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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?

Answers

Answer 1
Let’s assume that age of Timmy is x yrs.
Then we can conclude that age of Tommy is =
(23 -x) yrs.

Now we know that Timmy is 5 years older than Tommy, therefore,
x = 5 + (23-x)
x = 5 + 23 - x
x + x = 28
2x = 28
x = 28/2
x = 14 Answer. (Age of Timmy)

So, the age of Tommy is 23 - x = 23 - 14 = 9 yrs.
Answer 2

Answer:

Tommy's age is 9 years old.

Timmy's age is 14 years old.

Step-by-step explanation:

Take Tommy's age to be x and Timmy's age to be x+5

x+x+5=23

2x+5=23

2x=23-5=18

x=18÷2=9

x+5=9+5=14


Related Questions

The list shows the ages of first-year teachers in one school system. What is the mode of the ages? 23, 42, 21, 25, 23, 24, 23, 24, 37, 23, 39, 51, 63, 24, 55

Answers

the mode is 23. It’s the number that’s getting repeated most frequently

Answer:

La moda es 23

Step-by-step explanation:

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

By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series.
A. 1 + 1/5 + (1/5)^2 + (1/5)^3 + (1/5)^4 +.....+ (1/5)^n + .... = _____.
B. 1 + 5 + 5^2/2! + 5^3/3! + 5^4/4! +....+ 5^n/n! +....= _____.

Answers

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 e.

Answer the following.
(a) Find an angle between and that is coterminal with .
(b) Find an angle between and that is coterminal with . Give exact values for your answers.

Answers

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

find from first principle the derivative of 3x+5/√x​

Answers

Answer:

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

General Formulas and Concepts:

Algebra I

Exponential Rule [Powering]:                                                                          [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Exponential Rule [Rewrite]:                                                                              [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]:                                                                     [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]

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:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

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

Rewrite [Exponential Rule - Root Rewrite]:                                                     [tex]\displaystyle \frac{3x + 5}{x^\bigg{\frac{1}{2}}}[/tex]Quotient Rule:                                                                                                   [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{(x^\bigg{\frac{1}{2}})^2}[/tex]Simplify [Exponential Rule - Powering]:                                                          [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})\frac{d}{dx}[3x + 5] - \frac{d}{dx}[x^\bigg{\frac{1}{2}}](3x + 5)}{x}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]:                   [tex]\displaystyle \frac{d}{dx} = \frac{(x^\bigg{\frac{1}{2}})(3x^{1 - 1} + 0) - (\frac{1}{2}x^\bigg{\frac{1}{2} - 1})(3x + 5)}{x}[/tex]Simplify:                                                                                                             [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2}x^\bigg{\frac{-1}{2}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Rewrite]:                                                              [tex]\displaystyle \frac{d}{dx} = \frac{3x^\bigg{\frac{1}{2}} - (\frac{1}{2x^{\frac{1}{2}}})(3x + 5)}{x}[/tex]Rewrite [Exponential Rule - Root Rewrite]:                                                     [tex]\displaystyle \frac{d}{dx} = \frac{3\sqrt{x} - (\frac{1}{2\sqrt{x}})(3x + 5)}{x}[/tex]Simplify [Rationalize]:                                                                                       [tex]\displaystyle \frac{d}{dx} = \frac{3x - 5}{2x^\bigg{\frac{3}{2}}}[/tex]

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

Unit: Derivatives

Book: College Calculus 10e

For each one of the following statements, indicate whether it is true or false.
(a) If X = Y (i.e., the two random variables always take the same values), then Van X | Y = 0.
(b) If X = Y (the two random variables always take the same values), then Var (X | Y) = Var (X).
(c) If Y takes on the value y, then the random variable Var (X | Y) takes the value E[(X – E[X | Y = y])2 |Y = y].
(d) If Y takes on the value y, then the random variable Var (X | Y) takes the value E[(X - E[X | Y])2 | Y = y].
(e) If Y takes on the value y, then the random variable Var ( X | Y) takes the value E[(X – E[X])2 | Y = y].

Answers

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]

The mean incubation time of fertilized eggs is 19 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. Answer the following. For each question draw an appropriate distribution function​ (graph) to represent the​ data, shade the desired area, and show all​ work, including what you input into your calculator to attain your results.
(A) The 14th percentile for incubation times is __ days.
(B) The incubation times that make up the middle 97% of fertilized eggs are __ to __ days.

Answers

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

Please help how to do this

Answers

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.

Please help bbbsbsshhdbdvdvdvsvxggddvvdgddvd

Answers

(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

The largest angle in a triangle is six times the smallest angle. The middle angle is three times the smallest angle. Given that the sum of the angles in a triangle is , find the measure of each angle.

Answers

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:

Add the three to make sure they equal 180. Make sure the smallest is the smallest, and the largest is the largest.

24. What are the intercepts of -3x + 5y - 2z = 60?
(-20, 0, 0), (0, 12,0), (0, 0, -30)

(-60, 0, 0), (0, 60, 0), (0, 0, -60)
(-180, 0, 0), (0, 300, 0), (0, 0, -120)
(-3, 0, 0), (0,5, 0), (0, 0, -2)

Answers

I choose (-20,0,0) , (0,12,0), ( 0,0,-30)

Complete the sentences below:
The value of________ is negative because 240 is in quadrant III. The reference angle is___________. and the exact value of 240 degrees is_________.

Answers

Answer Deleted

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what is the formula for perimeter of a square​

Answers

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.

for the function f(x)=5 evaluate and simplify the expression: f (a+h)-f(a)/h

Answers

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.

please help me i begging.

Answers

Answer:

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

Step-by-step explanation:

18 or maybe 36 because the supermarkets fruit snacks x and y fill them in

the inner diameter of the top of am ornamental cup is 7,5cm and the diameter of the inner bottom is 3,0cm.the depth of the cup is 10cm.calculate the capacity of the cup​

Answers

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:

Matthew participates in a study that is looking at how confident students at SUNY Albany are. The mean score on the scale is 50. The distribution has a standard deviation of 10 and is normally distributed. Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
a) 93.32%
b) 6.68%
c) 0.07%
d) 43.32%

Answers

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.

The sum of -4 and the difference of 3 and 1

Answers

Answer: -2


Step 1: Write an equation

Before we are able to solve, we need to write an equation. We can do this by breaking down the equation. We are told to find the sum of -4 and the difference of another two numbers. Sum means addition, so we will add -4 to the difference of 3 and 1. Because we are adding to the difference, we will put 3 and 1 inside of parentheses, and find the difference before we add. Knowing this, we can write the equation. Let’s do this now.

-4+(3-1)

Step 2: Solve

Now that we have the equation we can solve for the answer. Let’s start by finding the difference, as indicated by the parentheses. After that, we can find the sum of that number and -4 by adding them together. We can do this now.

-4+(3-1)
-4+2
-2

This is your answer! The sum of -4 and the difference of 3 and 1 is -2. Hope this helps! Comment below for more questions.



2(2x + 4) + 2(x - 7) = 78. Determine the side lengths of this rectangle. ​

Answers

[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]

Suppose 35.45% of small businesses experience cash flow problems in their first 5 years. A consultant takes a random sample of 530 businesses that have been opened for 5 years or less. What is the probability that between 34.2% and 39.03% of the businesses have experienced cash flow problems?
1) 0.6838
2) 20.3738
3) 0.3162
4) - 11.6695
5) 1.2313

Answers

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.

Tell whether the following two triangles can be
proven congruent through SAS.
A.Yes, the two triangles are congruent
because two sides and their included
angle are congruent in both triangles.
B.No, the two triangles don't have
corresponding sides marked congruent.
C. Yes, the two triangles are congruent because they’re both right triangles.
D.No, the two triangles can only be proven congruent through SSA.

Answers

Answer:

B. No, the two triangles don't have

corresponding sides marked congruent.

what are the missing numbers ?

Answers

It is d 5,6,8,9
Cube root 8 is 2 + 7 is 9

When 4 times a positive number is subtracted from the square of the number, the result is 5. Find the number.

Answers

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.

Will give brainliest if correct

Which congruence theorem can be used to prove △BDA ≅ △BDC?


Triangles B D A and B D C share side B D. Sides B C and B A are congruent. Sides A D and D C are congruent.


HL

SSA

AAS

SSS

Answers

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.

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

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;

ΔBDA ≅ ΔBDC  [tex]{}[/tex]             By Side-Side-Side SSS, congruency rule

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

SSS

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.

Learn more about Side-Side-Side, SSS congruency rule here:

https://brainly.com/question/10684250

The sum of two numbers is 125. Their difference is 47. The two numbers are:
a)39 and 86.
b)40 and 85.
c)47 and 78.
d)None of these choices are correct.

Answers

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

What is the level of measurement for ​"year of birth​"?

Answers

interval level of mesurement

Answer:

interval?

Step-by-step explanation:

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

Exercise 2.2.3: The cardinality of a power set. (a) What is the cardinality of P({1, 2, 3, 4, 5, 6})

Answers

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.

g Vectors ???? and ???? are sides of an equilateral triangle whose sides have length 4. Compute ????⋅????. (Give your solution as a number to one decimal place.

Answers

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]

Find all solutions of the equation in the interval [0, 2pi); sqrt(3) * csc(theta) - 2 = 0

Answers

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].

What is trigonometric ratio?

" 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].

Learn more about trigonometric ratio here

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Suppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for repair or replacement. The manufacturer wants to estimate the magnitude of the problem in order to design a quality control program. How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence

Answers

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

A developer wants to purchase a plot of land to build a house. The area of the plot can be described by the following expression: (5x+1)(7x−7) where x is measured in meters. Multiply the binomials to find the area of the plot in standard form

Answers

Answer:

35x^2 - 28x - 7

Step-by-step explanation:

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