does y vary directly as x in this function? y= -3x+4

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.

To determine the speeds, we set up relative speed equations and solve for 'x'. The cyclist's average speed is 15 km/h and the car's average speed is 45 km/h.

Let's denote the cyclist's speed as 'x' km/h and the car's speed as '3x' km/h (since it's three times the cyclist's speed).

Given that speed is distance over time, we can set up the following equations:

For the cyclist: 225km / x = time, and for the car: 225km / 3x = time - 5.

By equating these two expressions, we get: 225/x = 225/3x + 5.

Solving this equation for 'x', we get x = 15. Thus, the average speed of the cyclist is 15 km/h and the car (3x) is 45 km/h.

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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:

Answer:

The answer is E

Step-by-step explanation:

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°.

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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.

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.

the answer is (-4 -8)

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: 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.

Answer:

The measure of the ∠A is 59°.  

Step-by-step explanation:

It is given that a quadrilateral ABCD is inscribed in a circle, and from the properties of circle, we know that the sum of the opposite angles of the quadrilateral inscribed in the circle is equal to 180°.

Therefore, ∠A+∠C=180°

⇒[tex]A+121^{\circ}=180^{\circ}[/tex]

⇒[tex]A=180-121[/tex]

⇒[tex]A=59^{\circ}[/tex]

Therefore, the measure of the ∠A is 59°.

Apologies on this being 4 years late, but to anyone else who stumbles across this; answer is 59°

I had taken the test and got it correct

Good luck, and i hope this helps!! :]

The probability that Natalie got all four quiz questions correct after guessing would be 6. 25 %.

If Natalie guessed on the last four true or false questions, there are two possible outcomes for each question (correct or incorrect), and she has a 50% chance of guessing correctly for each question since there are only two options.

To find the probability that she got all four quiz questions correct, you can multiply the probabilities for each question:

Probability of guessing a question correctly = 0.5 (since there are 2 options, and she has a 50% chance of guessing correctly)

Probability of getting all four questions correct = (0.5) * (0.5) * (0.5) * (0.5)

= 0.0625

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If you can't see the images here

36x2 − 4

Based on the mean score of the test, the percentage of students who scored above 85% in the test was 16%.

Based on the fact that this distribution is normally distributed, the percentage of students that scored higher or lower than 85% within 1 standard deviation is:

= 100% - 68%

= 32%

The number of students who scored above 85% would therefore be:

= 32% / 2

= 16%

Find out more on normal distributions at https://brainly.com/question/23418254.

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