can you plz help me with this​

Answer:

7

Step-by-step explanation:

Let a and b be the sides of the equilateral triangle and the regular hexagon respectively as shown in figures (1) and (2).

The area of the equilateral having side a is

[tex]A_T= \frac {\sqrt3}{2}a^2\cdots(i)[/tex]

Now, join all the 6 corner points of the regular hexagon to the center of the hexagon as shown in figure (3).

As there are 6 equal sides, so angle subtended by each side at the center is 360/6=60 degrees.

Considering the triangle POR:

[tex]\angle POR= 60[/tex] degree [angle at center]

As sides PO=RO, so [tex]\angle OPR = \angle ORP = 60[/tex] degree.

Hence, triangle POR is an equilateral triangle.

Similarly, all the remaining 5 triangles are equilateral triangles.

So, the area of hexagon = 6 x Area of triangle POR

As the length of sides of the triangle POR is b,

so the area of the triangle POR [tex]= \frac {\sqrt3}{2}b^2[/tex].

Hence, the area of the regular hexagon,

[tex]A_H = 6 \times \frac {\sqrt3}{2}b^2\cdots(ii)[/tex]

As the equilateral triangle and a regular hexagon have the same area, so from the equations (i)and (ii), we have

[tex]A_T=A_H\\\\\frac {\sqrt3}{2}a^2=6 \times \frac {\sqrt3}{2}b^2\\\\\Rightarrow a^2=6b^2\\\\\Rightarrow \frac {b^2}{a^2}=\frac 1 6\\\\\Rightarrow \frac {b}{a}=\frac {1}{\sqrt 6}\cdots(iii)[/tex]

Given that the ratio of the side length of the regular hexagon to the side length of the equilateral triangle, b/a= m/√n.

On comparing with the equation (iii), we have

m=1 and n=6

Hence, m+n=1+6=7.

Answer:

The volume of the solid is 243[tex]\sqrt{2} \ \pi[/tex]

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0  ≤ ρ²   ≤   81

0  ≤ ρ   ≤  9

The intersection that takes place in the sphere and the cone is:

[tex]x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81[/tex]

[tex]2(x^2 + y^2) =81[/tex]

[tex]x^2 +y^2 = \dfrac{81}{2}[/tex]

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

[tex]z = \sqrt{x^2+y^2}[/tex]

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; [tex]\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}[/tex]

Thus, volume: [tex]V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi[/tex]

[tex]V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho[/tex]

[tex]V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}[/tex]

[tex]V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ][/tex]

V = 243[tex]\sqrt{2} \ \pi[/tex]

Answer:

a

 The upper bound of the 99% prediction level is [tex] 98.2  [/tex]  

b

 The  95% confidence interval is [tex]9.7383 <  \mu < 10.2617 [/tex]

Step-by-step explanation:

Considering first question

From the question we are told that

   The sample size is  n  =  30  

   The sample mean is  [tex]\= x = 96.2\%[/tex]

   The standard deviation is [tex]s = 0.8\%[/tex]

Generally the degree of freedom is mathematically represented as

        [tex]df = n - 1[/tex]

=>      [tex]df = 30 - 1[/tex]

=>      [tex]df = 29[/tex]

From the question we are told the confidence level is  99% , hence the level of significance is    

      [tex]\alpha = (100 - 99 ) \%[/tex]

=>   [tex]\alpha = 0.01[/tex]

Generally from the t distribution table the critical value  of   at a degree of freedom of is  

   [tex]t_{\alpha , 29} = 2.462[/tex]

Generally the  99%  prediction level is mathematically represented as

      [tex]\= x \pm [(t_{\alpha  , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]

Generally the upper bound of the 99%  prediction level is mathematically represented as

      [tex]\= x + [(t_{\alpha  , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]  

=>    [tex] 96.2 + (2.462 ) * 0.8 * (\sqrt{1 + \frac{1}{ 30} } )}] [/tex]  

=>    [tex] 98.2  [/tex]  

Considering second question

 Generally the sample is mathematically represented as

             [tex]\= x = \frac{\sum x_i}{n}[/tex]

=>           [tex]\= x = \frac{ 9.8 + 10.2 + \cdots +9.6 }{7}[/tex]  

=>           [tex]\= x = 10[/tex]    

Generally the standard deviation  is mathematically represented as

           [tex]\sigma = \sqrt{ \frac{ \sum ( x_ i - \= x)}{n-1} }[/tex]

=>        [tex]\sigma = \sqrt{ \frac{ ( 9.8 -10)^2 + ( 10.2 -10)^2 + \cdots + ( 9.6 -10)^2 }{7-1} }[/tex]

=>        [tex]\sigma = 0.283[/tex]

Generally the degree of freedom is mathematically represented as

      [tex] df =  n- 1 [/tex]

=>    [tex] df =  7- 1 [/tex]

=>    [tex] df =  6 [/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the t distribution table the critical value  of   at a degree of freedom of  is  

   [tex]t_{\frac{\alpha }{2} , 6 } =  2.447[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = t_{\frac{\alpha }{2} , 6 } *  \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =2.447*    \frac{0.283 }{\sqrt{7} }[/tex]

=>    [tex]E =0.2617[/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

=>   [tex]10 -0.2617 <  \mu < 10 + 0.2617[/tex]

=>   [tex]9.7383 <  \mu < 10.2617 [/tex]

Answer:

Only line A is a well-placed line of best fit.

Step-by-step explanation:

I did this on Plato and got it correct.

Answer:

I'd say it's 0.03

Step-by-step explanation:

0.03 divided by 10 is 0.003 so it's 1/10

0.003 is 1/10th of 0.03.

A decimal is represented by a point or a dot it separates the decimal part and the fractional part for example 24.75 here the whole part is is 24 and the fractional part is 75.

if we divide 0.03 by 10  = [tex]\frac{0.03}{10}[/tex] = 0.003.                     (dividing a number by 10

                                                                                    moves the decimal point

                                                                                    to the left by 1 because                      

                                                                                    10 has 1 no. of zeroes)

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Answer:

A The first one

Answer:

A

Step-by-step explanation: 30 minutes is half an hour so 6 miles is half the miles he runs an hour. Azrael runs 12 miles in an hour. 15 minutes is 1/4 of an hour. 2 is 1/4 of the miles Simon runs in an hour. 2 times 4 is 8. I'm really bad at explaining, sorry. the answer is A.

Mixed fraction:

3 2/5 = 17/5

4 4/5 = 24/5

Miles she ran:

17/5 + 24/5

= 41/5 miles or 8.2 miles

Answer:

-14

Step-by-step explanation:

I might be wrong, but this is my interpretation of the problem.

To solve this problem, find the endpoints of the line in the interval. Then draw a line between those two points. Finally, find the slope of the line that passes between the two points.

The line is f(x) = -2x^(2) + 2x + 1

The interval (in standard notation) is (3 [tex]\leq[/tex] x [tex]\leq[/tex] 5)

So when x = 3,

-2x^(2) + 2x + 1

-2(3)^(2) + 2*3 + 1

-2 * 9 + 6 + 1

-18 + 7

- 11

One endpoint is: (3, -11).

When x = 5

-2x^(2) + 2x + 1

-2(5)^2 + 2*5 + 1

-2 * 25 + 10 + 1

-50 + 11

-39

The other endpoint is; (5, -39).

Find the slope of a line passing through these two points.

The formula to find the slope of a line is:

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]x_{1}[/tex] = 3

[tex]y_{1}[/tex] = -11

[tex]x_{2}[/tex] = 5

[tex]y_{2}[/tex] = -39

((-39) - ( -11))/((5) - (3))

Simplify

-28/2

-14

Answer:

A) f(x) = 0.85x

B) g(x) = x - 1500

C) g(f(x)) = $14650

D) f(g(x)) = $14875

Step-by-step explanation:

A) The list price is x and a 15% discount is applied.

Thus;

f(x) = x - 15%x

f(x) = 0.85x

B) We are told that the manufacturer offers a $1500 rebate for each purchase of a car.

Thus, the function g(x) to represent the price after the rebate is applied is;

g(x) = x - 1500

C)if the discount is applied before the rebate, the function is;

g(f(x))

Now,

f(x) = 0.85(19000)

f(x) = 16150

g(x) = x - 1500

Thus;

g(x) = 16150 - 1500

g(x) = $14650

D) If discount after rebate, then we have; f(g(x))

g(x) = 19000 - 1500

g(x) = 17500

f(g(x)) = 0.85(17500)

f(g(x)) = $14875

Step-by-step explanation:

sum of internal angles of any triangle = 180 degrees

sum of an exterior angle and an interior angle = 180 degrees

Answer:

-3

Step-by-step explanation:

y=3xy and subtract y on both sides that gives u -1 and then you have -1=3x and then divide 3 on both sides you are left with -3 =x

Answer:

3.4

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

there are two sets of parrallel lines.

Answer:

The equation of the line tangent to the graph of f at x = -1 is [tex]y = 7\cdot x +13[/tex].

Step-by-step explanation:

From Analytical Geometry we know that the tangent line is a first order polynomial, whose form is defined by:

[tex]y = m\cdot x + b[/tex] (1)

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]m[/tex] - Slope, dimensionless.

[tex]b[/tex] - Intercept, dimensionless.

The slope of the tangent line at [tex]x = -1[/tex] is:

[tex]f'(x) = -3\cdot x +4[/tex] (2)

[tex]f'(-1) = -3\cdot (-1) +4[/tex]

[tex]f'(-1) = 7[/tex]

If we know that [tex]m = 7[/tex], [tex]x = -1[/tex] and [tex]y = 6[/tex], then the intercept of the equation of the line is:

[tex]b = y-m\cdot x[/tex]

[tex]b = 6-(7)\cdot (-1)[/tex]

[tex]b = 13[/tex]

The equation of the line tangent to the graph of f at x = -1 is [tex]y = 7\cdot x +13[/tex].

Answer:

Step-by-step explanation:

should be A.

Answer:

10, 20, 30, 40

2.5, 5, 7.5, 10

120.8, 60.4, 30.2, 15.1

3624, 1812, 906, 453

hope this helps!

Answer:

16 miles

Step-by-step explanation:

there are 8 units between the points each unit is 2 miles so 8*2= 16

Answer:

11.077 cars / 11 cars (nearest whole number)

Step-by-step explanation:

6.5 hours → 72 cars

1 hour → 72/6.5 cars = 11.077 cars (5 s.f.)

Answer:

y=5

Step-by-step explanation:

125 +125+13y+9y=360

punch it into math-way.

250+22y=360

22y= 110

y=5

Answer: D) Side-Angle-Side  (SAS)

Check out the diagram below. Note the color coding to see how the angles and sides correspond to the given information. We aren't given RT = RT, but we use the reflexive property in this case. The angles are between the sides so we use SAS.

We don't have enough information to determine anything about the other angles, so we cannot use AAS or ASA. Also, recall that SSA is not a valid congruence theorem. Luckily the angle is between the sides so we don't have to worry about SSA.

Answer:

d = 256 ft.

Step-by-step explanation:

The distance an object falls is directly proportional to the square of the time it falls.

First, we name the variables.

Let d= the distance.

t= time

Write the formula for direct variation, where y varies directly with the square of x.

y=kx2

We will use d in place of y and t in place of x.

d=kt2

Substitute the given values for the variables.

d=144whent=3144=k⋅32

Solve for the constant of variation.

144916=k⋅99=k

Write the equation that relates d and t.

d=kt2

Substitute in the constant of variation.

d=16t2

Find d when t=4.

Write the equation that relates d and t.

d=16t2

Substitute the given value for t.

d=16⋅42

Simplify.

d=256

An object will fall 256 feet in 4 seconds.

The required distance fall by fall in 4 seconds is 192 feet.

Given that,
The distance an object falls is directly proportional to the square of the time it falls. A ball falls 144 feet in 3 seconds, how far will an object fall in 4 seconds is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.

here,
The rate of fall of the ball = 144 / 3
                                      = 48 feet second
Now distance fall by the ball in 4 seconds = 48 * 4 = 192 feets.

Thus, the required distance fall by fall in 4 seconds is 192 feet.

Learn more about arithmetic here:

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Answer:

Area = 324 ft²

Step-by-step explanation:

Given

Length = 15ft

Walkway = 3ft

Required

Determine the area of the pond + the walkway

To calculate the required area, we need to get the total length of a side .

This is calculated by adding the length of a side of the pond and the side of the walkway

Total Length = Pond Length + Walkway

Total Length = 15ft + 3ft

Total Length = 18ft

Now, the required area can be calculated as thus:

Area = Total Length * Total Length

Area = 18ft * 18ft

Area = 324 ft²

Answer:

69°

Step-by-step explanation:

m∠1 + 111° = 180° ⇒ m∠1 = 69°

m∠1 = m∠2 = 69°

Answer:

h(-3)=-1

Step-by-step explanation:

Replace all x in h(x)= -3x-10 by -3:

h(-3)=-3(-3)-10

Now multiply -3 and -3:

h(-3)=9-10

Simplify 9 and -10 (aka add 9 and -10 together):

h(-3)=-1

Answer: h(-3)=-1

Hope this helps!

Answer:

-1

Step-by-step explanation:

If h(x)= -3x-10 and we want to solve for h(-3) then we have to plug in -3 for all x variables. h(-3)= -3(-3)-10, then solve using PEMDAS.

First multiple h(-3)= 9-10, multiple -3*-3 to get 9.

Then subtract, h(-3)=-1

Answer:

40% as a decimal is 0.4

40% as a fraction is 2/5

Step-by-step explanation:

Let's go over each of these step by step.

First, let's see 40% as a fraction.

Since 40% is out of 100%, we can rewrite that as 40/100.

If you want to simplify it, let's do the following.

40/100

Divide both sides by 20, and you'll end up with:

2/5.

Now, let's do 40% as a decimal.

This is pretty simple.

40% is 40/100 as said before, and to find it as a decimal,

let's divide 40 and 100.

40 divided by 20 = 0.4

Therefore, we can conclude the following:

40% as a fraction is 40/100, or 2/5.

40% as a decimal is 0.4

Hope this helped! :)

Answer:

the dog was born on july 30th so the dog would be 3 months and a week old

Step-by-step explanation:

Answer:

it is 0.7x0.4=0.28

Step-by-step explanation:

Answer:

3627514

Step-by-step explanation:

Answer:

(3x - 1)(x + 1) = 3x² + 2x - 1

Step-by-step explanation:

[tex] \rm \longrightarrow (3x - 1)(x + 1) \\ \\ \rm \longrightarrow 3x(x + 1) - 1(x + 1) \\ \\ \rm \longrightarrow (3x)(x) + (3x)(1) + ( - 1)(x) + ( - 1)(1) \\ \\ \rm \longrightarrow 3 {x}^{2} + 3x + ( - x ) + ( - 1) \\ \\ \rm \longrightarrow 3 {x}^{2} + 3x - x - 1 \\ \\ \rm \longrightarrow 3 {x}^{2} + 2x - 1[/tex]

Answer:

(3x - 1)(x + 1) = 3x² + 2x - 1

Step-by-step explanation:

got it right on edge

Answer:

x is 2

Step-by-step explanation: