divide 64pi by 4 to find a quarter of the area of the circle, which is 16pi. Or if you want rounded to nearest tenth, 50.27

Answer:

257.8

Step-by-step explanation:

The angle of 4.5 radians is approximately equal to 257.8 degrees.

The formula to convert radians to degrees is written as follows:

degrees = radians x (180/π)

where π (pi) is approximately 3.14159.

To convert 4.5 radians to degrees, we can use the conversion factor 180/π, which is the number of degrees in one radian.

degrees = 4.5 x (180/π)

degrees ≈ 257.87 degrees (rounded to the nearest 10th).

Therefore, the angle of 4.5 radians is approximately equal to 257.8 degrees.

Learn about the conversion of  radians to degrees here:

https://brainly.com/question/31673497

#SPJ2

Answer:

1 5/7

Step-by-step explanation:

[tex]\frac{12}{7} \\= 12\div 7 = 1\: remainder\: 5\\\\= 1 \frac{5}{7}[/tex]

Answer: 1 and 5/7

Step-by-step explanation: To write an improper fraction as a mixed number,

divide the denominator into the numerator.

So here, we have 7 divided into 12.

7 divides into 12 one time, 1 × 7 is 7, and 12 - 7 is 5.

So 7 divides into 12 one time with a remainder of 5.

So we have 1 whole and 5 out of 7 parts or 1 and 5/7.

So the improper fraction 12/7 can be written

as the mixed number 1 and 5/7.

Answer:

Set notation: { x ∈ ℝ | -25 < x < 30 }

Interval notation: (-25, 30)

Step-by-step explanation:

In set notation,

"x ∈ ℝ" means "x is an element of all real numbers"

you then write the restrictions after that, which would be "-25 < x < 30"

this gives you { x ∈ ℝ | -25 < x < 30 },

"x is an element of all real numbers, such that x is larger than -25 and less than 30"

In interval notation, it is written as (-25, 30). The parentheses mean that the interval does not include the numbers -25 or 30.

If the interval does include those numbers, i.e. if it was "-25 ≤ x ≤ 30" instead of "-25 < x < 30" you would use brackets instead of parentheses,

giving you {-25, 30}.