A square-shaped park has an area of 324 yd2. What are the dimensions of the park?

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:

bold

Step-by-step explanation:

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A plane is a two dimensional figure.

Answer:

A) [tex]\int\frac{2x^2}{3}dx=\frac{2x^3}{9}+C[/tex]

B) [tex]\int(5-x)^{23}dx=-\frac{(5-x)^{24}}{24}+C[/tex]

Step-by-step explanation:

A)

So we have the integral:

[tex]\int\frac{2x^2}{3}dx[/tex]

First, remove the constant multiple:

[tex]=\frac{2}{3}\int x^2\dx[/tex]

Use the power rule, where:

[tex]\int x^ndx=\frac{x^{n+1}}{x+1}[/tex]

Therefore:

[tex]\frac{2}{3}\int x^2\dx\\=\frac{2}{3}(\frac{x^{2+1}}{2+1})[/tex]

Simplify:

[tex]=\frac{2}{3}(\frac{x^{3}}{3})[/tex]

And multiply:

[tex]=\frac{2x^3}{9}[/tex]

And, finally, plus C:

[tex]=\frac{2x^3}{9}+C[/tex]

B)

We have the integral:

[tex]\int(5-x)^{23}dx[/tex]

To solve, we can use u-substitute.

Let u equal 5-x. Then:

[tex]u=5-x\\du=-1dx[/tex]

So:

[tex]\int(5-x)^{23}dx\\=\int-u^{23}du[/tex]

Move the negative outside:

[tex]=-\int u^{23}du[/tex]

Power rule:

[tex]=-(\frac{u^{23+1}}{23+1})[/tex]

Add:

[tex]=-(\frac{u^{24}}{24})[/tex]

Substitute back 5-x:

[tex]=-(\frac{(5-x)^{24}}{24})[/tex]

Constant of integration:

[tex]=-\frac{(5-x)^{24}}{24}+C[/tex]

And we're done!

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:

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:

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:

$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:

e. Students were randomized into the two groups.

Step-by-step explanation:

Answer:

Length of QR = 7

Step-by-step explanation:

20 - 13 = 7

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:

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

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:

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

Step-by-step explanation:

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: the number of devices expected to fail during the second month is 24

Step-by-step explanation:

Given that

The device has a constant failure rate with MTTF of 2 months.

As the device has constant failure rate so it has exponential failure distribution

f(t) = λe^-λt

Here MTTF = 1/ λ

so  λ = 1/2 Months⁻¹ = 0.5 Months⁻¹ and from the question,  Number of devices = 100

E( 1 < x < 2) = E ( x < 2) - E (x < 1)

so E(x < X) can be calculated with λ  = 0.5 Months⁻¹ will be calculated as the failure function

f(x) = λ exp ( - λ×t) for t > 0

F (x>0) = 1 - exp( - λx)

so E ( 1 < x < 2) = E ( x < 2) - E (x < 1)

E ( x < 2) = 1 - exp(-0.5 × 2) = 0.6321 ; E (x<1) = 1 - exp(-0.5 × 2) = 1 - exp( -0.5) = 0.3934

so E ( 1 < x < 2) = 0.6321 - 0.3934 = 0.2387

so the number of devices expected to fail during the second month is;

100 × 0.2387 = 23.87 ≈ 24

Answer:

-5.8<2.9

Step-by-step explanation:

Answer:42.55

Step-by-step explanation:

Les get the big boi out of the way first. We see that it is 3.5 by 9 and if we multiply we get 31.5. Next left triangle 2 by 2 so four but divided by 2 is 2. God so many  2's. So total is 33.5 so far. Next triangle is 2 by 5 soo  10 divided by 2 is 5. total is 38.5. Last dude in the middle. We know one side is two so we have to subtract here from the triangles which gets u the other side of 2 so 4. Total is 42.5

The Area of the Shape Shown is 42.5 square units.

The area of Rectangle is length times of width.

The area of the rectangle in the given figure is

Area of rectangle=3.5×9

=31.5 square units.

The area of left side triangle is

Area of triangle=1/2×2×2

=2 square units

The area of right side triangle 1/2×5×2

=5 square units

Now the area of square =2²

=4 square units.

Now total area of figure is 31.5+2+5+4 is 42.5 square units.

Hence, the Area of the shape Shown is 42.5 square units.

To learn more on Area of Rectangle click:

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Answer:

[tex]FH=22[/tex]

Step-by-step explanation:

FH is the combined lengths of FG and GH.

In an equation, this is:

[tex]FH=FG+GH[/tex]

We already know that FG is 8 and that GH is 14. Thus:

[tex]FH=8+14[/tex]

Add:

[tex]FH=22[/tex]

So, the length of FH is 22.

And we're done!

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:

2 points

Step-by-step explanation:

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

Answer:

yes

Step-by-step explanation:

Answer:

8

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]

Learn more about Probability here

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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:

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:

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

(f+g)(x) = f(x) + g(x)

= 4x - 4 + 2[tex]x^{2}[/tex] - 3x

= 2[tex]x^{2}[/tex] + x - 4

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:

(√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