Determine the derivative of each function. Leave answers in simplified form. a) f(x)=2x4−3x3+6x−2 b) y=5/x4​ c) y (3x2−6x+1)7 d) y=e−x2−x e) f(x)=cos(5x3−x2) f) y=exsin2x g) f(x)=2x2/x−4​ h) f(x)=(4x+1)3(x2−3)4.

The length of a scale model of the scooter is 4 2/3 inches

Scale model involves enlarging or reducing the dimensions of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The scale model of the scooter is given as:

1 inch = 3/4 feet

The length of the scooter is given as:

Scooter = 3 1/2 feet

So, we have:

Scooter = 3 1/2 feet

1 inch = 3/4 feet

Cross multiply

Scooter * 3/4 feet = 1 inch * 3 1/2 feet

Cancel out the common units

Scooter * 3/4= 1 inch * 3 1/2

Evaluate the product

Scooter * 3/4= 3 1/2 inches

Divide both sides by 3/4

Scooter = 4 2/3 inches

Hence, the length of a scale model of the scooter is 4 2/3 inches

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Answer:

the answer is b

= 3 × 4

= 3 × 2²

x = 1

= 3 × 15 = 5x

= 45 /5 = x

= 9 = x

Answer:

Step-by-step explanation:

1. 4

2. 9

3. 7  ,14 , 21 , 28 ,35 , 42 , 49

4. 7 , 3

5. 527 , 752 , 572 , 725

6. 6 = d ( a / 2 )

   7 = e ( 2a )

   8 = a ( a * a )

   9 = b  ( 3a )

  10 = c ( 0 )

To solve equations with fractions and variables in the denominator, we need to eliminate it by moving it to the other side. To do this, we multiply both sides of the equation by the term in the denominator. This will cancel out the fraction and leave us with a simpler equation to solve.

For example, suppose we have the equation (3 + x) / x = 2. To get rid of the fraction, we multiply both sides by x. This gives us: x * (3 + x) / x = x * 2. The x in the numerator and denominator cancel out, leaving us with:

3 + x = 2x. Now we can solve for x by subtracting x from both sides: 3 = x

This is the solution of the equation.

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Answer: A) 71.498 ; b) 0.00152

Step-by-step explanation:

Given the following :

Number of atoms that decayed during 365 days period = 26,097

Number of days = 365

Mean number of radioactive atoms that decayed in a day:

Mean = number of decayed atoms / number rof days

Mean = 26,097 / 365

Mean = 71.498 atoms per day

B.) probability that 50 radioactive atoms decayed in a given day:

Using the poisson distribution formula :

P(x =x) = (m^x * e^-m) ÷ x!

Where m = mean

Mean (m) = 71.498

P(x = 50) = (71.498^50 * e^-71.498) / 50!

P(x = 50) = (71.498^50 * 2.7182818^-71.498) / 50!

= 4.60795E61 / 50!

= 0.0015150

4x² +x +19, is the standard equation. of the quadratic equation

Equatiοns are statements in mathematics that have twο algebraic expressiοns οn either side οf the equals (=) sign.

It shοws that the expressiοns printed οn the left and right sides have an equal relatiοnship.

In any mathematical equatiοn, we have LHS = RHS (left hand side = right hand side).

Equatiοns can be sοlved tο find the value οf an unknοwn variable that represents an unknοwn quantity.

If there is nο "equal tο" symbοl, a statement is nοt an equatiοn.

When twο expressiοns have equal values, a mathematical statement knοwn as an equatiοn includes the symbοl "equal tο" between them.

Hence, 4x² +x +19, is the standard equatiοn

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Answer:

Ciera is driving at a faster rate.

Step-by-step explanation:

You calculate speed, by dividing distance by time.

So 18 divided by 24 is 0.75. That is Ciera's speed.

And then to calculate the other person/thing's speed you have to divide 46 by 60 minutes (equal to one hour). The speed calculates to 0.7666666667

Therefore, Ciera is driving faster.

Answer:

double displacement reaction

Step-by-step explanation:

more ex:

NaOH +HCl =NaCl + H2O

Answer:

The sale this month = 79

Step-by-step explanation:

Let the amount he needs to sell this month = x

\(Average = \frac{sum\ of\ individual\ data\ }{number\ of\ entries}\)

\(Average= \frac{90\ +\ 45\ +\ 103\ +\ 68\ +\ x}{5}\)

Note that number of entries = number of months = 5

To maintain an average sales of 77, the amount of sale in month 5 is determined as follows:

\(77 = \frac{306\ +\ x}{5} \\cross-multiplying\\77\ \times\ 5\ = 306\ +\ x\\385 = 306\ +\ x\\x =385\ -\ 306\\x = 79\)

Answer: 2/9 is the slope

By using the Pythagorean identity and applying the half-angle formula for cosine, we can determine the value of cosθ/2. So, the exact value of cosθ/2, given that tanθ = 3/2 and 180° < θ < 270°, is \(\sqrt{\frac{(\sqrt{13} - 2) }{(2\sqrt{13})}}\).

We are given that tanθ = 3/2 and θ lies in the range 180° < θ < 270°. To find the value of cosθ/2, we first need to determine the value of cosθ.

Since tanθ = 3/2, we can construct a right-triangle in the third quadrant, where the opposite side is 3 units and the adjacent side is 2 units. By using the Pythagorean theorem, we can find the length of the hypotenuse, which is \(\sqrt{(3^2 + 2^2)} = \sqrt{13}\).

Now, let's find the value of cosθ. In the third quadrant, cosθ is negative, and since tanθ = 3/2, we have sinθ = -3/√13 and cosθ = -2/√13.

To find cos(θ/2), we can use the half-angle formula for cosine:

cos(θ/2) = ± √[(1 + cosθ) / 2].

Substituting the value of cosθ = -2/√13, we have:

cos(θ/2) = ± \(\sqrt{\frac{(1 - \frac{2}{\sqrt{13}}) }{2}}\)

Simplifying further:

cos(θ/2) = ± \(\sqrt{\frac{(\sqrt{13} - 2) }{(2\sqrt{13})}}\)

Since θ lies in the range 180° < θ < 270°, θ/2 lies in the range 90° < θ/2 < 135°. In this range, cos(θ/2) is positive.

Therefore, the exact value of cosθ/2 is \(\sqrt{\frac{(\sqrt{13} - 2) }{(2\sqrt{13})}}\)

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The population would be all the used passenger cars available for purchase in Cynthia's area, while the sample would be the subset of passenger cars that Cynthia looked at in the local used automobile publication and on a local internet site.

The population is the entire group being studied, while the sample is a subset of the population that is being studied to gain information about the population. In statistics, the sample should be representative of the population, and the sample size should be large enough to give an accurate representation of the population.

There are various types of sampling methods:

Simple random sampling: Each member of the population has an equal chance of being selected.

Stratified sampling: The population is first divided into homogeneous subgroups called strata, and then a simple random sample is taken from each stratum.

Cluster sampling: The population is first divided into heterogeneous subgroups called clusters. A random sample of clusters is taken, and then data is gathered from each member of the selected clusters.

Systematic sampling: Every kth member of the population is chosen after the first member has been randomly selected.In order to gain information about the population, a sample is used. The sample is a subset of the population that has been selected for research purposes. The goal of the sample is to gather data that is representative of the population.

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The expression in simplest form that represents the total cost for x students is 11.55x, the correct option is C.

Expression in mathematics can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that a student in a math class has to buy the items in the table.

Now,

x(9.65+0.65+1.25)

=9.65x+0.65x+1.25x

=11.55x

Therefore, the expression in simplest form will be 11.55x.

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Answer:

Step-by-step explanation:

Subset of A = { {} , {a} , {b}, {a.b} }

Answer:

Here is the sample space:

(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3)

SOLUTION

Recall the compound ineterse formula:

From the question it follows:

Substituting values gives:

Solving for A gives:

Therefore the amount to be paid back is $65039

An inequality that represents the situation is s > 140.

Let's use "s" to represent the number of milligrams of sodium in a serving.

Since a serving of food does not qualify as low sodium if it contains more than 140 milligrams of sodium, we can write the inequality:

s > 140

This inequality reads "s is greater than 140", indicating that any value of "s" that is greater than 140 milligrams of sodium per serving does not qualify as low sodium.

To graph this inequality, we can represent "s" on the vertical axis and mark the value of 140 with a dashed line.

Since the inequality is greater than 140, we shade the area above the line to represent all the possible values of "s" that do not qualify as low sodium.

The resulting graph would look like given in the attached image.

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The complete question:

Write and graph an inequality that represents the number of sodium 's' in a serving that does not qualify as low sodium.

For a food to be labeled low sodium, there must be no more than 140 milligrams of sodium per serving.

Therefore, Caleb paid approximately $14,067.90 for the shares.

Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.

Selling price = 130% of the amount paid

$18,189.27 = 1.3 * x

To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:

x = $18,189.27 / 1.3

Calculating this, we find:

x ≈ $14,067.90

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Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

It is simply the largest of the common factors.

We have:

12x³- 18x² + 6x

We find GCF of 12, 18 and 6:

GCF(12, 18, 6) = 6

12 = 2 · 6

18 = 3 · 6

6 = 1 · 6

and GCF of x³, x² and x:

GCF(x³, x², x) = x

x³ = x² · x

x² = x · x

x = 1 · x

Therefore:

Answer:

C

Step-by-step explanation:

I honestly put the question into a calculator for side angle side triangles

Considering the t-test applied, the number of degrees of freedom is given by:

d. 10.

For a sample of size n, the number of degrees of freedom is given by:

df = n - 1

When there are m samples, the amount of degrees of freedom is m multiplied by the sum of degrees of freedom of each sample.

In this problem, there are 2 samples with 6 - 1 = 5 df, hence:

2 x 5 = 10.

Option d is correct.

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By using Chebyshev's inequality, n = (o² * δ) / e² samples are sufficient to guarantee that P(|Sn - u| > e) < δ for the sample mean estimator.

In order to solve this question we need to consider Optimal Mean Estimation via Concentration Inequalities and use sample mean and median of means estimator.

To find the sample size n that guarantees P(|û - u| > e) < δ using Chebyshev's inequality, follow these steps:

1. Define Sn as the sample mean estimator:

Sn = (1/n) * Σ(Xi) for i = 1 to n.

2. We know the variance o² is known, and Chebyshev's inequality states that P(|X - E(X)| > k * σ) ≤ 1/k², where X is a random variable, E(X) is the expected value of X, σ is the standard deviation, and k is a constant.

3. Apply Chebyshev's inequality to Sn - u:

P(|Sn - u| > k * (o / sqrt(n))) ≤ 1/k², where k = e * sqrt(n) / o.

4. We want P(|Sn - u| > e) < δ, so we can rewrite Chebyshev's inequality as 1/k² < δ. Substitute k with e * sqrt(n) / o: 1/((e * sqrt(n) / o)²) < δ.
5. Solve for n: n = (o² * δ) / e².

By using Chebyshev's inequality, n = (o² * δ) / e² samples are sufficient to guarantee that P(|Sn - u| > e) < δ for the sample mean estimator.

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MY WORK:

First, you would cut it up into different parts/shapes

(I cut it up into rectangles)

Then, you would find the area of each.

The bottom rectangle: 10 ( 5 times 2 )

The middle rectangle: 12 ( 6 times 2 )

The top rectangle: 8 ( 4 times 2 )

Lastly, you would add!

10 + 12 + 8 = 30

Therefore, the answer is...

30!

My apologies if this is wrong but I hope I helped a little bit!

the probability that she picks 2 different types of drink is 71 / 105

let say E is an event then ,P(E) = favourable outcome /total outcome

given that ,

3 bottles of orange juice.

5 bottles of apple juice.

7 bottles of water.

Then  total of 3 + 5 + 7 = 15 bottles of drinks .

To calculate the probability of picking 2 different types of drinks, we need to calculate the total number of possible pairs of drinks that can be picked, and the number of pairs that consist of different types of drinks.

so,

The total number of possible pairs of drinks that can be picked is given by the combination formula:

C(15, 2) = 15! / (2! * (15-2)!) = 105

This formula calculates the number of ways to choose 2 items from a set of 15 items.

Now, the number of pairs that consist of different types of drinks. There are three types of pairs : orange juice and apple juice, orange juice and water, and apple juice and water.

The number of pairs of different types of drinks :

(3 * 5) + (3 * 7) + (5 * 7) = 15 + 21 + 35 = 71

So, the probability of picking 2 different types of drinks is:

71 / 105 ≈ 0.6762 or about 67.62%.

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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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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x and y are 166/12 and 56/18.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

2x + 3y = 37 ______(1)

4x - 2y = 18 _______(2)

From (1) we get,

2x = 37 - 3y

x = (37 - 3y)/2 ______(3)

Putting (3) in (2) we get,

4 [ (37 - 3y)/2 ] - 2y = 18

2(37 - 3y) - 2y = 18

74 - 6y - 2y = 18

74 - 8y = 18

74 - 18 = 8y

56 = 18y

y = 56 / 18 _____(4)

Now,

Putting (4) in (3) we get,

x = [37 - 3 x 56/18] / 2

x = (37 - 56/6)/2

x = (222 - 56) / 12

x = 166/12

Thus,

The value of x and y are 166/12 and 56/18.

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Answer:

A

Step-by-step explanation:

Since it's the 100th term you multiply -5 by 100 and then you add the number together

Answer:

Step-by-step explanation:

Use the nth term formula:

Substitute values:

Correct choice is D