Simplify. Your answer should contain only positive exponents.

9) 3^-1 • 3^0

Answer:

(i) The area of the rabbit cage when the width is 5.2 m is 81.5 m²

(ii) The area of the rabbit cage if Wilson has 40 meters of wire mesh is 75 m²

Step-by-step explanation:

(i) The given relation of the area, A to the width P of the rabbit cage is A = 3·p²

The graph of the function between the values of 0 and 6 inclusive is found as follows;

A,              3·p²

0,               0

1,                1

2,               12

3,               27

4,               48

5,               75

6,               108

Please find attached the graph of A to 3·p²

From the graph, we have when the the width, p, of the rabbit cage = 5.2, the area, A ≈ 81.5 m²

The area of the rabbit cage when the width is 5.2 m = 81.5 m²

(ii) Also from the graph given that the total wire mess with Wilson = 40 meters, we have;

The formula for the perimeter of the cage = The formula for the perimeter of a rectangle = 2×length + 2×width

The formula for the perimeter of the cage = 2×3×p + 2× p = 8·p

Where the total length of the wire mesh available = 40 meters for the cage

The 40 meters of wire mesh will be used round the perimeter of the cage

∴ 40 m. = 8·p

p = 40/8 = 5 m.

At p = 5 m. the area is given as A = 75 m².

Therefore, the area of the rabbit cage if Wilson has 40 meters of wire mesh = 75 m².

Answer:

He reached the top of the tree on the 31st day

Step-by-step explanation:

The total distance for the owl to climb is 93 units.

If the owl climbed 18 units up the tree every day without coming down, the owl would have taken 93/18 days to reach the top of the tree.

However, the owl descends by 15 units every night. This just reduces the overall distance covered at the end of each day's climb.

The net distance covered by the owl after each day is 18-15 units = 3 units of climb. This is the steady distance the owl gains up the three at the end of each day after the ascent and descent.

The time taken for the climb moving at this pace of 3 units per day will be

93 units / 3 units per day = 31 days

Answer:

  (-8,10)

Step-by-step explanation:

hope i helped!

u can substitute if u want to recheck

can i get brainliest pls?

-Zylynn

Answer:

b^8

Step-by-step explanation:

When multiplying exponents with the same base, we can add the exponents

b^2 * b^6

b^ (2+6)

b^8

Answer:b8 x

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "b6"   was replaced by   "b^6".  1 more similar replacement(s).

STEP

1

:

Multiplying exponential expressions

1.1    b2 multiplied by b6 = b(2 + 6) = b8

Final result :

 b8x

Answer:

f(x) =  3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x +  [tex]\frac{68}{3}[/tex]

Step-by-step explanation:

To find f'(x), we will follow the steps below:

We will start by integrating both-side of the equation

∫f'(x) = ∫(12x^3 - 2x^2 - 17)dx

f(x)  = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + C

Then we go ahead and find C

f(1) = 8

so we will replace x by 1 in the above equation and solve for c

f(1)  = 3(1)⁴ - [tex]\frac{2(1)^{3} }{3}[/tex] - 17(1) + C

8 = 3 - [tex]\frac{2}{3}[/tex] - 17 + C

C =8 - 3 + 17 + [tex]\frac{2}{3}[/tex]

C = 22 +  [tex]\frac{2}{3}[/tex]

C =[tex]\frac{66 + 2}{3}[/tex]

C = [tex]\frac{68}{3}[/tex]

f(x) =  3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x +  [tex]\frac{68}{3}[/tex]

Answer:

72.96

Step-by-step explanation:

Let the first circle's radius be r and quarter circle's radius be R

Area of circle = π[tex]r^{2}[/tex]

                       = 3.14 × 8 × 8

                       = 200.96 [tex]cm^{2}[/tex]

Area of quarter circle = π[tex]R^{2}[/tex]/4

                                     = 3.14 × 16 × 16

                                     = 803. 84/4

                                     =200.96

Area of shaded portion = (Area of Quarter circle - Area of semi-circle ACD - Area of triangle ABC) + (Area of the circle -  Area of semi-circle ACD - Area of triangle ABC)

Area of Semi-circle =   Area of the circle divided by 2

                                 = 100.48

Area of triangle = [tex]\frac{bh}{2}[/tex]

                           = [tex]\frac{16 * 8}{2}[/tex]

                           = 64

Therefore, The area of shaded portion= (200.96-100.48-64) + (200.96 - 100.48 - 64)

= 36.48 +36.48

=72.96

Answer:

24 cm

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

2304 pi = 4/3 pi r^3

Divide each side by pi

2304 = 4/3 r^3

Multiply each side 3/4

2304 * 3/4 = 4/3 r^3 * 3/4

1728 = r^3

Take the cube root of each side

1728 ^ 1/3 = r^3 ^ 1/3

12 = r

We want the diameter

d = 2*r

d = 2*12

d = 24

Answer:

24 centimeters

Step-by-step explanation:

A basketball is a sphere. The volume of a sphere can be found using the following formula:

V= 4/3 π r^3

We know that the volume is 2304 π cm^3, therefore we can substitute 2304π in for V.

2304π = 4/3 π r^3

We want to find out what r is. Therefore, we must get r by itself. First, divide both sides by pi.

2304π/π=4/3πr^3/π

2304π/π=4/3r^3

2304=4/3r^3

Next, divide both sides by 4/3, or multiply by the reciprocal of 4/3. The reciprocal of 4/3 is 3/4 (flip the numerator and denominator).

2304*3/4=4/3r^3*3/4

2304*3/4=r^3

1728=r^3

Now, take the cube root of both sides.

∛1728=∛r^3

∛1728=r

12=r

r= 12 cm

The radius is 12 centimeters, but the question asks us to find the diameter. The diameter is twice the radius.

d= 2r

d= 2* 12 cm

d= 24 cm

The diameter of the basketball is 24 centimeters.

Answer:

6 is the best estimate.

Step-by-step explanation:

(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.

Choose 6 as your best approximation.

Answer:

A graphing calculator is more accurate than graphing by hand. If the slope and/or y-intercept is a fraction or decimal, it is more difficult to accurately graph by hand.

Step-by-step explanation:

Answer:

WHEN U GRAPH WITH A CALCULATOR  IT IS MUCH MORE ACCURATE

ESPECIALLY IF THERE R FRACTIONS AND DECIMALS AND THE GRAPHING CALCULATOR GOES ON FOREVER WHERE AS THE GRAPHING PAPER  ENDS

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

          ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                         PEACE!

Answer: A. Factor 2 => 4x greater

                   Factor 3 => 9x greater

                   Factor 5 => 25x greater

Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

[tex]A_{1}[/tex] = 2πrh

If multiply both dimensions by a factor of 2:

[tex]A_{2}[/tex] = 2.π.2r.2h

[tex]A_{2}[/tex] = 8πrh

Comparing [tex]A_{1}[/tex] to [tex]A_{2}[/tex] :

[tex]\frac{A_{2}}{A_{1}}[/tex] = [tex]\frac{8.\pi.rh}{2.\pi.rh}[/tex] = 4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

[tex]A_{3} = 2.\pi.3r.3h[/tex]

[tex]A_{3} = 18.\pi.r.h[/tex]

Comparing areas:

[tex]\frac{A_{3}}{A_{1}}[/tex] = [tex]\frac{18.\pi.r.h}{2.\pi.r.h}[/tex] = 9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

[tex]A_{5} = 2.\pi.5r.5h[/tex]

[tex]A_{5} = 50.\pi.r.h[/tex]

Comparing:

[tex]\frac{A_{5}}{A_{1}}[/tex] = [tex]\frac{50.\pi.r.h}{2.\pi.r.h}[/tex] = 25

The new area is 25 times greater.

B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.

Answer:

$3 discount

Step-by-step explanation:

If Fredo originally had the markdown as $0 (meaning no change), then he arrived at the store, seeing the markdown was $2, the current markdown is $2.

Now that he has an extra $1 off, he gets 2+1 = $3 off the bread.

Hope this helped!

Answer:

i) Estimate the value of the population proportion = 0.8

ii) 95% confidence interval for the population proportion

(0.7214 , 0.8784)

iii)    Lower bound = 0.7214

     upper bound = 0.8784

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  he surveys 100 customers and finds that 80 paid at the pump

sample proportion

                     [tex]p = \frac{x}{n} = \frac{80}{100} = 0.8[/tex]

Step(ii):-

95% confidence interval for the population proportion is determined by

[tex](p^{-} - Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]

Level of significance  

∝ =0.05

Z₀.₀₅ = 1.96

[tex](0.8 - 1.96 \sqrt{\frac{0.8 X 0.2)}{100} } , 0.8 + 1.96 \sqrt{\frac{0.8 X 0.2}{100} })[/tex]

On calculation , we get

(0.8 - 0.0784 , 0.8 + 0.0784)

(0.7214 , 0.8784)

Conclusion:-

95% confidence interval for the population proportion

(0.7214 , 0.8784)

Answer:

slope is 2

Step-by-step explanation:

the equation of linear is y=mx+b, where m is the slope

therefore, m=2 which means the slope is 2

Answer:the slope is 2

Step-by-step explanation:

the equation y=mx+b represents m as the slope.

rational numbers are numbers which can be expressed in fraction form whereas irrational is just opposite

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by .  

Answer:

1and1/2yrs ago

Step-by-step explanation:

price dis year= 56545

reduction per year= 11309

...number of years ago = 73810-56545=17265

and is about 20% of annual deductions

so if 56545 +20% + 1/2 20% = 1nd1/2 yrs

Answer:

No they can't be equal

Step-by-step explanation:

L.H.S. :-

2/3 × ( -6/7 + 4/5 )

=> 2/3 × -2/35

=> -4/105

R.H.S

(2/3 × 4/5) × -6/7

=> 8/15 × -6/7

=> -48/105

L.H.S IS NOT EQUAL TO R.H.S.

Answer :

A. add x, subtract 1, divide by 4

D. subtract 3x, subtract 4, divide by -4

Step-by-step-explanation : Further explanation

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}\\1+3x-1=-x+4-1\\Simplify\\3x=-x+3\\\mathrm{Add\:}x\mathrm{\:to\:both\:sides}\\3x+x=-x+3+x\\Simplify\\4x=3\\\mathrm{Divide\:both\:sides\:by\:}4\\\frac{4x}{4}=\frac{3}{4}\\x=\frac{3}{4}[/tex]

I hope it helps:)

Answer:

1) true

2) false

hope it worked

and pls mark me as BRAINLIEST

Answer:

The bird is 2.44km high

Step-by-step explanation:

Hello,

To solve this question, we need to understand how they are and we can only get this with a correct pictorial diagram.

See attached document for better understanding.

From the first diagram, we understand that the bird is between them and also on top of them.

Assuming Susan, Mark and the bird all form a triangle at each other and the bird at the top, we can divide the the triangle into two equal parts.

But before then, we should know that sum of angles in a triangle is equal to 180°

Therefore,

20° + 50° + b° = 180

70° + b = 180

b = 180° - 70°

b = 110°

Dividing angle b into two equal parts = 55° on each side.

See the last attached document for better illustration.

Using SOHCAHTOA, we can find the adjacent of the triangle which corresponds to the height of the bird.

We have opposite = 3.4km and we're looking for adjacent. We can use tangent of the angle to find the adjacent.

Tanθ = opposite / adjacent

Tan 55° = 3.5 / adj

Adjacent = 3.5 / tan55

Adjacent = 3.5 / 1.43

Adjacent = 2.44km

The height of the bird is 2.44km

Answer:

A. 1.95

Step-by-step explanation:

PLATO

Answer: There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500

Step-by-step explanation:

given that;

n = 14

mean Ж = 19,850

standard deviation S = 1,084

degree of freedom df = n - 1 = ( 14 -1 ) = 13

H₀ : ц ≥ 20,500

H₁ : ц < 20,500

Now the test statistics

t = (Ж - ц) / ( s/√n)

t = ( 19850 - 20500) / ( 1084/√14)

t = -2.244

we know that our degree of freedom df = 13

from the table, the area under the t-distribution of the left of (t=-2.244) and for (df=13) is 0.0215

so P = 0.0215

significance ∝ = 0.05

we can confidently say that since our p value is less than the significance level, we reject the null hypothesis ( H₀ : ц ≥ 20,500 )

There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500

Answer: B

Step-by-step explanation:

The domain of a function is every x-value, and the range is every y-value.

Hope it helps <3

Answer:

B

Domain: (-∞,∞)

Range: (-∞,5]

Step-by-step explanation:

The domain is (-∞,∞) because the graph as you can see, is continuously going outwards forever.

The range is (-∞,5] because the graph as you can see, is always going down forever and the top point is at 5. The 5 is in a bracket because it is a defined number while ∞ is undefined!

Hope this helped and good luck :)

Answer:

x = 6 and x = 11.

Step-by-step explanation:

sqrt(x - 2) + 8 = x

sqrt(x - 2) = x - 8

(sqrt(x - 2))^2 = (x - 8)^2

x - 2 = x^2 - 16x + 64

x^2 - 16x + 64 = x - 2

x^2 - 17x + 66 = 0

We can use the discriminant to find whether there are solutions to the equation.

b^2 - 4ac; where a = 1, b = -17, and c = 66.

(-17)^2 - 4 * 1 * 66

= 289 - 264

= 25

Since the discriminant is positive, we know there are two valid solutions to the equation.

x^2 - 17x + 66 = 0

(x - 6)(x - 11) = 0

The solutions are when x - 6 = 0 and x - 11 = 0.

x - 6 = 0

x = 6

x - 11 = 0

x = 11

Hope this helps!

Answer:

x=11 solution

x=6 extraneous

Step-by-step explanation:

sqrt( x-2) + 8 = x

Subtract x from each side

sqrt(x-2) = x-8

Square each side

(sqrt(x-2))^2 = (x-8) ^2

x-2 = x^2 -8x-8x+64

x-2  = x^2 -16x+64

Subtract ( x-2) from each side

0 = x^2 -17x +66

Factor

0 = (x-6) ( x-11)

Using the zero product property

x=6  x=11

Checking the solutions

x=6

sqrt( 6-2) + 8 = 6

sqrt(4) +8 = 6

2 +8 = 6

False  not a solution

x=11

sqrt( 11-2) + 8 = 11

sqrt(9) +8 =11

3 +8 = 11

solution

Answer:

79%

Step-by-step explanation:

To find the median, you need to arrange the numbers in ascending order. Than pick the middle number. If there are two middle numbers then you add them together and then divide by 2.

Answer:

79%

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here,,

Sides of two sail are proportional.

Let the height be 'x'

Now,

[tex] \frac{a1}{b1} = \frac{a2}{b2} [/tex]

plug the values

[tex] \frac{25}{10} = \frac{x}{8} [/tex]

Apply cross product property

[tex]10x = 25 \times 8[/tex]

Multiply the numbers

[tex]10x = 200[/tex]

Divide both sides of the equation by 10

[tex] \frac{10x}{10} = \frac{200}{10} [/tex]

Calculate

[tex]x = 20 \: ft[/tex]

Hope this helps...

Best regards!!

Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

cosФ=0 then the angle=π/2=90 degrees

sinФ==1     sin 90=1

12) the original price of the console  that Amanda bought :

240+(240*50%)=360 dollars

the price before the tariffs:

360-(360*50^)=180 dollars

[tex]\dfrac{2ax+3}{ax+3}=-1[/tex]

Rewrite -1 as a fraction

[tex]\dfrac{2ax+3}{ax+3}=\dfrac{-1}{1}[/tex]

Cross multiply

[tex]2ax+3=-1(ax+3)[/tex]

Distribute the -1

[tex]2ax+3=-ax-3[/tex]

Add both sides by ax

[tex]3ax+3=-3[/tex]

Subtract both sides by 3

[tex]3ax=-6[/tex]

Divide both sides by 3a

[tex]x=-\dfrac{6}{3a}[/tex]

Simplify

[tex]=-\dfrac{2}{a}[/tex]

That's the value of x respect to a. Let me know if you need any clarifications, thanks!

Answer:

Step-by-step explanation:

[tex]\frac{2ax+3}{ax+3} =-1\\2ax+3=-ax-3\\2ax+ax=-3-3\\3ax=-6\\x=-\frac{2}{a}[/tex]

Answer:

The range consists of all real numbers where y ≠ 0

Step-by-step explanation:

reciprocal parent function is y = 1/x

If y = 0, then 1 would have to be divided by a number to equal 0. This would require x to equal a number that can divide 1 to equal 0. Because this is not possible, y cannot be 0.  

Answer:

Construction II

Step-by-step explanation:

Construct 3 perpendicular bisectors of the triangles sides; where they intersect is the point of concurrency. The distance from the point of concurrency to one of the vertices is the radius.

Answer:

Area of a rectangle is w • L

w = 5 while L = (b + 3)

Area is

5 • (b + 3) = 5b + 15

So answer is 2. 3. and 4. which are all similar forms of the same expression.

Step-by-step explanation:

Answer:

hello:

Step-by-step explanation:

If f(x) = -8x - 6 and g(x) = x+8 ,  (f • g) (- 7)= f(g(-7))

but g(-7)=-7+8=1

(f • g) (- 7)= f(1) =-8(1)-6 =-14