Follow the rules to create two number sequences that go to the fifth term each. Rule 1: Multiply by 3 starting from 10. Rule 2: Subtract 7 starting from 58. What is the first term that appears in both sequences? (2 points) a 30 b 55 c 60 d 180

[tex]cos^2(x) = cos^2(x)[/tex].

This equation is true for all values of x, so the solution is:
x ∈ ℝ (x is any real number).

To solve the equation[tex]cos^2(x)[/tex]= (power reducing formula),

we need to replace [tex]cos^2(x)[/tex] with the power reducing formula.

The power reducing formula for [tex]cos^2(x)[/tex] is:
[tex]cos^2(x) = (1 + cos(2x)) / 2[/tex]
Now, let's solve the equation:
[tex](1 + cos(2x)) / 2 = cos^2(x)[/tex]
We want to find x when this equation is true.

Since the left side is the power reducing formula for [tex]cos^2(x)[/tex],

we can simply write:
[tex]cos^2(x) = cos^2(x)[/tex].

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

The power reducing formula for sine is:

[tex]sin^2(x) = (1 - cos(2x))/2[/tex]

These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]

By solving for either [tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine [tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex]we can arrive at the power reducing formulas.

The power reducing formulas can be used to simplify trigonometric expressions and make them easier to work with.

For example, if you have an expression such as [tex]sin^4(x)[/tex], you can use the power reducing formula for sine to express [tex]sin^4(x)[/tex] in terms of [tex]sin^2(x),[/tex]and then use the power reducing formula for cosine to express [tex]sin^2(x)[/tex]in terms of cos(2x).

This can make the expression simpler and easier to integrate or differentiate.

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The mean of the game is 9

To find the mean of a game with two possible outcomes, we need to multiply the value of each outcome by its probability and then add the results.

Let X be the random variable representing the outcome of the game. The first outcome has a value of 5 and a probability of 0.2, while the second outcome has a value of 10 and a probability of 0.8.

Thus, the expected value or mean of the game can be calculated as:

E(X) = (0.2 x 5) + (0.8 x 10)

= 1 + 8

= 9

Therefore, the mean of the game is 9

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Answer:  the value of the expression is 24.6, which corresponds to option C.

Step-by-step explanation: In order to assess the expression, we must adhere to the sequence of operations (PEMDAS) and execute the computations in the subsequent manner:

Begin by calculating the expression in the parentheses as a priority: (31.5 squared minus 93) equals negative 61.5.

Next, perform the operation of dividing -61.5 by -2.5 which results in 24.6.

The measure of the third angle in the triangle is 80 degrees.

The sum of the angles in a triangle is always 180 degrees.

Therefore, to find the measure of the third angle in the triangle with angle measures of 40° and 60°,

We can subtract the sum of these two angles from 180°:

180° - (40° + 60°) = 180° - 100° = 80°

Therefore, the measure of the third angle in the triangle is 80 degrees.

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Answer:

D) a trapezoid with congruent diagnols

Explanation:

When none of the sides of a trapezoid are congruent, then it is a non isosceles trapezoid or a scalene trapezoid.

The complete factorization of the quadratic equation, would lead to the factor being (5y + 1)(4y - 1).

To factor the quadratic expression 20y² + 3y - 2 completely, we can use the "ac method" (product-sum method).

Rewrite the quadratic expression using these two numbers:

20y² - 5y + 8y - 2

Now, factor by grouping:

5y(4y - 1) + (4y - 1)

Now, we can see that there is a common factor of (4y - 1) in both terms:

(5y + 1)(4y - 1)

So, the factored form of the quadratic expression 20y² + 3y - 2 is (5y + 1)(4y - 1).

In conclusion, the factored form of the quadratic expression 20y² + 3y - 2 is (5y + 1)(4y - 1).

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Answer: It is simplified the way it is it can not be simplified anymore. its a trick question

Step-by-step explanation:

Answer:vvv

Step-by-step explanation:

Boss's nickname is Boss because they beat Glenna in the 1500m race.

Buzz's nickname is Buzz because they beat Juanita in the high jump.

Cosmo's nickname is Cosmo because they were with Tiger and Andre at the water station.

Tiger's nickname is Tiger because they lost to Juanita in the 400m race and tied with Glenna in the long jump.

Andre's nickname is not given, but we know they ran a leg of the relay race with Bilal.

Bilal's nickname is not given, but we know they ran a leg of the relay race with Andre.

Glenna's nickname is not given, but we know they tied with Tiger in the long jump.

Juanita's nickname is not given, but we know they lost to Buzz in the high jump and beat Tiger in the 400m race, and ran a leg of the relay race with Cosmo.

Answer:

Answers down below!

Step-by-step explanation:

Mean: 38.2

Median: 34

Range: 56

Mode: 13 and 34

Hope this helps!

Answer:

Option (3)

Step-by-step explanation:

Option (3) is not an equation. It is an expression. An equation is a mathematical statement where two expressions are equal to each other connected by an equal sign. In option (1), 3+1 is equal to 4+0 so it is an equation. In option (2), x2-2x is equal to 8, so it is also an equation. In option (4), 1+3 is equal to 6, so it is an equation, though it is not a true statement. However, in option (3), there is no equal sign, so it is not an equation. It is an expression that simplifies to 8x+2.

The complete sequence are 2, 3, 5, 8, 12, 17, 23, 30 38, 47, 1024, 512, 256, 128, 64 and 32.

Looking at the pattern, we can find the next two numbers in the sequence. All we need to do is notice that each term in the sequence is obtained by dividing the previous term by 2.

To get term after 128, we cam divide 128 by 2 which will give us:

= 128 / 2

= 64

To get term after 64, we divide 64 by 2 which give us:

= 64 / 2

= 32

Therefore, the last two numbers in the sequence are 64 and 32.

Full question: Find the last 2 numbers after the sequence of "2, 3, 5, 8, 12, 17, 23, 30 38, 47, 1024, 512, 256, 128, __ and ___.

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The normal approximation for the given binomial distribution with p = 0.10 and n = 40 has a mean of 4 and a standard deviation of 1.93.

The binomial probability distribution can be approximated by the normal distribution when certain conditions are met, such as a large sample size and a probability of success not too close to 0 or 1.

In this case, n = 40 and p = 0.10. To determine if the normal approximation is appropriate, we can check if both np and n(1-p) are greater than or equal to 10

np = 40 x 0.10 = 4

n(1-p) = 40 x 0.90 = 36

Both np and n(1-p) are greater than or equal to 10, so the normal approximation is appropriate.

The mean of the binomial distribution is given by μ = np = 4, and the standard deviation is given by σ = √(np(1-p)) = √(40 x 0.10 x 0.90) ≈ 1.93.

To find the mean and standard deviation of the normal approximation, we use the same mean and standard deviation values

μ = np = 4

σ = √(np(1-p)) ≈ 1.93

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Answer: 24 inches.

Step-by-step explanation:

We can use the formula for the area of a triangle to solve for the length of the base:

A = (1/2)bh

where:

A = the area of the triangle (in this case, 72 square inches)

b = the length of the base (what we're trying to find)

h = the height of the triangle (in this case, 6 inches)

Plugging in the values we know, we get:

72 = (1/2)b(6)

72 = 3b

b = 24

Therefore, the length of the base of the triangle is 24 inches.

Answer:

7) .15 + .7 = .85, .1 + .7 = .8

9) Another way to write 44n (44

times n) is 44•n.

Another way to write 44 ÷ n (44

divided by n) is 44/n.

10) $.25 × 7 = $1.75

11) A driver buys d gallons of gas at $3.25 per gallon. How much does the driver spend on gas?

The team that had the best overall record for the season is Panthers. Therefore the best way to explain the answer B. Panthers; they have a larger mean value of about 14.8 points.

For panthers, we calculate their mean values by totaling all their scores.

14+10+10+10+17+3+28+13+17+32+16+10+14+7+21 = 222

222/15 scores = 14.8

For Saints,  21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 210

210/15 score = 14

This shows that Panthers have a larger mean value. Also, Panthers have a larger median value than saints.  We find the median by arranging the scores from small to large and picking the number in between.

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The horizontal asymptote of the function f(x) = 2ˣ is y = 0.

In Mathematics and Geometry, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the line passing through the ordered pair (0, 1) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 0, as shown in the image attached above.

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Answer:

Step-by-step explanation:

This is a trinomial quadratic equation

x^2-9x+8

= x^2 -x-8x+8

= (x-1)(x-8)

Her current checking account balance is $2,641.50.

To find Carrington's current checking account balance, we need to add up all the deposits and subtract all the withdrawals from her starting balance.

Starting balance = $800

Deposits = $2,800

Withdrawals = $310 + $88 + $35.50 + $150 + $375 = $958.50

Therefore, Carrington's current checking account balance is:

$800 + $2,800 - $958.50 = $2,641.50

Her current checking account balance is $2,641.50.

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The calculated value of the length of segment KL is 4 units

From the question, we have the following parameters that can be used in our computation:

Radius, r = 3

LM = 2

JK = 3

The length KL is calculated as

KL² = JL² - JK²

Where

JL = r + LM = 3 + 2 = 5

Substitute the known values in the above equation, so, we have the following representation

KL² = 5² - 3²

KL² = 16

Take the square roots

KL = 4

Hence, the length is 4 units

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The polynomial p(x) has option (c) three real zeros because it has a relative maximum at (-2, 4), a relative minimum at (1,1), a relative maximum at (5,7), and a negative leading coefficient.

Since p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7), it means that the degree of the polynomial must be odd and at least three.

Moreover, we know that p(x) has no other critical points. This means that p(x) does not change sign between these relative extrema, which in turn implies that there are no real zeros between these extrema.

Therefore, the number of real zeros of p(x) is either one or three. To determine the answer, we need to consider the leading coefficient of p(x).

If the leading coefficient is positive, then p(x) must eventually increase on both ends, since the degree is odd. This means that there is exactly one real zero.

If the leading coefficient is negative, then p(x) must eventually decrease on both ends. In this case, since there are three relative extrema, there must be three real zeros.

Thus, we need to find the sign of the leading coefficient of p(x). This can be done by looking at the relative extrema.

Since p(x) has a relative maximum at (-2, 4), we know that the leading coefficient is negative.

Therefore, the correct option is (c) three.

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A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.

A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1, 1), and a relative maximum at (5, 7), with no other critical points. This means there are turning points at these coordinates. Since there are two relative maxima and one relative minimum, the polynomial must have at least 3 turning points.

A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.

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The percent of change in the price of the book is 50%.

To calculate the percent of change, we first need to find the difference between the original price and the new price. In this case, the original price of the book was $10, and the new price is $5. To find the difference, we can subtract the new price from the original price, which is:

$10 - $5 = $5

Now, we need to express this difference as a percentage of the original price. To do this, we divide the difference by the original price and then multiply by 100. In other words, we need to find the percentage that the original price has changed by. This can be represented mathematically as:

Percent of change = (Difference / Original price) x 100

Plugging in the values we found earlier, we get:

Percent of change = ($5 / $10) x 100

Percent of change = 0.5 x 100

Percent of change = 50%

This means that the price of the book has decreased by 50% from the original price of $10 to the sale price of $5.

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The expression[tex](2x^3y)(3x^4y^2)[/tex] simplifies to [tex]6x^7y^3[/tex]. The coefficients are multiplied, and the variables are combined by adding their exponents. Option C.

To simplify the expression [tex](2x^3y)(3x^4y^2),[/tex] we can multiply the coefficients and combine the variables with the same base by adding their exponents.

Multiplying the coefficients, we have:

2 * 3 = 6

For the variables, we multiply the x terms by adding their exponents (3 + 4 = 7), and the y terms by adding their exponents (1 + 2 = 3).

Therefore, simplifying the expression [tex](2x^3y)(3x^4y^2)[/tex] gives us:

[tex]6x^7y^3[/tex]

Hence, the simplified form of[tex](2x^3y)(3x^4y^2)[/tex] is[tex]6x^7y^3[/tex]. Option c is correct.

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Answer:

C:6x7y3

Step-by-step explanation:

i took the test and got it right

The estimated standard error and measures of effect size such as r2 and Cohen's d larger variance increases the standard error but decreases measures of effect size. B.

Larger variance increases the standard error but decreases measures of effect size.

The standard error is a measure of how much the sample mean is likely to vary from the true population mean.

It is calculated as the standard deviation of the sample divided by the square root of the sample size.

If the sample variance is large, the standard deviation of the sample will also be large, resulting in a larger standard error.

Measures of effect size, such as r2 and Cohen's d, indicate the strength of the relationship between variables or the size of the difference between groups, respectively.

Larger sample variances indicate greater variability in the data, which can make it more difficult to detect significant effects.

This can result in smaller effect sizes, as the magnitude of the effect is reduced relative to the variability in the data.

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Answer:

  D.  the length of the quarter

Step-by-step explanation:

Given Patrick started playing 4 minutes into the 2nd quarter, and played until the end of the 3rd quarter, you want to know how long Patrick played.

If q is the length of a quarter, Patrick's playing time is ...

  2q -4 . . . . minutes

In order to give this a numerical value, we need to know the value of q.

The most important variable to the problem is ...

  D.  the length of a quarter.

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After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.

To calculate the 90% confidence interval for the true mean income per month of a person who works from home in sales, we can use the following formula:

[tex]CI = X' ± Z\frac{a}{2}[/tex] * (σ/√n)

here:
X' = sample mean
Zα/2 = z-score that corresponds to the desired level of confidence (in this case, 90%)
σ = population standard deviation
n = sample size

Placing the  values

CI = 2350 ± 1.645 * (175 / √12)
= [2146.47, 2553.53]

After calculating the 90% confident true mean income per month of a person who works from home in sales falls between $2146.47 and $2553.53.
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The equation represents a linear function.

What is quadratic equation?

A quadratic equation is a polynomial equation of degree two which can be written in the form: ax² + bx + c = 0, where x is the variable and a, b, and c are constants with 'a' not equal to 0. The term 'quadratic' comes from the Latin word 'quadratus', which means 'square'.

The equation given in the image is a quadratic equation in standard form, which means it is written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

To determine which statement is true about this equation, we need to analyze its discriminant, which is given by the expression b^2 - 4ac. The discriminant tells us about the nature of the solutions of the quadratic equation.

If the discriminant is positive, then the equation has two distinct real roots.

If the discriminant is zero, then the equation has one real root (also known as a double root).

If the discriminant is negative, then the equation has two complex roots (conjugate pairs).

In the given equation, a = 3, b = -4, and c = 1. Substituting these values into the discriminant formula, we get:

b^2 - 4ac = (-4)^2 - 4(3)(1) = 16 - 12 = 4

Since the discriminant is positive, we know that the quadratic equation has two distinct real roots. Therefore, statement (A) is true.

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The number of permutations of the letters in the word indistinguishable such that the strings git, tin, and nab do not appear in the permutation is

3,172,973,824,000

Let A be the set of stages that contain the string "git",

B be the set of changes that contain the string "tin", and

C be the set of stages that contain the string "nab".

We need to discover the number of stages that don't contain any of these strings, which is the same as finding the measure of the set (A∪B∪C)'.

Utilizing the guideline of inclusion-exclusion, we have:

|A∪B∪C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|

We need to discover |(A∪B∪C)'|, which is the complement of the set A∪B∪C. In this manner:

|(A∪B∪C)'| = n! - |A∪B∪C|

Now we have to discover the measure of the sets A, B, and C, and their convergences.

For set A, able to settle the string "git" in its put in 3! ways, and after that permute the remaining 14 letters in 14! ways. In this manner, |A| = 3!×14!.

Essentially, we will discover |B| = 3!×14! and |C| = 3!×14!.

For the convergences, we are able to settle the comparing strings in their places and permute the remaining 11 letters in 11! ways. In this manner,

|A∩B| = 2!×11!,

|A∩C| = 2!×11!,

and |B∩C| = 2!×11!.

At long last, we have |A∩B∩C| = 1!×11! since we are able to settle all three strings in their places and permute the remaining 11 letters in 11! ways.

Substituting these values into the inclusion-exclusion equation, we get:

|A∪B∪C| = 3(3!×14!) - 3(2!×11!) + 1!×11!

|A∪B∪C| = 13608000

Subsequently:

|(A∪B∪C)'| = 17! - 13608000

|(A∪B∪C)'| = 3172973824000

So there are 3,172,973,824,000 permutations of the letters within the word "indistinguishable" such that the strings "git", "tin", and "nab" don't show up within the stage. 

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The likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4%

To illuminate this issue, we will utilize Bayes' hypothesis. Let's characterize the taking after occasions:

A: the persistent is contaminated with HIV

B: the persistent tests positive for HIV

We need to calculate P(A|B), the likelihood that an understanding is contaminated with HIV given that they tried positive for HIV.

By Bayes' hypothesis:

P(A|B) = P(B|A) * P(A) / P(B)

where

1. P(B|A) is the likelihood of testing positive for HIV given that the persistent is tainted with HIV (97%)

2. P(A) is the predominance of HIV within the clinic (8%)

3. P(B) is the likelihood of testing positive for HIV, which can be calculated utilizing the law of adding up to likelihood:

P(B) = P(B|A) * P(A) + P(B|A') * P(A')

where

1. P(B|A') is the likelihood of testing positive for HIV given that the persistent isn't tainted with HIV (4%)

2. P(A') is the complement of A, i.e., the likelihood of a quiet not being tainted with HIV (1 - 8% = 92%)

Substituting the values we have:

P(B) = 0.97 * 0.08 + 0.04 * 0.92 = 0.0736

P(B) =  0.0736

Hence,

P(A|B) = 0.97 * 0.08 / 0.0736 ≈ 0.104

P(A|B) = 0.104

So the likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4% (adjusted to three decimal places). 

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