Find an equation of the tangent line to the graph of: f(x) = 3x3 - 2x at (2, 20)

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The translation is as shown in the figure in option B

Translation transformation is a type of geometric transformation that moves every point of a figure the same distance and direction. This transformation does not change the size, shape, or orientation of the figure, but only its position in space.

The transformation required ahs the rule defined as

Applying the rule arrives the image in option B

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The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

$20.70

Step-by-step explanation:

5 × $3.70 = $18.50 + $2.20 =

$20.70

Let X be the number of people who experience mild side effects after taking the drug. X follows a binomial distribution with parameters n = 100 (the number of people taking the drug) and p = 0.75 (the probability of mild side effects).

To find the probability that more than 70 people will experience mild side effects, we need to calculate:

P(X > 70) = 1 - P(X ≤ 70)

Using the cumulative distribution function (CDF) of the binomial distribution, we can find:

P(X ≤ 70) = F(70) = ∑(i=0 to 70) [nCi * p^i * (1-p)^(n-i)]

where nCi is the binomial coefficient for choosing i items out of n.

We can use a software or calculator to calculate this sum, or use an approximation like the normal approximation to the binomial distribution.

Assuming normal approximation is appropriate, with mean μ = np = 75 and standard deviation σ = sqrt(np(1-p)) = 3.354, we can calculate the z-score:

z = (70.5 - μ) / σ = (70.5 - 75) / 3.354 = -1.33

Using a standard normal distribution table or a calculator with normal distribution functions, we can find the probability of z-score less than -1.33 is 0.0918, which is the probability of 70 or fewer people experiencing mild side effects.

Therefore, the probability of more than 70 people experiencing mild side effects is:

P(X > 70) = 1 - P(X ≤ 70) = 1 - 0.0918 = 0.9082

Using the binomial distribution, there is a probability of approximately 0.9082 that more than 70 people will experience mild side effects out of 100 people who take the drug.

From 125 yards, a marksman hit 55.6 of the targets last year, which is equal to (55.6 × 100)% that is 5560%

A percentage (from Latin: per centum, "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A percentage is a dimensionless (pure) number; it does not have a unit of measurement.

A percentage is a fraction or a ratio in which the full number is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of a possible 100. It is written as 30/100 in fraction form and 30:100 in ratio form.

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Full question

Rewrite the decimal in the sentence below as a percentage.

From 125 yards away, a marksman hit 55.6 of the targets last year.

300000 in standard form is 3 x 10^5.

To convert a number to standard form, you need to express it as a number between 1 and 10 multiplied by a power of 10.

Here are the steps to convert a number to standard form:

1.Count the number of digits in the original number.

2.If the original number is greater than or equal to 10, then move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point. This will be the power of 10 in the standard form.

3.If the original number is less than 1, then move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. Count the number of places you moved the decimal point. This will be a negative power of 10 in the standard form.

4.Write the original number with the decimal point in its new position, and multiply it by 10 raised to the power determined in step 2 or step 3.

Answer:

standard form is used when numbers are very large or very small.

300000=3×10000

=3×104

this is now written in standard form

Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Step-by-step explanation:

hope this helps

Equations are represented with the = sign. It means both sides of the equation are equal. \(11=t+11.5-t\) has no solution

Given that:

\(11=t+11.5-t\)

Start by collecting like terms

\(11-11.5=t-t\)

Evaluate like terms

\(-0.5 = 0\)

-0.5 is not equal to 0.

Hence, the equation has no solution

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The coordinates of point Q that is 2/3 of the way along the directed segment from R(-7,-2) to S(2,4) is \((\frac{-17}{5} ,\frac{2}{5} )\)

Explanation :

the coordinates of point Q that is 2/3 of the way along the directed segment from R(-7,-2) to S(2,4)

Apply section formula to find coordinates of point Q

\((\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n} )\)

Ratio m:n is 2:3 and point R is (x1,y1) , point S is (x2,y2)

Substitute all the values inside the formula

\((\frac{2(2)+3(-7)}{2+3} , \frac{2(4)+3(-2)}{2+3} )\\\\(\frac{-17}{5} ,\frac{2}{5} )\)

The coordinates of point Q is \((\frac{-17}{5} ,\frac{2}{5} )\)

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Answer: 75th term

Step-by-step explanation:

If you look at the first terms, you can see that we're subtracting 12 from the previous term to get the number. Knowing this, we can write an expression for the nth term. The expression would be -12n + 20. Since this specific term has value of -880, we set -880 equal to the value of -12n+20. By setting your equation like this -12n + 20 = -880 and solving, you get n = 75, which means the 75th term has a value of -880.

Answer:

Step-by-step explanation:

Based on the given conditions, formulate: 24 times 5 dived ( 5 + 3 )

Calculate the product or quotient: {120}{5 + 3}

Calculate the sum or difference: 120}{8}

Cross out the common factor:15

get the result:15

Answer: 15

D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.

Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.

We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:

(PDP^(-1))^2 = PDP^(-1) + 1.

Expanding the square and applying the matrix multiplication rules, we get:

PD^2P^(-1) = PDP^(-1) + 1.

Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:

P(D^2)P^(-1) = PDP^(-1) + 1.

Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:

D^2 = D + 1.

This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.

Therefore, the correct answer is D) A^2 = A + 1.

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The equation of the trigonometric graph is 3cosx/4.

A trigonometric graph is a graphical representation of a trigonometric function, which is a mathematical function that relates an angle of a right triangle to the ratio of two sides of the triangle. The most commonly used trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

Trigonometric graphs are typically plotted on a coordinate plane, with the horizontal axis representing the angle in radians or degrees, and the vertical axis representing the value of the function. The shape of the graph depends on the specific trigonometric function being plotted, as well as the amplitude and period of the function.

The sine function, for example, produces a wave-like graph that oscillates between -1 and 1, with a period of 2π. The cosine function produces a similar wave-like graph, but with a phase shift of π/2, so that the maximum value occurs at x = 0 instead of x = π/2. The tangent function produces a graph that is asymptotic to vertical lines, with vertical asymptotes occurring at regular intervals.

Now the graph when comes at point zero then its value is 1. which is the property of the cosine .

so equation of the trigonometric graph is  3cosx/4.

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The correct answer is C. $11,250.

To calculate the interest on a 90-day, 9% note for $50,000, we can use the simple interest formula:

Interest = Principal × Rate × Time

Given:

Principal (P) = $50,000

Rate (R) = 9% = 0.09 (decimal)

Time (T) = 90 days

Since the interest is calculated based on a 360-day year, we need to convert the time in days to a fraction of a year:

Time (T) = 90 days / 360 days = 0.25 (fraction of a year)

Now we can calculate the interest:

Interest = $50,000 × 0.09 × 0.25

Interest = $11,250

Rounded to the nearest dollar, the interest on the 90-day, 9% note for $50,000 is $11,250.

Therefore, the correct answer is C. $11,250.

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Dan could be charged with larceny, which is a felony offense in some states.

Dan could be charged with larceny, which is the taking of another person's property without their permission or consent. In this case, Dan took money from the tip jar without the permission of the ice cream shop or its owners. In some states, this type of larceny is considered grand larceny, which is a felony offense.

Larceny is a crime of intent, meaning that the perpetrator had the intent to deprive the victim of their property permanently. In the case of Dan, he intended to take the money from the tip jar for his own use, not to return it. As such, he could be charged with larceny.

In some states, the punishment for grand larceny is prison time or fines, and the length of the sentence or amount of the fines is determined by the value of the stolen property. In this case, the stolen property was five dollar bills, so the sentence or fine could be quite severe.

It is important to note that in some states, a minor's age may be taken into account when determining the sentence for a crime such as this one. For example, if Dan was a minor, his sentence could be reduced or his charges could be dropped altogether.

In conclusion, Dan could be charged with larceny, which is a felony offense in some states. Depending on the laws of the state, the age of the perpetrator, and the value of the stolen property, Dan could face prison time, fines, or a combination of both.

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1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Its C. He substituted incorrectly when calculating the constant of variation.

Reason: He said so

The first error in Nick's work is he substituted incorrectly when calculating the constant of variation. The correct answer is C.

The unknown term which is need to be calculated using system of equations is called variable.

Given  s= 4, t= 12 to calculate value of k in the equation

s = kt²

4 = k (12)²

k = 0.02777

Thus, the first error he made is substituted incorrect values while calculating constant k.

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The correlation coefficient between the student's height and the distance they were able to jump is -1.13.

To compute the correlation coefficient (r) between the person's height and the distance they were able to jump, we need to use the given formula:

\(r = \sum (xi - \bar x)(yi -\bar y) / \sqrt{(\sum (xi - \bar x)^2 * \sum (yi -\bar y)^2)\)

Where:

In our case,

\(\bar x\) = 64.44

\(\bar y = 6.06\)

Square the differences and sum them:

\(\sum ((xi -\bar x)^2) =307.84\\\\\sum ((yi -\bar y )^2) = 2.7224\)

Calculate the correlation coefficient using the formula:

\(r = -32.63 / \sqrt{(307.84 * 2.7224)}\\\\r = -32.63 / \sqrt{838.74158}\\\\\r = -32.63 / 28.96\\\\r = -1.128\)

Therefore, the correlation coefficient (r) for the linear fit between height and jump distance is approximately -1.13.

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Bayes' rule involves three main elements:

Prior Probability: The prior probability represents our initial belief or knowledge about the probability of an event or hypothesis before considering any new evidence. It is typically denoted as P(H), where H represents the hypothesis or event. The prior probability is based on previous experience, background information, or subjective assessments.

Likelihood of the Evidence: The likelihood is the probability of observing the given evidence (E) assuming that the hypothesis (H) is true. It is denoted as P(E|H), where P(E|H) represents the probability of the evidence E given the hypothesis H. The likelihood quantifies how well the hypothesis explains the observed data or evidence.

Posterior Probability: The posterior probability represents the updated probability of the hypothesis or event given the observed evidence. It is denoted as P(H|E), where P(H|E) represents the probability of the hypothesis H given the evidence E. The posterior probability is the main result of applying Bayes' rule and combines the prior probability with the likelihood of the evidence.

Mathematically, Bayes' rule is expressed as:

P(H|E) = (P(E|H) * P(H)) / P(E)

Here, P(H|E) is the posterior probability, P(E|H) is the likelihood, P(H) is the prior probability, and P(E) is the probability of the evidence.

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Bayes' rule involves three main elements:

Prior Probability:

The prior probability represents our initial belief or knowledge about the probability of an event or hypothesis before considering any new evidence. It is typically denoted as P(H), where H represents the hypothesis or event.

The prior probability is based on previous experience, background information, or subjective assessments.

Likelihood of the Evidence:

The likelihood is the probability of observing the given evidence (E) assuming that the hypothesis (H) is true. It is denoted as P(E|H), where P(E|H) represents the probability of the evidence E given the hypothesis H.

The likelihood quantifies how well the hypothesis explains the observed data or evidence.

Posterior Probability:

The posterior probability represents the updated probability of the hypothesis or event given the observed evidence. It is denoted as P(H|E), where P(H|E) represents the probability of the hypothesis H given the evidence E.

The posterior probability is the main result of applying Bayes' rule and combines the prior probability with the likelihood of the evidence.

Mathematically, Bayes' rule is expressed as:

P(H|E) = (P(E|H) * P(H)) / P(E)

Here, P(H|E) is the posterior probability, P(E|H) is the likelihood, P(H) is the prior probability, and P(E) is the probability of the evidence.

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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On rationalizing the expression 7/(2-√5) 7/(2-√5), the value is obtained as -7 (2 + √5).

What is rationalization?

In order to get rid of the irrational number in the denominator, the procedure of rationalisation is performed in elementary algebra. There are numerous rationalisation strategies that are used on the denominator.

The given expression is - 7/(2-√5).

Multiply the denominator and numerator by the (2 + √5).

= 7 × (2 + √5)/(2-√5) × (2 + √5)

= (14 + 7√5)/(2)² - (√5)²

Simplify it further -

= (14 + 7√5)/4 - 5

= (14 + 7√5)/-1

= -(14 + 7√5)

= -7 (2 + √5)

Therefore, the simplified expression is -7 (2 + √5).

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The two linear expressions:

-(3x - 7 - 1/2) and 7.5 - 3x

Are equivalent expressions.

Here we are given two linear expressions:

-(3x - 7 - 1/2)

and:

7.5 - 3x

And we want to see if these are equivalent, to check that, we just need to see if we can rewrite one of the equations into the other.

If we start with the first one:

-(3x - 7 - 1/2)

And we simplify it we will get:

-(3x - 7 - 1/2)

-(3x - 7 - 0.5)

-(3x - 7.5)

Now remember the rule of signs, we can expand the above expression as:

-(3x - 7.5)

-3x + 7.5

This is the other expression, so we conclude that the two linear expressions are equivalent.

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Answer:

11.5 hrs

Step-by-step explanation:

Divide 230 by 25. Then multiply your quotient by 1.25 which is 1 1/4 to get the number of hours. 230 divided by 25 is 9.2. 9.2 times 1.25 is 11.5

Hope This Helps!

Step-by-step explanation:

f(x) = 2x² - 5x

= f(x-4) + f(x)

= [2.(x-4)² - 5.(x-4)] + [2x² - 5x]

= [2.(x² - 8x + 16) - 5x + 20] + [2x² - 5x]

= [2x² - 16x + 32 - 5x + 20] + [2x² - 5x]

= [2x² - 21x + 52] + [2x² - 5x]

= 4x² - 26x + 52

Total 250 adult tickets are sold.

Let a = number of adult tickets sold

Let s = number of student tickets sold

a + s = 553

s = a + 53

From above equations;

a + a + 53 = 553

2a = 553 - 53

2a = 500

a = 250

Total 250 adult tickets are sold.

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To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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