Quick!!!Geoffrey buys 48 shares of Ignyta, Inc. (RXDX) at $6.15 each, and his broker charges him a commission of $81. How much did Geoffrey pay for his stock?A.$376.20
B.$295.20
C.$450.30
D.$219.60

Final answer:

To find the height of the digital monitoring system, we rearrange the given parabolic equation to solve for y, substitute the known distance of 3 inches, and determine that the monitoring system is attached 6 inches above the focal point.

Explanation:

The equation given for the reflecting telescope by the library for their astronomy program is x = \frac{1}{12} y^2. To solve for the height of the digital monitoring system as a function of the distance x, we need to rewrite the equation in terms of y. First, we multiply both sides by 12 to get 12x = y^2. Then, take the square root of both sides to solve for y, which gives us y = \sqrt{12x}. Given that the distance between the base and the focal point is 3 inches, we substitute x with 3 to find the height of the monitoring system. Thus, we have y = \sqrt{12 \cdot 3} which simplifies to y = \sqrt{36} or y = 6 inches. This means the digital monitoring system is attached 6 inches above the focal point of the telescope.

Answer:

There are 248 windows on the first eight floors.

Step-by-step explanation:

As given:

The ground floor has 52 windows.

This question is based on arithmetic sequence:

a1 = 52

d = - 6 (each floor has six fewer windows than the floor below it)

[tex]a_n=a1+(n-1)d[/tex]

[tex]a_8 =a1+7d[/tex]

=> [tex]52+[7 \times (-6)][/tex]

=> [tex]52-42 =10[/tex]

We know:

[tex]S_n= n/2 \times (a1 +a _n)[/tex]

[tex]S_8 =8/2 \times(52+10)[/tex]

= 248

Therefore, there are 248 windows on the first eight floors.

Answer:

The answer is E

Step-by-step explanation:

Final answer:

To find the length of a side of the square, calculate the square root of the sum of the areas of the circle (36 cm²) and the additional 12 cm². This results in a square side length of approximately 6.93 cm.

Explanation:

We are given that the area of the circle is 36 cm², and we know that the area of a square is greater than the area of the circle by 12 cm², which means the area of the square is 36 cm² + 12 cm² = 48 cm².

The area of a square is given by A = a², where a is the length of the side of the square. So, we need to find the value of a that satisfies the equation a² = 48 cm².

By taking the square root of both sides of the equation, we get a = √(48 cm²). Simplifying the square root of 48 gives us a ≈ 6.93 cm. Therefore, the length of a side of the square is approximately 6.93 cm.

Answer:

n=6

Step-by-step explanation:

Since, we know that  when two chords intersect each other inside a circle, the products of their segments are equal. Thus, using this property, we have

[tex](n+8)5=(n+4)7[/tex]

⇒[tex]5n+40=7n+28[/tex]

⇒[tex]40-28=7n-5n[/tex]

⇒[tex]12=2n[/tex]

⇒[tex]n=6[/tex]

Thus, the value of n is 6.

Answer:

[tex]n=6[/tex]

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the value of n.

We can see that two chords of our given circle are intersecting inside it, so we will use intersecting chords theorem to solve for n.

Intersecting chords theorem states that when two chords of a circle intersect inside the circle, then product of the segments of both chords is equal.

Using intersecting chords theorem we can set an equation as:

[tex]5(n+8)=7(n+4)[/tex]

Using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,

[tex]5*n+5*8=7*n+7*4[/tex]

[tex]5n+40=7n+28[/tex]

Subtracting 40 and 7n from both sides we will get,

[tex]5n-7n+40-40=7n-7n+28-40[/tex]

[tex]-2n=-12[/tex]

Dividing both sides by -2 we will get,

[tex]\frac{-2n}{-2}=\frac{-12}{-2}[/tex]

[tex]n=6[/tex]

Therefore, the value of n is 6.

Answer:

Option C. is the correct option.

Step-by-step explanation:

The given expression is [tex]log_{2}(x+11)=4[/tex]

We further solve this

[tex](x+11)=2^{4}=16[/tex]

[tex]x = 16-11=5[/tex]

Now we evaluate the options

A). [tex]log_{5}16\neq 2[/tex]

But the expression is given as [tex]log_{2}(x+11)=4[/tex]

Wrong expression so not correct.

B). [tex]log_{5}16\neq 4[/tex]

Wrong expression again so not correct

C). By putting x = 5 in the expression

[tex]log_{2}(x+11)=4[/tex]

[tex]log_{2}(5+11)=log_{2}(16)=log_{2}(2^{4})=4[/tex]

Therefore this option is the correct option.

D). By putting x = 5 in the expression

[tex]log_{4}(5+11)=log_{4}(16)=log_{4}(4^{2})=2[/tex]

But the expression is [tex]log_{2}(x+11)=4[/tex]

So this option is also not correct.

Answer:

c

Step-by-step explanation:

the answer is (-4 -8)

Answer: D) About 314 inches

Step-by-step explanation:

Since, the radius of the wheel = 25 inches

Also, the angle in one turns of the wheel [tex]= 2\pi[/tex]

⇒ The angle in 2 turn of the wheel [tex]= 4\pi[/tex]

Hence, the distance it will cover in two turns

[tex]= 4\pi\times 25[/tex]       ( Arc length = central angle × radius)

[tex]= 4\times 3.14\times 25[/tex]

[tex]=314.159265\approx 314\text{ inches}[/tex]

⇒ Fourth option is correct.

Final answer:

The probability of a light switch failing after 1,200 operations can be calculated by first finding the likelihood of it not failing across those operations with the formula [tex]0.999^{1200}[/tex], and then subtracting that result from 1.

Explanation:

The question asks about the probability that a light switch will fail after being turned on or off 1,200 times, given that the probability it will fail on any given operation is 0.001. This can be approached by calculating the probability that the switch does not fail in all 1,200 operations and then subtracting that probability from 1.

To calculate the probability of the switch not failing in a single operation, we subtract the failure probability from 1: 1 - 0.001 = 0.999. The probability of the switch not failing in all 1,200 operations is [tex]0.999^{1200}[/tex].

Finally, the probability of the switch failing at least once in 1,200 operations is [tex]1 - 0.999^{1200}[/tex]. When you calculate this, it gives the probability of failure after 1,200 operations.

Final Answer:

The height of the box is 9 units.

Explanation:

Let's denote the width of the box as w, the length as l, and the height as h. According to the problem, we have the following relationships:
l = 2w (the length is twice the width) and
l = h - 4 (the length is also 4 less than the height).

The surface area SA of a rectangular box is calculated by the formula:
SA = 2lw + 2lh + 2wh.

Given that the surface area is 160, we set up our equation:
160 = 2lw + 2lh + 2wh.

Now let's substitute the relations l = 2w and l = h - 4 into the surface area equation:
Since l = 2w, 160 = 2(2w)w + 2(2w)h + 2wh.

Simplifying the equation, we have:
160 = 4w² + 4wh + 2wh
160 = 4w² + 6wh

Now we use the fact that l = h - 4 to substitute for h:
h = l + 4
h = 2w + 4

Now substitute h back into the surface area equation:
160 = 4w² + 6w(2w + 4) ,

Expand the terms:
160 = 4w² + 12w^2 + 24w,

Combine like terms:
160 = 16w² + 24w

Now, we must solve for w. Let's move all terms to one side to solve the quadratic equation:
16w² + 24w - 160 = 0

Divide all terms by 8 to simplify:
2w² + 3w - 20 = 0

We can now attempt to factor the quadratic equation:
(2w - 5)(w + 4) = 0

This gives us two solutions:
2w - 5 = 0 or  w + 4 = 0

Solving the first equation for w:
2w = 5,[tex]\( w = \frac{5}{2} \)[/tex]

w = 5/2
We can disregard the second solution w + 4 = 0 for w, as it gives us a negative width, which isn't possible for a box.

Now that we have w, we can find h.
Using our earlier substitute for h:
h = 2w + 4 ,
[tex]h = 2 \cdot \frac{5}{2} + 4[/tex] ,
h = 5 + 4 ,
h = 9 .
Thus, the height of the box is 9 units.

The angle at which the rays of the sun hit the ground is equivalent to {β} = 31.22°.

Its an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.

Given is that a building that is 115 feet tall casts a shadow that is 190 feet long

Assume that the angle of elevation or the angle at which the rays of the sun hit the ground is equivalent to {β}. Then, with respect to the question, we can write -

tan{β} = (height of building)/(length of shadow)

tan{β} = (115/190)

tan{β} = 0.606

{β} = tan⁻¹(0.606)

{β} = 31.22°

Therefore, the angle at which the rays of the sun hit the ground is equivalent to {β} = 31.22°.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

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Gina is travelling to the beach 20 miles away from her house.

On Ginas map her house and the beach are 4 inches apart

That is a distance of 20 miles is represented by the Ginas map in 4 inches

Therefore, on Ginas map one inch will be = 20/4 miles = 5 miles

So, the scale used for Gina's map is 1 inch = 5 miles

Hope this helps..!!

Thank you :)

Answer:

C 44 ft2 i just took the test .

Step-by-step explanation: