Help please!!!!!!!!!!!

Answer:

[tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative Property [Addition/Subtraction]:                                                            [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                               [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{3x + 5}{\sqrt{x}}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

80 telephones should be sampled

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

89% confidence level

So [tex]\alpha = 0.11[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.11}{2} = 0.945[/tex], so [tex]Z = 1.6[/tex].

How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?

n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.09 = 1.6\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.09\sqrt{n} = 1.6*0.5[/tex]

[tex]\sqrt{n} = \frac{1.6*0.5}{0.09}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.6*0.5}{0.09})^2[/tex]

[tex]n = 79.01[/tex]

Rounding up(as 79 gives a margin of error slightly above the desired value).

80 telephones should be sampled

Answer:

0.0106 = 1.06% probability that 2 or fewer will withdraw

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they withdraw, or they do not. The probability of an student withdrawing is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

25% of its students withdraw without completing the introductory statistics course.

This means that [tex]p = 0.25[/tex]

Assume that 30 students registered for the course.

This means that [tex]n = 30[/tex]

Compute the probability that 2 or fewer will withdraw:

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{30,0}.(0.25)^{0}.(0.75)^{30} = 0.0002[/tex]

[tex]P(X = 1) = C_{30,1}.(0.25)^{1}.(0.75)^{29} = 0.0018[/tex]

[tex]P(X = 2) = C_{30,2}.(0.25)^{2}.(0.75)^{28} = 0.0086[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0002 + 0.0018 + 0.0086 = 0.0106[/tex]

0.0106 = 1.06% probability that 2 or fewer will withdraw

Answer:

16 sq units

Step-by-step explanation:

[tex]2(2x + 4) + 2(x - 7) = 78[/tex]

[tex]4x + 8 + 2x - 14 = 78[/tex]

[tex](4x + 2x) + (8 - 14) = 78[/tex]

[tex]6x - 6 = 78[/tex]

[tex]6x = 78 + 6[/tex]

[tex]6x = 84[/tex]

[tex]x = \frac{84}{6} [/tex]

[tex]x = 14[/tex]

Answer:

30 minutes

Step-by-step explanation:

that problem description is imprecise.

I think what is meant here : they each keep jogging at their own same speed.

Diane's speed is 1/3 miles / 10 min.

Jack's speed is 2/3 miles / 10 min.

now, to bring this to regular miles/hour format, we need to find the factor between 10 minutes and an hour (60 minutes) and multiply numerator and denominator (top and bottom of the ratio) by it.

60/10 = 6.

so, we need to multiply both speeds up there by 6/6 to get the miles/hour speeds.

Diane : (1/3 × 6) / hour = 2 miles / hour

Jack : (2/3 × 6) / hour = 4 miles / hour

since Jack is running twice as fast as Diane, she will finish one length in the same time he finishes a round trip (back and forth).

Diane running 1 mile going 2 miles/hour takes her 30 minutes.

Jack running 2 miles (back and forth) going 4 miles/hour will take him also 30 minutes.

so, they will meet at his starting point after 30 minutes.

Answer:

6.284

Step-by-step explanation:

* means multiply

formula is arc length = radius * theta

theta is fancy way of saying

make degrees into radians

you have to make 60 degrees into radians

you do that by

60 * Pi/180 = Pi/3

then you multiply that with the radius

6 * Pi/3 = 2 * Pi = 6.284

Answer:

Step-by-step explanation:

The measure for each angle is shown below.

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Given:

As, ∆ABC and ∆DBE is an equilateral triangle.

In Equilateral Triangle all the angles are Equal.

So,  4x+ 3= 9x- 7

5x = 50

x= 10

and, <1 = <9 = 4x+ 3= 43

and, <4 = <5 = <6 = 180/ 3= 60

ans, <3 = <8 = 180-60= 120

Also, <2 = < 7 = 180- <1- <3= 17

Learn more about Equilateral Triangle here:

https://brainly.com/question/3461022

#SPJ2

Answer:

interval?

Step-by-step explanation:

I'm not sure. I think so....hope its correct :)

Answer:

Here,

Angle TUV + Angle NUV=TUV

By substituting the provided or given value ls in the question we obtain,

1+38x+66 Degree= 105x

1+66 Degree= 67x

67 Degree= 67x

1 Degree = x

x = 1 Degree

Therefore

Angle TUN=1+38x=39

Angle NUV=66 Degree

Therefore

1+38x+66 Degree= 105x

=39 Degree+66 Degree= 105 Degree

Therefore

Angle TUV=105 Degree

Answer:

total pencil = 5 orange pencils + 8 yellow pencils + 4 green pencils

= 17 pencils

P (g n y) = 4/17 + 8/17

= 0.706

Step-by-step explanation:

1. first find the total number of pencils

2. since there is a replacement the demoinator remains the same

3. find the probability of each green and yellow

4. add the two probability

Answer:

1/4

Step-by-step explanation:

The answer is 1/4.

1/2 is equivalent to 2/4.

2/4-1/4=1/4

Answer:

1) 0.6838

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

35.45% of small businesses experience cash flow problems in their first 5 years.

This means that [tex]p = 0.3545[/tex]

Sample of 530 businesses

This means that [tex]n = 530[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.3545[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.3545(1-0.3545)}{530}} = 0.0208[/tex]

What is the probability that between 34.2% and 39.03% of the businesses have experienced cash flow problems?

This is the p-value of Z when X = 0.3903 subtracted by the p-value of Z when X = 0.342.

X = 0.3903

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.3903 - 0.3545}{0.0208}[/tex]

[tex]Z = 1.72[/tex]

[tex]Z = 1.72[/tex] has a p-value of 0.9573

X = 0.342

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.342 - 0.3545}{0.0208}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a p-value of 0.27425

0.9573 - 0.2743 = 0.683

With a little bit of rounding, 0.6838, so option 1) is the answer.

Answer:

Independent

Step-by-step explanation:

From the word independent, which means being able ot stand alone, that is the absence or presence of one has no impact on the outcome of each phenomenon. Two events A and B are said to be independent, if the occurence of one has no bearing on the probability or chance that B will occur. This means that each event occurs without reliance on the occurence of the other. This is different from mutually exclusive event whereby event A has direct bearing in the probability of the occurence of event B.

Answer:

Yes it is. Graph will go down as it moves from left to right.

Step-by-step explanation:

This question is incomplete, the complete question is;

In the year 2005, the age-adjusted death rate per 100,000 Americans for heart disease was 222.3. In the year 2009, the age-adjusted death rate per 100,000 Americans for heart disease had changed to 213.4.

a) Find an exponential model for this data, where t = 0 corresponds to 1999

Answer:

the exponential model for this data will be; y = 222.3( 0.9898 )^t

Step-by-step explanation:

Given the data in the question;

{ 2005 }, at t = 0, death rate was 222.3

In 2009, { 2009 - 2005 = 4 }, at t = 4 death rate was 213.4

Now, let the exponential equation be;

y = ab^(t)

so at t = 0

222.3 = a × b^(0)

222.3 = a × 1

a = 222.3

at t = 4

213.4 = a × b^(4)

213.4 = 222.3 × b^(4)

b⁴ = 213.4 / 222.3

b = (  213.4 / 222.3 )^(1/4)

b = 0.9898

y = ab^(t)

Hence, the exponential model for this data will be; y = 222.3( 0.9898 )^t

Answer:

b) 6.68%

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean score on the scale is 50. The distribution has a standard deviation of 10.

This means that [tex]\mu = 50, \sigma = 10[/tex]

Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?

The proportion is 1 subtracted by the p-value of Z when X = 65. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{65 - 50}{10}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

1 - 0.9332 = 0.0668

0.0668*100% = 6.68%

So the correct answer is given by option b.

Answer:

i think the mistake was in step 1

Step-by-step explanation:

Answer: (5) -5 > -18​

Step-by-step explanation:

-5 is 5 away from zero, making it larger than -18 since it's closer to 0, while -18 is 18 away from zero.

Hi there!  

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I believe your answer is:  

[tex]w = 5, -5[/tex]

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Here’s why:  

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Therefore:

[tex]w =\pm5[/tex]

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Hope this helps you. I apologize if it’s incorrect.  

Answer:r=v^2/A

Step-by-step explanation: To solve for r means you have to isolate r on one side and put all the other terms on the other. To get r out from under the fraction, multiply both sides by r. This leaves:

A*r=v^2     so to isolate r, divide by A and get:

r=v^2/A.

Answer:

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.

Step-by-step explanation:

idontknow

Answer:

35x^2 - 28x - 7

Step-by-step explanation:

Answer:

Cluster sample

Step-by-step explanation:

i did it before

Answer:

The answer is "0.9102"

Step-by-step explanation:

P(student spell correct) = 0.6

P(student spell incorrect)=1-0.6=0.4

X=the pupil will be allowed to sit down after receiving three slaps on the hand Thus, X would assume Value

X=0 (student sit sans getting whacks)

X=1 (student sit down without receiving 1 whack) (student sit down without receiving 1 whack)

X=2 (student take a seat before receiving 2 whacks)

X=3 (student sit down after receiving 3 punches)

[tex]\to P(X)=0.6 \times 0.4^0 +0.6 \times 0.4 + 0.6 \times 0.4 ^2 + 0.6 \times 0.3^3[/tex]

             [tex]=0.6 \times 1+0.24 + 0.6 \times 0.09 + 0.6 \times 0.027\\\\=0.6 +0.24 + 0.054 + 0.0162\\\\=0.9102\\\\[/tex]

Answer:

∠AED

Step-by-step explanation:

Vertical angles are the opposite angles of intersecting lines. ∠BEC and ∠AED are opposite and would therefore also be congruent angles.

Answer:

[tex]\angle BEC=\angle AED [vertical ~angle][/tex]

[tex]\angle AED~vertical~ angle ~to~ \angle BEC[/tex]

[tex]ANSWER:\angle AED[/tex]

-----------------------------

hope it helps...

have a great day!!

The answer is (a)..........

Answer:

Cardinality of the power set of the given set = [tex]2^6=64[/tex]

Step-by-step explanation:

Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.

Example set:

{1,2,3}

All the possible subsets of this set:

{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}

The power set of the above set is written as:

P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })

Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.

Cardinality of the power set of a given set is expressed by a formula: [tex]2^n[/tex]

where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.

Hence in the given case, we have  n = 6.

Answer:

7.3

Step-by-step explanation:

When you round, you look at the number to the right of which you are rounding to.

1 decimal place would be the tenths place.

7.263

So we would look at the 6, in the hundredths place.

6 is larger than 5, so 2 would be bumped up to 3.

7.3.

I hope this helps!

Answer:

7.3

Step-by-step explanation:

rounding up from 7.263 is 7.3