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Timmy and Tommy are two boys whose ages add up to 23. Timmy is 5
years older than Tommy. How old are they?

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:

Step-by-step explanation:

Solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is [tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

" Trigonometric ratios are defined as relation of the ratio of the sides of the triangle to the acute angle of the given triangle enclosed in it."

Formula used

[tex]cosec\theta = \frac{1}{sin\theta}[/tex]

According to the question,

Given trigonometric ratio equation,

[tex]\sqrt{3} (cosec\theta) -2=0[/tex]

Replace trigonometric ratio [tex]cosec\theta[/tex] by [tex]sin\theta[/tex]  in the above equation we get,

[tex]\sqrt{3} (\frac{1}{sin\theta} ) -2=0\\\\\implies \sqrt{3} (\frac{1}{sin\theta} ) = 2\\\\\implies sin\theta=\frac{\sqrt{3} }{2}[/tex]

As per given condition of the interval [ 0, 2π) we have,

[tex]\theta = sin^{-1} \frac{\sqrt{3} }{2} \\\\\ implies \theta = \frac{\pi }{3} or \frac{2\pi }{3}[/tex]

Hence, solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is

[tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

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Answer:

let x represent the bigger number

x+x-47=125

2x-47=125

2x=125+47

2x=172

2x/2=172/2

x=86

the smaller number=x-47

86-47

39

therefore the answer is a) 39 and 86

Answer:

A

Step-by-step explanation:

To find the sum of 125, you have to add the numbers.

39+86 = 125

To find the difference of 47, you have to subtract the numbers.

86-39 = 47

Answer: P = 4s

Step-by-step explanation:

P = 4s where s = the length of each side.  

Since each side of a square is the same length, the side length is multiplied by 4.

[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:

Frustum Volume =

[PI * height * (small radius^2 + (small radius * large radius) * + large radius^2)] / 3

Frustum Volume = PI * 10 * ( 1.5^2 + 1.5*3.75 + 3.75^2 ) / 3

Frustum Volume = 31.41592654 * (2.25 +5.625 +14.0625) / 3

Frustum Volume = (31.41592654 * 21.9375) / 3

Frustum Volume = 689.1868884713 / 3

Frustum Volume = 229.72896282 cubic cm

Source: http://www.1728.org/volcone.htm

Step-by-step explanation:

Answer:

0 is the answer assuming the whole thing is a fraction where the numerator is f(a+h)-f(a) and the denominator is h.

Step-by-step explanation:

If the expression for f is really a constant, then the difference quotient will lead to an answer of 0.

If the extra for f is linear (including constant expressions), the difference quotient will be the slope of the expression.

However, let's go about it long way for fun.

If f(x)=5, then f(a)=5.

If f(x)=5, then f(a+h)=5.

If f(a)=5 and f(a+h)=5, then f(a+h)-f(a)=0.

If f(a+h)-f(a)=0, then [f(a+h)-f(a)]/h=0/h=0.

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:

La moda es 23

Step-by-step explanation:

23 es el numero que mas se repite es decir la moda

Answer:

SSS or D on edge

Step-by-step explanation:

.

The three sides of triangle ΔBDA are equal to the three sides of triangle ΔBDC.

Reasons:

The given parameters are;

The common side to ΔBDA and ΔBD = BD

BC ≅ BA

AD ≅ DC

The two column proof is presented as follows;

Statement [tex]{}[/tex]                     Reasons

BC ≅ BA [tex]{}[/tex]                        Given

AD ≅ DC [tex]{}[/tex]                       Given

BD ≅ BD [tex]{}[/tex]                         By reflexive property

Therefore, we have;

The congruency theorem that can be used to prove ΔBDA ≅ ΔBDC is therefore;

The Side-Side-Side congruency rule states that if three sides of on triangle are congruent to three sides of another triangle, then the two triangles are congruent.

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The first sum is a geometric series:

[tex]1+\dfrac15+\dfrac1{5^2}+\dfrac1{5^3}+\cdots+\dfrac1{5^n}+\cdots=\displaystyle\sum_{n=0}^\infty\frac1{5^n}[/tex]

Recall that for |x| < 1, we have

[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

Here we have |x| = |1/5| = 1/5 < 1, so the first sum converges to 1/(1 - 1/5) = 5/4.

The second sum is exponential:

[tex]1+5+\dfrac{5^2}{2!}+\dfrac{5^3}{3!}+\cdots+\dfrac{5^n}{n!}+\cdots=\displaystyle\sum_{n=0}^\infty \frac{5^n}{n!}[/tex]

Recall that

[tex]\exp(x)=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]

which converges everywhere, so the second sum converges to exp(5) or e⁵.

I believe this is your question:

A.) find an angle between 0 degrees and 360 degrees that is coterminal with 570 degrees.

Answer:

210 degrees

Explanation:

Coterminal angles begin on the same initial side and end or terminate on the same side as an angle. Example 45 degrees and 405 degrees are coterminal angles because they both begin and end on the same side.

To find an angle between 0 and 360 that is coterminal with 570 degrees, w simply subtract 360 degrees from 570, hence:

570-360=210 degrees

570 degrees is coterminal with 210 degrees

Answer:

[tex]v \cdot w = 8.0[/tex]

Step-by-step explanation:

See comment for complete question

Given

[tex]|v| = |w| = 4[/tex] --- the side lengths

Required

[tex]v \cdot w[/tex]

[tex]v \cdot w = |v| \cdot |w| \cdot (cos\theta)[/tex]

From the question, we understand that v and w are sides of an equilateral triangle.

This means that:

[tex]\theta = 60^o[/tex] --- angles in an equilateral triangle

So:

[tex]v \cdot w = |v| \cdot |w| \cdot (\cos 60)[/tex]

So, we have:

[tex]v \cdot w = 4 * 4 * 0.5[/tex]

[tex]v \cdot w = 8.0[/tex]

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:

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:

35x^2 - 28x - 7

Step-by-step explanation:

Answer:

Frumpyton

Step-by-step explanation:

Since the standard deviation of Frumpyton is a lower number, this means a higher percentage of outcomes (job salaries) will be within a closer range to the mean salary. Since Frumpyton's standard deviation is $2,000 and the window your looking for is $32,000 to $36,000, if you go one interval up or down from the mean of $34,000, it falls in that range. Whereas, Dirtballville's standard deviation is $3,000 so it's more likely to fall outside of that range.

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:

Smallest: 18° Middle: 54° Largest: 108°

Step-by-step explanation:

We can start by writing out what we know in a series of equations:

s= smallest angle, m= medium angle, L= largest angle.

Since the largest is 6 times the smallest we have:

L=6s

Since the middle is 3 times the smallest we have:

m=3s

Since the 3 interior angle measures of a triangle always must equal 180°, we have:

s+m+L=180

Then we plug in our L and m into the third equation:

s+3s+6s=180

Combining like terms and solving:

10s=180

s=18

Then we plug in 18 for s into the first 2 equations to get:

L= 6* 18

L= 108

and

m= 3* 18

m= 54

So s= 18, m= 54, and L=108.

To check the answer we can:

Answer:

5

Step-by-step explanation:

x² - 4x = 5

x² - 4x - 5 = 0

the solution of a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

a = 1

b = -4

c = -5

x = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2

x1 = (4 + 6)/2 = 5

x2 = (4 - 6)/2 = -1

since we are looking only for a positive number, x=5 is the answer.

Answer Deleted

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Answer:

The two equivalent expressions are 6(x − y) and 6x − 6y.

Step-by-step explanation:

Answer:

interval?

Step-by-step explanation:

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

(B)

Step-by-step explanation:

The graph has zeros at x = -5 and x = 3 and passes through (4, 9). We can write the equation for the graph as

[tex]y = (x + 5)(x - 3) + c[/tex]

Since the graph passes through (4, 9), we can solve for c, which gives us c = 0. Therefore, the equation for the graph is

[tex]y = (x + 5)(x - 3) = x^2 + 2x - 15[/tex]

Answer:

Step-by-step explanation:

The answer is B) y= x^2+2x-15

Answer:

a)17.92

b) 16.83 .... 21.17

Step-by-step explanation:

ρ→   z

0.14 = -1.080319341

-1.080 = (x - 19)/1 = 17.92

~~~~~~~~~~~~~~~~~~

3% / 2 = 1.5%

1.5% - 98.5%

ρ→   z

0.015 = -2.170090378 ....  -2.17 = (x-19) =16.83

0.985 = 2.170090378  ....   2.17 = (x-19) =21.17

Solution :

a). [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y)$[/tex]

  Now, if X = Y, then :

  [tex]P(X|Y)=\left\{\begin{matrix} 1,& \text{if } x=y \\ 0, & \text{otherwise }\end{matrix}\right.[/tex]

Then, E[X|Y] = x = y

So, [tex]$\text{Var} (X|Y) =E((X-X)^2 |Y)$[/tex]

                      [tex]$=E(0|Y)$[/tex]

                      = 0

Therefore, this statement is TRUE.

b). If X = Y , then Var (X) = Var (Y)

And as Var (X|Y) = 0, so Var (X|Y) ≠ Var (X), except when all the elements of Y are same.

So this statement is FALSE.

c). As defined earlier,

  [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex]

  So, this statement is also TRUE.

d). The statement is TRUE because [tex]$\text{Var} (X|Y) =E ((X-E(X|Y))^2 |Y=y)$[/tex].

e). FALSE

   Because, [tex]$\text{Var} (X|Y) =E ((X-E(X|Y=y))^2 |Y=y)$[/tex]

Answer:

B. No, the two triangles don't have

corresponding sides marked congruent.