1) Determine the period of the function in exact terms of pi: y = 6 sin (10x)

2) Determine the period of the function in exact terms of pi: y = 7 sin (x/3)

3) If the period of a sinusoidal function is equal to 18, which of the following gives its frequency?

a) π/9
b) 18π
c) π/18
d) 6π

4) When the period of a sine function doubles, the frequency

a) doubles
b) increases by 2
c) is halved
d) decreases by 2

In this case, The critical numbers are x = 1.

To find the critical numbers of g(y) = (y-2)/(y^2-2y+4), we first find the derivative g'(y) and then set it equal to zero or find where it's undefined.

g'(y) = (2y-2)/((y^2-2y+4)^2).

The critical numbers are y = 1. 2.

For f(x) = x^(-2)ln(x), you probably meant f(x) = x^(-2)ln(x).

In this case, find the derivative f'(x) and set it equal to zero or find where it's undefined.

f'(x) = -2x^(-3)ln(x) + x^(-2)(1/x).

The critical numbers are x = 1.

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There are 56 different sequences of coin toss results that Kathy could have gotten, given that she got 3 heads and 5 tails in 8 tosses.

To find the total number of different sequences of coin toss results that Kathy could have gotten, we can use the formula for permutations:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, the total number of coin tosses) and r is the number of objects selected (in this case, the number of heads or tails that Kathy got).

Since Kathy got 3 heads and 5 tails, there are 8 choose 3 (or 8 choose 5) ways to arrange the sequence of heads and tails. This is equivalent to the number of ways to select 3 objects out of 8, or 5 objects out of 8:

8C3 = 8! / (3! x (8 - 3)!) = 56

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The base of a ladder should be set out a distance equal to one-fourth (1/4) the height to the point of support. This ensures stability and safety while using the ladder. It is important to pay attention to this detail when using a ladder to prevent accidents and injuries.

The base of a ladder should be set out a distance equal to 1/4 the height to the point of support.

Determine the height to the point of support (H).
Calculate the appropriate distance for the base of the ladder by using the formula: Distance = 1/4 * H.
Set the ladder's base at the calculated distance from the wall or support.

The base of a ladder should be set out a distance equal to one-fourth (1/4) the height to the point of support. This ensures stability and safety while using the ladder. It is important to pay attention to this detail when using a ladder to prevent accidents and injuries.
                                This guideline ensures that the ladder is placed at a safe angle to prevent it from slipping or falling.

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Step-by-step explanation:

The histogram for the given data is shown above where the class interval is represented on x−axis and frequency is equal to the height of the bars on y−axis.

solution

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SIMILAR QUESTIONS

star-struck

Draw a Histogram for the following data :

Class Interval Frequency

0−10 35

10−20 70

20−30 20

30−40 40

40−50 50

Answer:

=3x−3

Step-by-step explanation:

=(3)(x+−1)

=(3)(x)+(3)(−1)

Answer:

3x - 3

Step-by-step explanation:

distribution

Answer:

1/4x^2 + 7x + 49

Step-by-step explanation:

Use binomial theorem (a + b)^2 = a^2 + 2ab + b^2 to expand (1/2x + 7)^2

Answer:

x^2(5x-2)

Step-by-step explanation:

The gcf of the whole expression is x^2. You then factor out it from the expression to get x^2(5x-2)

Answer:

1. a. 1,000 = 10³ = 10 × 10 × 10

b. 100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10² = 300

b. 2.16 × 10⁴ = 21,600

c. 800 ÷ 10³ = 0.8

d. 754.2 ÷ 10² = 7.542

Step-by-step explanation:

3. a. 1,000

There are 3 zeros in 1000. This is equivalent to 10 raised to the power of 3. Writing this in multiplication sentence using 19 as the only factor, we would have:

1,000 = 10³ = 10 × 10 × 10

b. 100 × 100

Using the same logic as explained in (a) above, we would have:

100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10²

Convert 10² to 100 and multiply both numbers

3 × 10² = 3 × 10 × 10 = 3 × 100 = 300

b. 2.16 × 10⁴

2.16 × 10 × 10 × 10 × 10 = 2.16 × 10,000

Multiplying both numbers, since we have 4 zeros, move the decimal point 4 places to the right.

2.16 × 10,000 = 21,600

c. 800 ÷ 10³ = 800 ÷ 10 × 10 × 10

800 ÷ 1,000

There are 3 zeros in 1000, since we are dividing, move the decimal point 3 places to the left.

800 ÷ 1,000 = 0.8

d. 754.2 ÷ 10² = 754.2 ÷ 10 × 10

754.2 ÷ 100

Move the decimal point 2 places to the left.

754.2 ÷ 100 = 7.542

Answer: \(2(x-5)(x+7)\) <---- \(this\) \(is\) \(your\) \(answer\)

Step-by-step explanation:

(\(2x^2+4x-70\))

\(2((x-5)(x+7))\)

\((-1,-72)\)

\((-1, -\frac{575}{8} )\)

\(x=-1\)

\(y=-\frac{577}{8}\)

Factor the polynomial completely.

Group and factor out the greatest common factor (GCF), then combine.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

So the answer is \(2(x-5)(x+7)\)

Hope this helps out :)

Answer:

2 real solutions.

Step-by-step explanation:

\(x^{2}\) - 3x = 5

\(x^{2}\) - 3x -5 = 0

D =\((-3)^{2}\) - 4 x 1 x (-5)

D = 29 Quadratic has 2 real solutions.

Answer:

a. ∠AMB, ∠BMC

b. ∠BMC, ∠CMD

Step-by-step explanation:

supplementary=angles add up to 180°

Complementary=angles add up to 90°

The probabilities for the hypergeometric distribution with the given parameters are:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

To determine the probabilities for the hypergeometric distribution with the given parameters, we can use the following formula:

P(X = k) = (choose(K, k) * choose(N-K, n-k)) / choose(N, n)

where "choose(a, b)" represents the binomial coefficient, calculated as a! / (b! * (a - b)!)

Let's calculate the probabilities:

a. P(X = 1):

P(X = 1) = (choose(20, 1) * choose(100-20, 4-1)) / choose(100, 4)

        = (20 * 80) / 3921225

        ≈ 0.000407

b. P(X = 6):

P(X = 6) = (choose(20, 6) * choose(100-20, 4-6)) / choose(100, 4)

        = (38760 * 0) / 3921225

        = 0

c. P(X = 4):

P(X = 4) = (choose(20, 4) * choose(100-20, 4-4)) / choose(100, 4)

        = (4845 * 80) / 3921225

        ≈ 0.098117

d. P(X = 0):

P(X = 0) = (choose(20, 0) * choose(100-20, 4-0)) / choose(100, 4)

        = (1 * 77) / 3921225

        ≈ 1.97e-05

Therefore:

a. P(X = 1) ≈ 0.000407

b. P(X = 6) = 0

c. P(X = 4) ≈ 0.098117

d. P(X = 0) ≈ 1.97e-05

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The complete question is:

Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. P(X = 0).

Answer:

i got stuck on this after solving the triangle. Below shows where I ended.

Step-by-step explanation:

1/2 * 12 * 25=150

Answer: next time put the answer we don’t care on how you solved it or where you left off. So if anybody got the answer put it here

Step-by-step explanation:

Answer:

I think it's 7 batches

Step-by-step explanation:

150/25 < 22b/25 < 225/25

6<b <9

The number of lemonade should be more than 6 and less than 9.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

we need at least 150 cups of lemonade but less than 225 cups of lemonade for a picnic.

Each batch of lemonade = 25 cups of lemonade.

let the number of lemonade be x

So, 150 < 25x < 225

or, 6 < x < 10

Hence, the number of lemonade should be more than 6 and less than 9.

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Answer:

1)

4(x+3)+4x=28

Solve

4x+12+4x=28

Combine

8x+12=28

Isolate

8x=16

Isolate

x=2

Substitute

4(2+3)=20

4*2=8

Now find each side

20/4=5

8/4=2

So one side is 5

Other side is 2

The length of legs are 8 in and 4 in , when hypothenuse is √73 in

The Pythagorean Theorem states that a right triangle's hypotenuse (the side across from the right angle) has a square perimeter equal to the sum of its legs

Formula : a² + b² = c²

Where , a and b are legs and c is hypotenuse

According to the  question,

Hypothenuse of right angle triangle : c =√73

sum of legs => 11 = a + b

Using Pythagoras theorem ,

a² + b² = c²

=> a² + b² = (√73)²

=>  a² + b² = 73 ---------(1)

As we know ,

(a + b)² = a² + b² + 2ab

=> a² + b² = (a + b)² -2ab

Substituting the value in equation (1)

=> (a + b)² -2ab = 73

=> 11² - 2ab = 73

=> 2ab = 121 - 73

=> 2ab = 48

=> ab = 24

=> a = 24/b

Substituting the value of a,

24/b + b = 11

=> 24 + b² = 11b

Solving the quadratic equation,

b = 8 , 3

Therefore , When a = 3 , b = 8

and when a = 8 , b = 3

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Answer: d

Step-by-step explanation: i took the test

Answer:

d

Step-by-step explanation:

Angles p and q are complementary, which means that their sum is equal to 90 degrees. Let's assume the size of angle q is x degrees. Since p is four times the size of q, we can write the equation p = 4q.

To find the size of q, we need to substitute the value of p in terms of q into the equation for the sum of the angles: p + q = 90.

Substituting 4q for p, we get:

4q + q = 90

Combining like terms:

5q = 90

To solve for q, we divide both sides of the equation by 5:

q = 90/5

Simplifying:

q = 18

Therefore, the size of angle q is 18 degrees.

when angles p and q are complementary and p is four times the size of q, the size of angle q is 18 degrees.

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Because the critical region is all on one side in a one-tailed test and needs to be split between the two tails in a two-tailed test.

In a one-tailed test, the alternative hypothesis is directional and the critical region is all on one side of the distribution. In a two-tailed test, the alternative hypothesis is non-directional and the critical region is split between the two tails of the distribution.

It is easier to reject the null hypothesis with a one-tailed test because the critical region is all on one side of the distribution, making it more likely to observe a significant difference and reject the null hypothesis. In contrast, the critical region is split between the two tails in a two-tailed test, making it less likely to observe a significant difference and reject the null hypothesis.

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Step-by-step explanation:

I think...

18×9=9×18

hope it helps

Answer:

\(x(3x + 2) = 3x^2 + 2x\)

Step-by-step explanation:

Given

\(x(3x + 2)\)

Required

Apply distributive property

\(x(3x + 2)\)

Distribute

\(x(3x + 2) = x * 3x + x * 2\)

\(x(3x + 2) = 3x^2 + 2x\)

Answer: 76%

Step-by-step explanation: 38/50 × 100/1

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:

  x = -7y/(4 +5y)

Step-by-step explanation:

You can treat y as though it were a constant. As in any 2-step linear equation, you separate the variable term(s) from the constant term, then divide by the coefficient of the variable.

  4x +5xy = -7y . . . . . subtract 7y

  x(4 +5y) = -7y . . . . . factor out x, so we can see its coefficient

  x = -7y/(4 +5y) . . . . divide by the coefficient of x

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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The 99.8% confidence interval for the proportion of those who work in computer-related jobs who have changed jobs in the past six months is approximately (0.495, 0.705).

To construct a 99.8% confidence interval for the proportion of those who work in computer-related jobs who have changed jobs in the past six months, you will need the sample proportion (p), the sample size (n), and the critical value (z) associated with the 99.8% confidence level.

First, find the critical value (z) for a 99.8% confidence level. You can look up this value in a standard normal (z) distribution table, or use a calculator that provides critical values. For a 99.8% confidence interval, the critical value (z) is approximately 3.090.

Next, calculate the standard error (SE) using the formula SE = sqrt[p(1-p)/n], where p is the sample proportion and n is the sample size. Make sure you have the values for p and n from your sample.

Once you have the standard error, you can construct the confidence interval using the formula:

Confidence Interval = p ± (z * SE)

Substitute the values of p, z, and SE into the formula, and round the answers to at least three decimal places.

For example, if the sample proportion (p) is 0.60 and the sample size (n) is 200:

SE = sqrt[0.60 * (1-0.60) / 200] ≈ 0.034
Confidence Interval = 0.60 ± (3.090 * 0.034) ≈ 0.60 ± 0.105

Thus, the 99.8% confidence interval for the proportion of those who work in computer-related jobs who have changed jobs in the past six months is approximately (0.495, 0.705).

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The value 4 in the function s(m) = 5 + 4(m-1) represents the number of stamps Rudy adds to his collection every month. Therefore, the correct answer is d) Rudy adds 4 more stamps to his collection every month.

In the given function, s(m), m represents the number of months Rudy has been collecting stamps. The expression (m-1) represents the number of months minus one, indicating that the calculation starts from the second month. The coefficient 4 represents the number of additional stamps Rudy adds to his collection each month. For example, if we substitute m = 2 into the function, we get s(2) = 5 + 4(2-1) = 5 + 4(1) = 9. This means that after the second month, Rudy's collection would have 9 stamps in total, indicating the addition of 4 more stamps. Therefore, the value 4 in the given function represents the number of stamps Rudy adds to his collection every month.

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