The length of Tom’s rectangular classroom floor is 8 feet longer than 2 times the
width. The perimeter of his classroom floor is 124 feet. Write and solve an
equation to find the length of his classroom.

Answer:         n = 3                                              n = 4                

               Upper Sum ≈ 3.41                      Upper Sum ≈ 3.25

               Lower Sum ≈ 2.15                      Lower Sum ≈ 2.25

Step-by-step explanation:

You are trying to find the area under the curve.  Area = height x width.

Height is the y-value at the given coordinate --> f(x)

Width is the distance between the x-values --> dx

n = 3

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 3 sections because n = 3 --> dx = 2/3

So the points we will evaluate is when x = {-1, -1/3, 1/3, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/3) = 1 + (-1/3)² = 1 + 1/9 --> 10/9

f(1/3) =  1 + (1/3)² = 1 + 1/9 --> 10/9

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/3}          f(-1) = 2                   f(-1/3) = 10/9

{-1/3, 1/3}        f(-1/3) = 10/9           f(0) = 1   (vertex lies in this interval)

{1/3, 1}             f(1) = 2                   f(1/3) = 10/9

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\quad A=\dfrac{2}{3}\bigg(2+\dfrac{10}{9}+2\bigg)\\\\.\qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{46}{9}\bigg)\\\\.\qquad \qquad \qquad =\dfrac{92}{27}\\\\.\qquad \qquad \qquad =\large\boxed{3.41}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{2}{3}\bigg(\dfrac{10}{9}+1+\dfrac{10}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{29}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{58}{27}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.15}[/tex]

*****************************************************************************************

n = 4

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 4 sections because n = 4 --> dx = 2/4 = 1/2 (simplified)

So the points we will evaluate is when x = {-1, -1/2, 0, 1/2, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/2) = 1 + (-1/2)² = 1 + 1/4 --> 5/4

f(0) = 1 + (0)² = 1

f(1/2) =  1 + (1/2)² = 1 + 1/4 --> 5/4

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/2}          f(-1) = 2                   f(-1/2) = 5/4

{-1/2, 0}          f(-1/2) = 5/4            f(0) = 1  

{0, 1/2}           f(1/2) = 5/4             f(0) = 1

{1/2, 1}            f(1) = 2                   f(1/3) = 5/4

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\qquad A=\dfrac{1}{2}\bigg(2+\dfrac{5}{4}+\dfrac{5}{4}+2\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{26}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{13}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{3.25}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{1}{2}\bigg(\dfrac{5}{4}+1+1+\dfrac{5}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{18}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{9}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.25}[/tex]

Answer:

3 to 12

Step-by-step explanation:

3 months (January, June, July) and 12 monthes

Answer: the answer is 3 to 12

Step-by-step explanation: hope this will help

Answer:

$1.5 unit

Step-by-step explanation:

According to the given situation, the calculation of the unit rate is shown below:-

Candy bars = 6

Amount of candy bars = $9:00

Unit rate

[tex]= \frac{Amount\ of\ candy\ bars}{Number\ of\ candy\ bars}[/tex]

Now we will put the values into the above formula

[tex]= \frac{\$9:00}{6}[/tex]

Which gives result

= $1.5 unit

Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.

Answer:

Length of QR = 7

Step-by-step explanation:

20 - 13 = 7

Answer:

0 - 1 - 2 + 3 - 4 + 5 - 6 +7 - 8 + 9 = 3

Step-by-step explanation:

Since there is 28 cards, the chance of drawing 1 card will be [tex]\frac{1}{28}[/tex]

Therefore, [tex]P(13)=\frac{1}{28}[/tex].

There are 13 numbers less than 14 and greater than 0.

Therefore [tex]P(>14)=\frac{13}{28}[/tex]

There are 26 numbers that are not 2 or 17.

Therefore [tex]P(\neq 2,17)=\frac{26}{28}=\frac{13}{14}[/tex]

Hope this helps.

頑張って!

Probability of

Option (1). P(13) =[tex]\frac{1}{28}[/tex]

Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]

Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur

Given,

Total number of card = 28

Probability = Number of favorable outcome / Number of total outcome

Probability of picking 13 = [tex]\frac{1}{28}[/tex]

Probability of picking a card less then 14 = [tex]\frac{13}{28}[/tex]

Probability of not picking 2 or 17 = [tex]\frac{26}{28}=\frac{13}{14}[/tex]

Hence, the probability of

Option (1). P(13) =[tex]\frac{1}{28}[/tex]

Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]

Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]

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Answer:

The yellow polygon is the scaled version of the red one (scaled by 3×), so the variable w = 9

Answer:

9

Step-by-step explanation:

The similarity ratio is 4/x = z/9 = 2/6 = 3/w = y/15

2/6 = 3/w cross multiply expressions 2w = 18 and w = 9

Answer:

Step-by-step explanation:

Since x is used a lot as a variable in algebra, I would use another symbol for multiplication. Though if your teacher requires you to use x as a multiplication symbol, then keep it as is. I use the asterisk symbol

Example: 2 times 3 = 2*3

------------------------------------------

For problem 2, you have the parenthesis in the wrong spots. Saying "the sum of four plus five" means we have 4+5 as you'd expect. Then you multiply that group with 2. So you'd really have (4+5)*2

How is this different from 4+5*2 back in problem 1? It comes down to how the order of operations handles things. To evaluate 4+5*2, we multiply first, then add. So we have 4+5*2 = 4+10 = 14

With the other expression, we add first because it is in the parenthesis block. Afterward we multiply the values to get (4+5)*2 = 9*2 = 18

Answer:

The answer is  -8.4

Answer:

x = 3

Step-by-step explanation:

mid point means it bisects the segment into two equals halfs meaning

ST = TU

8x + 11 = 12x - 1

8x + 12 = 12x

12 = 4x

3 = x

Answer:

2 points

Step-by-step explanation:

0+3-4-2+5=2 points

Answer:

16

Step-by-step explanation:

Let x be the number of chocolates obtained by each student

Since the number of chocolates obtained by each student = the number of students in the class, then, number of students in the class = x

256/x = x

Multiply both sides by x

256 = x × x ( x squared)

Multipy powers raised on both sides by 1/2

X = 16

Answer:

[tex]|x - 85| = 12[/tex]

[tex]x = 73 \ (smaller\ number )[/tex]

[tex]x = 97 \ (larger \ number )[/tex]

Step-by-step explanation:

From the question we are told that

  The  grade is  [tex]k = 85\%[/tex]

   The  variation is  [tex]v = 12 \%[/tex]

Generally the absolute value equation is mathematically represented as

        [tex]|x - 85| = 12[/tex]

=>  [tex]x -85 = \pm 12[/tex]

So

    [tex]x = 85 + 12[/tex]

    [tex]x = 97 \ (larger \ number )[/tex]

And

     [tex]x = -12 + 85[/tex]

=>  [tex]x = 73 \ (smaller\ number )[/tex]

Answer:

The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°

Answer:

147 toys

Step-by-step explanation:

for 1 person, 28toys/8hours = 3.5toys/ 1hour

for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour

~Hope it Helps!~

Answer:

.8L

Explanation:

Logic

The liters of water left are 0.8 liters.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The quantity of water in a water bottle is 1 liter.

The amount of water Tom drank is 200 milliliters.

Let x be the amount of water left in the bottle.

The liter has to be converted into milliliters.

1 liters = 1000 milliliters

The equation formed is,

1000 - 200 = x

x = 1000 - 200

x = 800 milliliters.

The water left in the water bottle is 800 milliliters.

1000 milliliters = 1 liters

800 milliliters = 0.8 liters

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Answer:

bold

Step-by-step explanation:

hshsjjsududidididiidododododokdodkdjdndndnjdudududuididjdjdjd

A plane is a two dimensional figure.

Answer:

-3/2

Step-by-step explanation:

Take two points from the table and use the slope formula

m= (y2-y1)/(x2-x1)

   = ( 19 - 13)/ ( -4 - 0)

   = 6/-4

   = -3/2

Answer:

e. Students were randomized into the two groups.

Step-by-step explanation:

Answer:

Absolute value equation is; |x - 25| ≤ 3

Minimum number of bolts is 22 while Maximum number of bolts is 28

Step-by-step explanation:

We are told that;

Each bag should have 25 bolts in it but 22 or 28 is acceptable.

Since 22 or 28 is acceptable, it means the allowable error is ±3.

Thus, if x is the number of bolts in the bag, the absolute value equation would be;

|x - 25| ≤ 3

Minimum number of bolts is 22 while maximum is 28

3 tests at 75% each = 3 x 75 = 225 total points

First two tests = 79 + 84 = 163

Third test needs to be at least: 225 - 163  = 62%

So any score less than 62 would get you into trouble.

Answer:

(√2 + √6)/4.

Step-by-step explanation:

Use the addition formula

sin (A+ B) = sinAcosB + cosAsinB

sin (7pi/12) =  sin( 3pi/12 + 4pi/12)

= sin(pi/4 + pi/3) =  sin pi/4 cos pi/3 + cos pi/4 sin pi/3

= 1/√2 * 1/2 + 1/√2 * √3/2     (using the 45-45-90 and 30-60-90 triangles)

= 1 / 2√2 + √3/2√2

=   √2/4 + √6/4

= (√2 + √6)/4

Answer:

-5.8<2.9

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:  [tex]l=\dfrac{P}{2}-b[/tex]

Step-by-step explanation:

P = 2(l + b)

Divide both sides by 2:

[tex]\dfrac{P}{2}=l+b[/tex]

Subtract b from both sides:

[tex]\dfrac{P}{2}-b=l[/tex]

Note: You can also multiply b by  [tex]\frac{2}{2}[/tex] if you want the left side to be one fraction.

[tex]\dfrac{P}{2}-\bigg(\dfrac{2}{2}\bigg)b=l\\\\\\\dfrac{P-2b}{2}=l[/tex]

Answer:

y = 2  when x = 150

Step-by-step explanation:

Inverse variation is

xy = k

5*60 = k

300 = k

xy = 300

150y = 300

Divide by 150

150y/150 = 300/150

y = 2

Answer:

-7

Step-by-step explanation:

g(x)= 5-2x and h(x) = - x^2

g(-2) + h(4)

First find g(-2)

g(-2) = 5 -2(-2) = 5 +4 = 9

Then find h(4) = - 4^2 = -16

g(-2) + h(4) = 9-16 = -7

Answer:

-7

Step-by-step explanation:

Substitute -2 into g(x) equation,

g(x) = 5 - 2x

g(-2) = [5 - 2(-2)] = 9

Substitute 4 into h(x) equation,

h(x) = -x^2

h(4) = [-(4)^2] = -16

Therefore,

g(-2) + h(4) = 9 + (-16) = -7

Answer:

17/20

Step-by-step explanation:

Total no. of beads = 6 + 3 + 11 = 20

We need RED or GREEN bead .

So no. of beads needed = 6 + 11 = 17

So probability of getting GREEN or RED beads = 17/20

Answer:

Emma's recipe will be more lemony because

5/2=2.5

2/1=2

Step-by-step explanation:

Answer:

The ratio of lemon juice to water in Emma’s recipe is 5 to 2; the ratio in Clair’s recipe is 4 to 2. Emma’s recipe will taste more lemony because it has a greater ratio of lemon juice to water.

Step-by-step explanation:

Sample Answer