Answer the question in the pic...

Answer:

12 meters

Step-by-step explanation:

Draw a picture of the two pathways 30° apart.  Add a circle representing the illumination of the light on one of the pathways.  Draw a line from the center of the circle to the last point where it intersects the pathway without lights.

This forms a triangle.  One leg is x, the length of the pathway without lights.  Another leg is 5n, where n is an integer.  This represents how far the light is from where the pathways meet.  The third and final leg is 6, the radius of the illumination.

Use law of cosine to solve:

6² = x² + (5n)² − 2x(5n) cos 30°

36 = x² + 25n² − 5√3 xn

0 = x² − 5√3 xn + 25n² − 36

In order to have a solution, the discriminant must be greater than or equal to 0.

b² − 4ac ≥ 0

(-5√3 n)² − 4(1)(25n² − 36) ≥ 0

75n² − 100n² + 144 ≥ 0

144 − 25n² ≥ 0

144 ≥ 25n²

144/25 ≥ n²

12/5 ≥ n

So n must be an integer less than 12/5, or 2.4.  Therefore, the largest value of n is 2.  Substituting:

0 = x² − 5√3 x(2) + 25(2)² − 36

0 = x² − 10√3 x + 64

Solve with quadratic formula:

x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)

x = (10√3 ± √44) / 2

x = 5√3 ± √11

x ≈ 5.34 or 11.98

We want the larger value of x.  So approximately 12 meters of the pathway without lights is illuminated.

Answer:

Step-by-step explanation:

Confidence interval for population proportion is expressed as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

From the information given,

Sample proportion, p = 65/100 = 0.65

q = 1 - 0.65 = 0.35

n = 200

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96

Margin of error = 1.96√(0.65)(0.35)/200

Margin of error = 0.066 = 6.6%

The maximum boundary of the interval is

0.65 + 0.066 = 0.716

(V.O.A) means vertically opposite angle.

Answer:

The area of the image is 2,070.25 cm^2

Step-by-step explanation:

The first thing we do here is to scale up the square using the factor given.

Thus, for a length of 14 cm scaled up by 3.25, the new length becomes 14 * 3.25 = 45.5 cm

Mathematically, the area of the square is L^2

where L in this case is 45.5 cm

The area of the scaled up square would be 45.5 * 45.5 = 2,070.25 cm^2

Answer:

x = 4

x = -10

Step-by-step explanation:

(x + 3)² = 49

Take the square root of both sides.

x + 3 = ±7

The equation is x + 3 = 7 or x + 3 = -7.

x + 3 = 7

Subtract 3 on both sides.

x = 4

x + 3 = -7

Subtract 3 on both sides.

x = -10

Answer:

x₁ = -10

x₂ = 4

Step-by-step explanation:

(x + 3)² = 49

x + 3 = ± 7

x + 3 = -7 → x = -10

x + 3 = 7 → x = 4

Hope this helps! :)

Answer: 19 miles

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the distance between the hiker and the camp) and a and b are the other sides.  

Replacing with the values given:  

x^2 = 6^2 + 18^2  

x^2 = 36+324

x^2 = 360

x = √360

x = 18.97miles = 19 miles

Feel free to ask for more if needed or if you did not understand something.  

Answer:

[tex](A) y=1.5[/tex]

[tex](B)x=\dfrac27[/tex]

[tex](C)x=2\dfrac23[/tex]

[tex](D)x=-5.25[/tex]

Step-by-step explanation:

(A)

[tex]3y - 2 = - y + 4\\3y+y=4+2\\4y=6\\y=\dfrac64\\\\y=1.5[/tex]

(B)

[tex]5 - 4x = x + 3 + 2x\\5 - 4x = 3 +3x\\5-3=3x+4x\\7x=2\\x=\dfrac27[/tex]

(C)

[tex]-12 - 9x = - 4 - 12x\\-9x+12x=-4+12\\3x=8\\x=\dfrac83\\\\x=2\dfrac23[/tex]

(D)[tex]- x - 6 + 3x = -2x + 8x + 15[/tex]

[tex]2x-6 = 6x + 15\\2x-6x=15+6\\-4x=21\\x=\dfrac{21}{-4} \\\\x=-5.25[/tex]

Answer:

115/5 23 so 20% =23 23x4 =92

Answer:

PEMDAS DAT

Step-by-step explanation:

I know you don't need this anymore but for the ones who do this is the answer.........Look at the graph and trust it. Yes, I know it says to substitute and you can following the last page on part a) Doing what they do in the tables and it will get you the same answer as if you'd just look at the graph.

The answer for the y- value at x=p IS 8. and the answer for the y-value at x=p+k IS 5. So go ahead and write that down if you haven't already!

For step2 Find the difference between the endpoints of the interval on the y-axis. The answer to your question, Is and always will be 3! The difference is 3 because you subtract 3 from 8 and you get 5.

If you didn't read clearer, I'll write it for you again, The length interval is K, it is the length between p and p+k.

For the following questions, does your answer to step 2 depend on p, well I suppose. This is why....The answer does depend on p because we are dealing with a slope. if you move up or down the slope it will not be the same.

For the question..... Is the difference between the y-values the same regardless of where the interval starts? The answer is yes!!! And No!!! But WRITE YES! Why? Because if the interval moves as a whole the difference between the y-values is the same! Try it for yourself. Move K back two x-values and the difference for the y-values will be the same, IT WILL STILL BE THREE.

Hope you understood!

And for part one the answer on part c (-2). It depends on K.

Answer:

7.5 mL

Step-by-step explanation:

If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.

Answer:

slope m=1/7

Step-by-step explanation:

x-7y=-6

-7y=-x-6

y=-x/-7 -6/-7

y=1/7 x+6/7

Answer:

Step-by-step explanation:

f(x)=x²-25=(x-5)(x+5)

g(x)=x-5

(f/g)(x)=(x-5)(x+5)/(x-5)=x+5;   for x≠5

D=R-{5}

Explanation:

The vertex of a parabola is either the highest point or the lowest point, depending on how the parabola is oriented. In this case, it is the lowest point.

For the red f(x) curve, we see the vertex is (0,0)

The blue g(x) curve has its vertex at (3,1)

In general, the vertex is represented by (h,k)

For the blue curve, (h,k) = (3,1) so h = 3 and k = 1 pair up together

We will plug those values along with a = 1 into the vertex form below

y = a(x-h)^2 + k

y = 1(x-3)^2 + 1

y = (x-3)^2 + 1

The blue curve is the result of shifting the red curve 3 units to the right and 1 unit up. No vertical stretching or compressing has been applied, which is why a = 1 stays the same.

Answer:

e.29 d.1

Step-by-step explanation:

we will replace with the values we have :

Answer:

Option (1). 17

Step-by-step explanation:

Length of a segment having coordinates (x₁, y₁) and (x₂, y₂) is given by the formula,

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Coordinates of points A and C are (4, 3) and (19, 11).

To get the length of segment AC we will substitute the coordinates in the formula,

AC = [tex]\sqrt{(19-4)^2+(11-3)^2}[/tex]

     = [tex]\sqrt{(15)^2+8^2}[/tex]

     = [tex]\sqrt{225+64}[/tex]

     = [tex]\sqrt{289}[/tex]

     = 17

Therefore, length of segment AC = 17 units.

Option (1) will be the answer.

Answer:

Area = 147.03 cm²

Step-by-step explanation:

Area of parallelogram = [tex]Base*Heigth[/tex]

Where base = 16.9 cm, Height = 8.7 cm

Area = 16.9*8.7

Area = 147.03 cm²

Answer:

147.03 square cm

Step-by-step explanation:

[tex]area \: of \: parallelogram \\ = base \times height \\ = 16.9 \times 8.7 \\ = 147.03 \: {cm}^{2} \\ [/tex]

Answer:

5/18

Step-by-step explanation:

Let's say the original packaging was 1 lb of packaging for $1.

The cost was $1/lb.

Then the weight went down by 10% and the price went up by 15%.

Now 0.9 lb of packaging cost $1.15.

The new unit cost is $1.15/(0.9 lb)

The difference is

$1.15/(0.9 lb) - $1/lb =

= $1.15/(0.9 lb) - $0.9/(0.9 lb)

= $0.25/(0.9 lb)

=$25/(90 lb) = $5/(18 lb)

The price went up by 5/18.

Answer:

√3 + 1

Step-by-step explanation:

Step below are self-explanatory

Answer:

4 AND 2

Step-by-step explanation:

Answer:

Hello!

______________________

This question is very easy.

2 + 2 = 4

1 + 1 = 2

Step-by-step explanation: Add.

Hope this helped you!

Answer:

In counting to a base, when we get to the point where the base integer comes up, we replace by 10, on the first time and by 10 at every other time the integer is about to come up

We now this in base 10 as when we get to 10 we input 10 and so and so till we get to 99 where since we are in base 10 the next number is 100 because that is the highest we can go while in base 11 100 in base is equivalent to 91

So we have for base 5

1 , 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 200

We see that on getting to 4 instead of the next digit to be 5 we replace it with 10 because 5 cannot be displayed in base 5

Similarly after 14 is 20 because 5 cannot be displayed at 24 the next number is 30 because 5 cannot be displayed

at 34 the next  40, while at 44 the next is (we could have written 50 but 5 is 10 in base 5 so we write 100) 100

At 144, we note that 44 = 100 + 44, therefore, the next number will be 100 + 44+ 1 = 100 + (45 but 45 = 100 in base 5) 100 so that the next number is 200

Base 2

In base 2 we have;

1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 101111, 110000, 110001, 110010

We see that there are no 2s and after 11 we get 100 just like after 99 we get 100 in base 10 and after 44 we get 100 in base 5

So we need to still have an idea of the number system just as we did for base 10

Step-by-step explanation:

Answer:

Mean = 0.38082 checks per day

Variance = 0.38082

Standard deviation = 0.61711

Step-by-step explanation:

In a Poisson distribution, the variance (V) is equal to the mean value (μ), and the standard deviation (σ) is the square root of the variance.

A year has 365 days,, if 139 checks were written during a year, the mean number of checks written per day is:

[tex]E(x)=\mu=\frac{139}{365}\\ \mu=0.38082\ checks/day[/tex]

Therefore, the variance and standard deviation are, respectively:

[tex]V=\mu=0.38082\\\sigma=\sqrt{V}=\sqrt{0.38082}\\ \sigma =0.61711[/tex]

Answer:

3rd option

Step-by-step explanation:

The ratio of 1:3 mean that one part is 1 to the other part being 3.

That means the total is 1 + 3 = 4.

1 part to 3 parts is the same as 1 part to a whole of 4 and 3 parts to a whole of 4.

Answer: 3rd option

Answer:

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

Step-by-step explanation:

I like to call the numbers in the ratio 1 : 3 "ratio units".

That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).

_____

Coment on the answer wording

I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".

In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."

Answer:

it is a many to one function:)

Step-by-step explanation:

The statement which best describes the function F(x)=2x^2-3x+1 is it is a many to one function.

A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.

f(x) = x2 shows us that function "f" takes "x" and squares it. Example: with f(x) = x2: an input of 4. becomes an output of 16.

Learn more about piecewise function at https://brainly.com/question/27262465

#SPJ2

Answer:

Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.

Step-by-step explanation:

Sea x el precio de los perros calientes y y el precio de las hamburguesas.

Escribiendo los datos de la primera familia en forma de ecuación tenemos:

[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)

Escribiendo los datos de la segunda familia:

[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)

Vamos a resolver este sistema de ecuaciones por el método de suma y resta:

[tex]4x+3y=43,000\\5x+y= 34,500[/tex]

Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:

[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]

Por lo tanto, un perro caliente cuesta 5,500 pesos.

Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:

[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]

Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una

Answer:

[tex]\boxed {\red {0.035m}}[/tex]

Step-by-step explanation:

[tex]1m = 100cm \\ x = 3.5cm[/tex]

[tex]use \: \: cross \: \: multipication[/tex]

[tex]3.5 \times 1 = 100 \times x \\ 3.5 = 100x \\ \frac{3.5}{100} = \frac{100x}{100} \\ x = 0.035m[/tex]

Answer:

Angle B is the answer

Answer:

Step-by-step explanation:

You have to use the Law of Cosines here to solve for C. For us the equation will take on the form

[tex]c^2=a^2+b^2-2abcosC[/tex] for which we have all the values except C. Filling in:

[tex]12^2=28^2+18^2-2(28)(18)cosC[/tex] which will simplify to

144 = 784 + 324 - 1008cosC.  Simplify a bit more to

144 = 1108 - 1008cosC. Subtract 1108 from both sides to get

-964 = -1008cosC. Divide both sides by -1008 to get

.9563492063 = cosC

Press the 2nd button and then the cos button on your calculator. You should see this on your screen:

[tex]cos^{-1}([/tex]

After that open parenthesis, enter that long decimal and hit "enter". You should get that your angle is 16.99 which I imagine you would round to 17, which is choice D. If you did not get 16.99 but you got .29655, you are in radian mode and you need to be in degree mode. Hit "mode" and change it with your arrow key and hit "enter" and it's changed!

Answer:

x=-20 or x=68

Step-by-step explanation:

you can either make it so 47 remains the largest number and so take 67 from 47 (=-20) or you can leave 1 as the smallest number and add 67 to 1 (=68)