Hassan built a fence around a square yard. It took 48\text{ m}^248 m 2 48, start text, space, m, end text, squared of lumber to build the fence. The fence is 1.51.51, point, 5 meters tall. What is the area of the yard inside the fence? \text{m}^2m 2

Answer:

The third option: x= [tex]\frac{8}{3} \pi[/tex]

Step-by-step explanation:

Arc length formula=[tex]\frac{Central Angle}{360} * 2\pi r[/tex]

Arc length = [tex]\frac{120}{360} *2\pi (4)[/tex]

=[tex]\frac{8}{3}\pi[/tex]

Answer:

A) The number halfway between -2 and 6 is 2.

B) -10 is halfway between -18 and 8

Answer:

44

Step-by-step explanation:

base = 3- -5 = 8

height = 8 - -3 = 11

1/2 bh

1/2(8)(11) = 44

false

Step-by-step explanation:

false

( a ) Well we know that the limit for the range is 400 dollars, as ( 1 ) her greatest balance was 400 dollars, and ( 2 ) the balance is dependent on the days, and hence represents the range. Respectively the limit for the domain would be 3 weeks.

( b ) Remember that B(0) models the balance over the course of 0 days. As you can see that starting mark is about half of the greatest balance on the graph, 400 dollars. Therefore you can estimate B(0) to be $200.

( c ) B(12) models the balance over the course of 12 days. It mentions that at B(12) the balance reaches $0, so in function notation that would be :

B(12) = 0

( d ) Segment 4 would represent that information. As you can see on the graph, the only time period with which the balance became 0 is represented by the fourth segment.

Answer:

83 adult tickets and 217 student tickets.

Step-by-step explanation:

Let number of adult tickets sold = [tex]x[/tex]

Given that total number of tickets = 300

So, number of student tickets = 300 - [tex]x[/tex]

Cost of adult ticket = $15

Cost of student ticket = $11

Total collection from adult tickets = $[tex]15x[/tex]

Total collection from student tickets =  [tex](300-x)\times 11 = 3300-11x[/tex]

Given that overall collection = $3630

[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]

So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.

Now , collection = $3632

Answer:

Average speed during the trip = 24 km/h

Step-by-step explanation:

Given:

Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr

Speed of cyclist on flat ground = 24 km/h

Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h

Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.

That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h

To find:

Average speed during the entire trip = ?

Solution:

Let the distance between Beast Island and Aopslandia = D km

Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]

[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]

Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]

Formula for speed is given as:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]

[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]

Formula for average speed is given as:

[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]

Here total distance = D + D = 2D km

Total Time is [tex]T_1+T_2[/tex] hours.

Putting the values in the formula and using equations (1) and (2):

[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]

So, Average speed during the trip = 24 km/h

Answer:  AE = 5

Step-by-step explanation:

I sketched the triangle based on the information provided.

since ∠A = 90° and is divided into three equal angles, then ∠BAD, ∠DAE, and ∠CAE = 30°

Since AB = 5 and BC = 10, then ΔCAB is a 30°-60°-90° triangle which implies that ∠B = 60° and ∠C = 30°

Using the Triangle Sum Theorem, we can conclude that ∠ADB = 90°, ∠ADE = 90°, ∠ AED = 60°, AND ∠ AEC = 120°

We can see that ΔAEC is an isosceles triangle. Draw a perpendicular to divide it into two congruent right triangles. Label the intersection as Z. ΔAEZ and ΔCEZ are 30°-60°-90° triangles.

Using the 30°-60°-90° rules for ΔABC we can calculate that AC = 5√3.

Since we divided ΔAEC into two congruent triangles, then AZ = [tex]\dfrac{5\sqrt 3}{2}[/tex]

Now use the 30°-60°-90° rules to calculate AE = 5

Answer:

Initially 18,500 students

Every 1 year

increase by a factor 1.03

Step-by-step explanation:

The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.

F(t) = 18,500 * (1.03)^t

Answer:

Step-by-step explanation:

5x = 21 and 21 = 5x are identical relationships, and so the solution would be the same in both cases.  (Commutative Property:  order of addition/subtraction is immaterial)

Answer: 6√2

Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36, then recognize 36 as a perfect square, 6 · 6.

There's no need to factor further because the 6's pair up

so a 6 comes out of the radical leaving a 2 inside.

So our answer is 6√2.

Always be on the lookout for perfect squares!

Work is attached below.

Answer: |p-72% |≤ 4%

Step-by-step explanation:

Let p be the population proportion.

The absolute inequality about p using an absolute value inequality.:

[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion

Given:  A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .

|p-72% |≤ 4%

⇒    72% - 4% ≤ p ≤ 72% +4%

⇒  68%  ≤ p ≤  76%.

i.e. p is most likely to be between 68% and 76% (.

The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

An expression using absolute functions and inequality signs is known as an absolute value inequality.

We know that the absolute value inequality about p using an absolute value inequality is written as,

[tex]|p-\hat p| \leq E[/tex]

where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.

Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,

[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]

Thus, the p is most likely to be between the range of 68% to 76%.

Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,

[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]

Thus, the p is most likely to be between the range of 29.8% to 34.2%.

Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

Learn more about Absolute Value Inequality:

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180 degree

Step-by-step explanation:

supplementary means anhke havinv sum of 180 degree

so sum to two supplemrntary angles is 180 drgree

Supplementary angles always add to 180.

One way I think of it is "supplementary angles form a straight angle", and both the words "supplementary" and "straight" start with the letter "S".

In contrast, complementary angles form a corner. Both "complementary" and "corner" start with "co". By "corner", I mean a 90 degree corner.

Answer:

Manuel made his first mistake in step 2 leading to the continuous mistakes

Final answer=185

Step-by-step explanation:

Manuel made at least one error as she found the value of this expression. 2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50) Step 1: 2(-20) + 3(-25) + 5(20) + 4(50) Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50) Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405 Identify the step in which Chris made her first error. After identifying the step with the first error, write the corrected steps and find the final answer.

2(-20) + 3[5/4(-20)] + 5[2/5(50)] + 4(50)

Step 1: 2(-20) + 3(-25) + 5(20) + 4(50)

Step 2: -40 - 75 + 100 +

200

Step 3: -115 + 300

Step 4: 185

Manuel made his first error in step 2 by combining two different terms into one as he has done

(3 + 2)(-20 + -25) and also (5 + 4)(20 + 50)

Step 2: (3 + 2)(-20 + -25) + (5 + 4)(20 + 50)

Step 3: 5(-45) + 9(70) Step 4: -225 + 630 Step 5: 405

He should have evaluated the terms separately as I have done above, giving us 185 as the final answer in contrast to his 405 final answer.

Answer:

6n = 1.50

and

13n = 3.12

Step-by-step explanation:

Here in this question, we are interested in writing equations that relate the number of ears of corn sold and the cost.

For Al’s produce stand, let the price per corn sold be n

Thus;

6 * n = 1.50

6n = $1.50 •••••••(i)

For the second;

let the price per corn sold be n;

13 * n = $3.12

-> 13n = 3.12 •••••••••(ii)

Answer:

x = 50

Step-by-step explanation:

Let x be the original price.

He got 30% off

The discount is .30x

Subtract this from the original price to get the price he paid

x - .30x = price he paid

.70x = price he paid

.70x = 35

Divide each side  by .7

.70x/.7 = 35/.7

x=50

Answer:

[tex] \boxed{\sf Time \ taken = 15 \ minutes} [/tex]

Given:

Initial speed (u) = 65 km/h

Final speed (v) = 85 km/h

Acceleration (a) = 80 km/h²

To Find:

Time taken for car to achieve a speed of 85 km/h in minutes

Step-by-step explanation:

[tex]\sf From \ equation \ of \ motion:[/tex]

[tex] \boxed{ \bold{v = u + at}}[/tex]

By substituting value of v, u & a we get:

[tex] \sf \implies 85 = 65 + 80t[/tex]

Substract 65 from both sides:

[tex] \sf \implies 85 - 65 = 65 - 65 + 80t[/tex]

[tex] \sf \implies 20 = 80t[/tex]

[tex] \sf \implies 80t = 20[/tex]

Dividing both sides by 80:

[tex] \sf \implies \frac{ \cancel{80}t}{ \cancel{80}} = \frac{20}{80} [/tex]

[tex] \sf \implies t = \frac{2 \cancel{0}}{8 \cancel{0}} [/tex]

[tex] \sf \implies t = \frac{ \cancel{2}}{ \cancel{2} \times 4} [/tex]

[tex] \sf \implies t = \frac{1}{4} \: h[/tex]

[tex] \sf \implies t = \frac{1}{4} \times 60 \: minutes[/tex]

[tex] \sf \implies t = 15 \: minutes[/tex]

So,

Time taken for car to achieve a speed of 85 km/h in minutes = 15 minutes

240

using pascals trianle

for the power 6 it is

1, 6,15,20, 15,6, 1

and for the third term (2x)^4 and (-1)^2

[tex]15 \times {(2x)}^{4} \times {( - 1)}^{2} [/tex]

[tex]240 {x}^{4} [/tex]

Since only the coefficient is needed

the answer is 240.

The required coefficient of third term is 480.

Coefficient of the third term of (2x−1)^6 to be determine.

Coefficient is defined as the integer present adjacent to the variable.

Here,  (2x−1)^6
Using binomial expansion,
Third term = P(6,2)(2x)^6-2(-1)^2
                  =   6*5*16x^4
                  = 480x^4

Thus, the required coefficient of third term is 480.

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Answer:

1) f(x) = 4·x² - 3·x + 6

2) f(x) = -2·x² + 5·x - 1

3) y = 2·(x - 3)² + 5

Step-by-step explanation:

1) The quadratic function that is represented by the points (0, 6), (2, 16), (3, 33) is found as follows

The general form of a quadratic function is f(x) = a·x² + b·x + c

Where, in (x, y), f(x) = y, and x = x

Therefore for the point (0, 6), we have;

6 = 0·x² + 0·x + c

c = 6

We have c = 6

For the point (2, 16), we have;

16 = a·2² + b·2 + 6

10 = 4·a + 2·b.............................(1)

For the point (3, 33), we have;

33 = a·3² + b·3 + 6

27 = 9·a + 3·b............................(2)

Multiply equation (1) by 1.5 and subtract it from equation (2), we have;

1.5 × (10 = 4·a + 2·b)

15 = 6·a + 3·b

27 = 9·a + 3·b - (15 = 6·a + 3·b) gives;

27 - 15 = 9·a - 6·a+ 3·b - 3·b

12 = 3·a

a = 12/3 = 4

a = 4

From equation (1), we have;

10 = 4·a + 2·b = 4×4 + 2·b

10 - 4×4 = 2·b

10 - 16 = 2·b

-6 = 2·b

b = -3

The function, f(x) = 4·x² - 3·x + 6

2) Where the points are (-1, -8), (0, -1), (1, 2), we have;

For point (-1, -8), we have -8 = a·(-1)² - b·(-1) + c = a - b + c......(1)

For point (0, 1), we have -1 = a×0² + b×0 + c = c.........................(2)

For point (1, 2), we have 2 = a×1²+ b×1 + c = a + b + c..............(3)

Adding equation (1) to equation (3) gives

-8 + 2 = a - b + c +  a + b + c = 2·a + 2·c  where, c = -1, we have

-8 + 2 = -6 = 2·a + 2

2·a = -6 + 2 = - 4

a = -8/2 = -2

From equation (3), we have;

2 = a + b + c

b = 2 - a - c = 2 - (-2) - (-1) = 2 + 2 + 1 = 5

f(x) = -2·x² + 5·x - 1

3) The equation of a parabola that has vertex (3, 5) and passing through the point (1, 13) is given by the vertex equation of a parabola

The vertex equation of a parabola is y = a(x - h)² + k

Where;

(h, k) = Vertex (3, 5)

(x, y) = (1, 13)

We have

13 = a·(1 - 3)² + 5

13 = a·(-2)² + 5

13 - 5 = a·(-2)² = 4·a

4·a = 8

a = 8/4 = 2

The equation is y = 2·(x - 3)² + 5.

Answer:

2x^2 +5x-12

Step-by-step explanation:

(2x - 3)(x + 4)

FOIL

first 2x*x = 2x^2

outer  2x*4 = 8x

inner  -3x

last -3*4 = -12

Add these together

2x^2 +8x-3x-12

Combine like terms

2x^2 +5x-12

Answer: 96

Step-by-step explanation:

Ok, lines a and b are parallel.

We can separate this problem in two cases:

Case 1: 2 vertex in line a, and one vertex in line b.

Here we use the relation:

"In a group of N elements, the total combinations of sets of K elements is given by"

[tex]C = \frac{N!}{(N - K)!*K!}[/tex]

Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.

Then if we have two vertices in line a, we have:

N = 6, K = 2

[tex]C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]

And the other vertex can be on any of the four points on the line b, so the total number of triangles is:

C = 15*4 = 60.

But we still have the case 2, where we have 2 vertices on line b, and one on line a.

First, the combination for the two vertices in line b is:

We use N = 4 and K = 2.

[tex]C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6[/tex]

And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:

C = 6*6 = 36

Then, putting together the two cases, we have a total of:

60 + 36 = 96 different triangles

Answer:

Hey there!

The angle is 24 degrees.

The angle complementary to the 66 degrees is 24 degrees, and the unknown angle is also 24 degrees because these  are alternate interior angles.

Let me know if this helps :)

Answer:

the answer is 41

Step-by-step explanation:

C. 41

Step-by-step explanation:

Answer:

Unpainted  surface area = 514.28 cm²

Step-by-step explanation:

Given:

Side of cube = 20 Cm

Radius of circle = 20 / 2 = 10 Cm

Find:

Unpainted  surface area

Computation:

Unpainted  surface area = Surface area of cube - 6(Area of circle)

Unpainted  surface area = 6a² - 6[πr²]

Unpainted  surface area = 6[a² - πr²]

Unpainted  surface area = 6[20² - π10²]

Unpainted  surface area = 6[400 - 314.285714]

Unpainted  surface area = 514.28 cm²

Answer:

-2x^6 + 7x^4 + 3x³ - 3x² + 11x + 20

Step-by-step explanation:

(-2x³ + x - 5)(x³ - 3x - 4) = -2x^6 + 6x^4 + 8x³ + x^4 - 3x² - 4x - 5x³ + 15x + 20

= -2x^6 + 7x^4 + 3x³ - 3x² + 11x + 20

B is the same thing but switching which trinomial is written first.

Step-by-step explanation:

find 30% of 455

which is = 136.5

then subtract 136.5 from the original number(455)

455 - 136.5

=318.5 student

Answer:

The answer is below

Step-by-step explanation:

The volume of a cuboid is the product of its length, height and breadth. It is given by:

Volume = length × breadth × height

Since the volume is given by the expression 12y² + 8y - 20. That is:

Volume = 12y² + 8y - 20 = 4(3y² + 2y - 5) = 4(3y² + 5y - 3y -5) = 4[y(3y + 5) -1(3y + 5)]

Volume = 4(y-1)(3y+5)

Or

Volume = 12y² + 8y - 20 = 2(6y² +4y - 10) = 2(6y² + 10y - 6y -10) = 2[y(6y + 10) -1(6y + 10)]

Volume = 2(y-1)(6y+10)

Therefore the dimensions of the cuboid are either 4, y-1 and 3y+5 or 2, y-1 and 6y+10

Answer:

plz mark me as brainiest

Answer:

Mean = 32.8

Step-by-step Explanation:

Mean is given as Mean = (Σfx)/Σf

First, find the mid-point, x, of each class, and multiply by the frequency (f) of the class to get fx:

Class ==> f ==> x ==> fx

0-10   =>  3   =>  5  => 15

10-20 =>  8  => 15 => 120

20-30 => 10 => 25 => 250

30-40 => 15 => 35 => 525

40-50 =>  7  => 45 => 315

50-60 =>  4  => 55 => 220

60-70 =>  3  => 65 => 195

Sum the fx of all classes together to get Σfx:

Σfx = 15 + 120 + 250 + 525 + 315 + 220 + 195 = 1,640

Σf = 3 + 8 + 10 + 15 + 7 + 4 + 3 = 50

(Σfx)/Σf = [tex] \frac{1,640}{50} [/tex]

(Σfx)/Σf = [tex] 32.8 [/tex]

Mean = 32.8

Answer:

1. 2/5,-3 2. [tex]x=\frac{-5+-\sqrt{13} }{6}[/tex]

Step-by-step explanation:

i used the quadratic formula to find x also please note that 2 has 2 answers bc of the +- beofre the sqrt of 13  

Step-by-step explanation:

5x² + 13x - 6 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

a = 5 , b = 13 c = - 6

We have

[tex]x = \frac{ - 13± \sqrt{ {13}^{2} - 4(5)( - 6) } }{2(5)} [/tex]

[tex]x = \frac{ - 13± \sqrt{169 + 120} }{10} [/tex]

[tex]x = \frac{ - 13± \sqrt{289} }{10} [/tex]

[tex]x = \frac{ - 13±17}{10} [/tex]

[tex]x = \frac{ - 13 + 17}{10} \: \: \: \: \: or \: \: \: \: x = \frac{ - 13 - 17}{10} [/tex]

3x² + 5x + 1 = 0

a = 3 , b = 5 , c = 1

[tex]x = \frac{ -5 ± \sqrt{ {5}^{2} - 4(3)(1)} }{2(3)} [/tex]

[tex]x = \frac{ - 5± \sqrt{25 - 12} }{6} [/tex]

[tex]x = \frac{ - 5± \sqrt{13} }{6} [/tex]

[tex]x = \frac{ - 5 + \sqrt{13} }{6} \: \: \: \: or \: \: \: x = \frac{ - 5 - \sqrt{13} }{6} [/tex]

Hope this helps you

Answer:2 c^2 - 10c

Step-by-step explanation: