-3(-3x^2 + 2x)

How do I distribute?

Answer:

2x-y-1=0

Step-by-step explanation:

.

The solutions of the equation 2sinθ - 1 = 0 in the interval (0, 2π) are θ = π/6 and θ = 13π/6.

To find all solutions of the equation 2sinθ - 1 = 0 in the interval (0, 2π), we can solve for θ by isolating the sine term and then using inverse sine (arcsin) to find the angles.

Start with the equation: 2sinθ - 1 = 0.

Add 1 to both sides of the equation: 2sinθ = 1.

Divide both sides by 2: sinθ = 1/2.

Take the inverse sine (arcsin) of both sides: θ = arcsin(1/2).

The inverse sine (arcsin) of 1/2 is π/6, so we have one solution θ = π/6.

However, we need to find all solutions in the interval (0, 2π). Since the sine function has a periodicity of 2π, we can add 2π to the solution to find additional solutions.

Adding 2π to π/6, we get θ = π/6 + 2π = π/6, 13π/6.

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Answer:

a.y=6

b.-1/8

c.1/2

d.2800

e.-8

f.7.71

Step-by-step explanation:

Answer:

B) Adjacent

Step-by-step explanation:

The hypotenuse will ALWAYS be designated as the longest side in a right triangle.

Pretend that the angle (the one with the round line) is an eyeball that is looking outwards. The eye is looking out at side BC. That means that line BC is opposite of the angle.

This leaves one side left: the adjacent side. The adjacent side is the side next to the angle. But it is the side that is NOT the hypotenuse.

Answer:

= 40.5π square inches

Step-by-step explanation:

Oatmeal is packaged in a right circular cylindrical container that has a radius of 1.5 inches and a height of 12 inches. What is the surface area of this container in terms of π?

The formula for the surface Area of a cylinder = 2πr( r + h)

r = 1.5 inches

h = 12 inches

Hence,

2 × π × 1.5( 1.5 + 12)

3π(13.5)

= 40.5π square inches

The surface area of the cylinder is

= 40.5π square inches

The absolute minimum value of the function f(x) = x³ (4-x) on the interval [-1, 4] is -64, and the absolute maximum value is 64.

To find the absolute minimum and maximum values of the function f(x) = x³ (4-x) on the interval [-1, 4], we need to evaluate the function at its critical points and endpoints.

First, we find the critical points by setting the derivative of the function equal to zero: f'(x) = 3x² - 4x² + 12x - 4 = 0. Simplifying this equation, we get 8x² - 12x + 4 = 0. Solving for x, we find two critical points: x = 1/2 and x = 1.

Next, we evaluate the function at the critical points and the endpoints of the interval [-1, 4]. We find f(-1) = -3, f(1/2) = 9/16, f(1) = 0, and f(4) = 0.

Comparing these values, we see that the absolute minimum value of the function is -64 at x = -1, and the absolute maximum value is 64 at x = 4.


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Answer: check out the image. Hope this helps n can u give me brainliest

Step-by-step explanation:

Answer:

Step-by-step explanation:

5 in.

a.

(6.257 25) in.

-

b. (6.25π – 12.5√2)in.²

d.

Find the value of x and y rounded to the nearest tenth.

C.

(6.25π- 12.5) in.2

s + t = 617

206 + 391 = s

s = 597

617 - 597 = number of teachers

there are 20 teachers

Answer:

2x + 11

Step-by-step explanation:

We are given

6 - 2x + 5 + 4x

Combining like terms with x, we have

6 + 5 + 2x

Combine like terms again, this time constants

11 + 2x

The random variable x in this case is a binomial random variable, representing the number of cars that need to be inspected until a car fails an inspection. A binomial random variable is defined as the number of successes, “s”, in “n” independent trials. In this case, “s” would be 1 (the single failure) and “n” would be the number of cars that John inspects until a car fails inspection.

The probability of success, “p”, in this case is 0.06 since 6% of cars fail inspection. The probability of failure is “q”, which would be 0.94 in this case (1 - 0.06). The mean, “μ”, of the random variable x is equal to n * p, or the total number of trials times the probability of success. In this case, the mean would be equal to n * 0.06, or 6%.

The variance, “σ2”, of the random variable x is equal to n * p * q, or the total number of trials times the probability of success times the probability of failure. In this case, the variance would be equal to n * 0.06 * 0.94, or 5.64%.

The binomial random variable x can be used to calculate the expected number of inspections it will take John until a car fails an inspection, as well as the probability of a car failing an inspection. By knowing the probability of success, the number of trials, and the probability of failure, we can calculate the mean, variance, and expected value of the binomial random variable x.

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Answer: 80 cm

Step-by-step explanation:

2.4 divided by 3 is 0.8

To convert m to cm multiply by 100

100 x 0.8 = 80

Answer:

Each piece of ribbon will be 80 cm or 0.8m

Step-by-step explanation:

Hope this helps!

The average value of y for the part of the curve \(y = 4x - x^3\) in the first quadrant is 2.

To find the average value of y for the part of the curve \(y = 4x - x^3\) in the first quadrant, we need to calculate the definite integral of y with respect to x over the interval where x ranges from 0 to the x-coordinate of the point where the curve intersects the x-axis.

The curve \(y = 4x - x^3\) intersects the x-axis at two points, (0, 0) and (2, 0). Therefore, the interval of interest for calculating the average value of y in the first quadrant is from x = 0 to x = 2.

To find the average value of y, we can use the following formula:

Average value of y = (1 / (b - a)) * ∫[a, b] y dx

In this case, a = 0 and b = 2, and y = 4x - x^3.

Therefore, the average value of y in the first quadrant can be calculated as follows:

Average value of y = (1 / (2 - 0)) * ∫\([0, 2] (4x - x^3) dx\)

Simplifying the integral:

Average value of

\(y = (1 / 2) * \int\limits[0, 2] (4x - x^3) dx\)

\(= (1 / 2) * [2x^2 - (1/4)x^4]\ evaluated \ from \ 0 \ to \ 2\\= (1 / 2) * [(2(2)^2 - (1/4)(2)^4) - (2(0)^2 - (1/4)(0)^4)]\\= (1 / 2) * [(8 - 4) - (0 - 0)]= (1 / 2) * [4]= 2\)

Therefore, the average value of y for the part of the curve \(y = 4x - x^3\) in the first quadrant is 2.

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At least 75% of the flights (or 15 out of the 20 flights) will last between 3 days and 11 days, according to Chebyshev's Theorem.

Chebyshev's Theorem states that for any given number k greater than 1, at least (\(1-\frac{1}{k^2}\)) of the data values in any data set will fall within k standard deviations of the mean.

In this case, we can use Chebyshev's Theorem to determine the minimum number of flights that lasted between 3 and 11 days.

Given:

Mean (μ) = 7 days

Standard Deviation (σ) = 2 days

To find the number of flights within the range of 3 to 11 days, we need to calculate how many standard deviations away from the mean these values are.

Lower Bound:

Value = 3 days

Number of standard deviations away from the

\(mean = \frac{(Value - Mean)}{ Standard Deviation}\)

\(mean =\frac{(3 - 7) }{2}\)

\(mean =\frac{-4}{2}\)

\(mean = -2\)

Upper Bound:

Value = 11 days

Number of standard deviations away from the

\(mean = \frac{(Value - Mean)}{Standard Deviation}\)

\(mean = \frac{(11 - 7)}{2}\)

\(mean = \frac{4}{2}\)

\(mean = 2\)

According to Chebyshev's Theorem, the minimum proportion of data values within k standard deviations of the mean is given by \((1- \frac{1}{k^2} )\).

So, we need to determine the proportion of data within 2 standard deviations, which is k = 2.

Proportion within 2 standard deviations = \(1-\frac{1}{2^2}\)

\(=1-\frac{1}{4}\)

\(= 1 - 0.25\)

\(= 0.75\)

Now, we can find the percentage of \(0.75\):

\(= 0.75\times 100\)

\(= 75\%\)

Therefore, at least 75% of the flights (or 15 out of the 20 flights) will last between 3 days and 11 days, according to Chebyshev's Theorem.

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Answer:

C≈47.12, or 47.1

Step-by-step explanation:

To find the circumference you just use the formula C=2\(\pi\)r.

The radius of your circle is 7.5 which is half of 15, now multiply 2\(\pi\)(7.5) which gives you your answer!

An even easier way to do this is to use the other formula C=d\(\pi\),

Just multiply your diameter (which is what was given to you) by pi and you also get your answer!

Hope this helps! :)

The largest possible integer n such that 9421 is divisible by 15 is 626.

To determine if a number is divisible by 15, we need to check if it is divisible by both 3 and 5. First, we check if the sum of its digits is divisible by 3. In this case, 9 + 4 + 2 + 1 = 16, which is not divisible by 3. Therefore, 9421 is not divisible by 3 and hence not divisible by 15.

The largest possible integer n such that 9421 is divisible by 15 is 626 because 9421 does not meet the divisibility criteria for 15.

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Answer:

A) x = 4, y = 3.

B. x = 0, y = -4.

Step-by-step explanation:

A) 2x+ 3y =11 .........(a)

x+ y = 4.......(b)

Multiply equation (b) by 2:

2x + 2y = 8

Subtract this from equation (a):

y = 11-8 = 3.

Substitute y = 3 into equation (a):

2x + 3*1 = 11

2x = 11 - 3 = 8

x = 4.

B) 4x+ 3y = -12

   2x - y= 4

Multiply second equation by 2:

4x - 2y = 8

Subtract this from first equation:

3y - (-2y) = -12 - 8

5y = -20.

y = -4.

Substitute y = -4 into equation 1:

4x + 3*(-4) = -12

4x = -12 + 12 = 0

x = 0.

Answer:

(9, 13, 22)

Step-by-step explanation:

We can use the triangle inequality theorem to help us solve this problem. We know that the two shortest sides of a traingle added up (their sum) needs to always be greater than the longest side of the triangle. Taking that information, we can figure out that 9+13=22. 22=22, not 22>22. This means that is the right answer, hopefully that helps!

Answer:

A translation of 5 units up

and

A translation of 2 units to the right

Step-by-step explanation:

Simplifying the expression gives 6x√3x

Adding and subtracting surds is applicable where the numbers underneath the root symbols also known as radicands are the same.

From the information given, we have:

5x √3x + 2x√3x  - x√3x

We can see than the numbers within the root symbols '3x' are the same for all the three surds.

Note that if the root cases are the same, the numbers cannot be added or substracted.

Now, let's add the values outside the roots

5x √3x + 2x√3x  - x√3x

= 5x + 2x - x

= 7x - x

= 6x

We have;

6x√3x

Thus, simplifying the expression gives 6x√3x

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Answer:

Step-by-step explanation:

Solution

verified

Verified by Toppr

Correct option is D)

p p

∼p⇒q  ∼(∼p⇒q)

T  T  T  F

T  F  T  F

F  T  T  F

F  F  F  T

p  q  p∧q  p∧∼q ∼p∧q   ∼p∧∼q

T  T  T  F  F  F

T  F  F  F  F  F

F  T  F  T  T  F

F  F  F  F  F  T

So we see the given relation is logically equivalent to option D, as shown in last column.

Effect size is a measure of the strength of the relationship between two variables. It does not indicate whether one variable causes another. The amount of variance in a set of scores is measured by the variance.

Whether an obtained research finding is valid is determined by statistical significance. Effect size is a quantitative measure of the magnitude of the experimental effect.

It is a way of quantifying the strength of the relationship between two variables. Effect sizes are typically reported on a standardized scale, such as Cohen's d or r.

Effect size does not indicate whether one variable causes another. Causation can only be inferred from a well-designed experiment that controls for confounding variables.

Effect size can be used to assess the strength of the relationship between two variables, but it cannot be used to determine whether one variable causes another.

The amount of variance in a set of scores is measured by the variance. Variance is a measure of how spread out the scores are in a set.

A high variance indicates that the scores are spread out over a wide range, while a low variance indicates that the scores are clustered together.

Whether an obtained research finding is valid is determined by statistical significance. Statistical significance is a measure of how likely it is that the observed results could have occurred by chance. A statistically significant result means that the observed results are unlikely to have occurred by chance alone.

Effect size, variance, and statistical significance are all important concepts in statistics. Effect size measures the strength of the relationship between two variables,

variance measures the spread of scores in a set, and statistical significance measures the likelihood that the observed results could have occurred by chance.

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She invested $5,000 at 7% and $4,000 at 9%

How much is invested at each rate of return?

The amount invested at 7% can be assumed to be x, such that the amount invested at 9% would be total investment of $9000 minus x, which has been invested at the initial rate of 7%

total interest at 7%=interest rate*amount invested

interest rate=7%

amount invested=x

total interest at 7%=7%*x=0.07x

total interest at 9%=9%*(9000-x)

total interest at 9%=810-0.09x

total interest on both accounts=0.07x+810-0.09x

total interest on both accounts=810-0.02x

total interest earned=$710

710=810-0.02x

0.02x=810-710

0.02x=100

x=100/0.02

x=amount invested in the account which earns 7%=$5,000

amount invested at 9%=$9000-$5000

amount invested at 9%=$4,000

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Answer:

yes

Step-by-step explanation:

start by solving for the missing value. all angles of a triangle should add up to 180. Subtract 31 adn 106 from 180 from the left side, you will get 43. Now do the same to the other side. 180 subtracted by 31 and 43 make 106. Thus, making the triangles the same. hope this helps

The success rates of the three treatments in preventing cardiac events are approximately 90.91% for the stress management program, 79.41% for the exercise program, and 70% for usual heart care.

a. Two-way table:
| Treatment | Cardiac Events | No Cardiac Events |
|-----------|-----------------|----------------------|
| Stress Management | 3 | 30 |
| Exercise | 7 | 27 |
| Usual Care | 12 | 28 |
b. The success rates of the three treatments in preventing cardiac events can be calculated as the percentage of people in each group who did not experience a cardiac event.
- Stress management: 90.9% success rate (30/33)
- Exercise: 79.4% success rate (27/34)
- Usual care: 70% success rate (28/40)
Therefore, the stress management program had the highest success rate in preventing cardiac events, followed by the exercise program and then usual care.

Stress management and its impact on reducing heart attacks. Let's analyze the study results and create a two-way table, as well as calculate the success rates of the three treatments in preventing cardiac events.
a. Two-way table:
| Treatment          | Cardiac Events | No Cardiac Events | Total |
|--------------------|----------------|-------------------|-------|
| Stress Management  | 3              | 30                | 33    |
| Exercise Program   | 7              | 27                | 34    |
| Usual Heart Care   | 12             | 28                | 40    |
| Total              | 22             | 85                | 107   |
b. Success rates of the three treatments in preventing cardiac events:
1. Stress Management:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (30 / 33) * 100
Success rate ≈ 90.91%
2. Exercise Program:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (27 / 34) * 100
Success rate ≈ 79.41%
3. Usual Heart Care:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (28 / 40) * 100
Success rate = 70%

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After 17 tosses, you would expect to gain $7.50. In each toss, there are two possible outcomes: heads or tails. If the coin comes down heads, you win $2, and if it comes up tails, you lose $0.50.

Since the probability of getting heads or tails in a fair coin toss is equal (0.5), we can calculate the expected gain by multiplying the probability of each outcome by its corresponding value and summing them up.

For each toss, the expected gain is calculated as (0.5 * $2) + (0.5 * -$0.50) = $1.25. Therefore, after 17 tosses, the total expected gain is 17 * $1.25 = $21.25. However, since you start with zero dollars, the net gain would be $21.25 - $14.75 = $7.50. Thus, you would expect to gain $7.50 after 17 tosses.

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