Convert 30°to radians. Leave answer as a reduced fraction in terms of π.

a: pi/3
b: pi/6
c: pi/4
d:pi/2

Answer:

229.23 feet.

Step-by-step explanation:

The pictorial representation of the problem is attached herewith.

Our goal is to determine the height, h of the tree in the right triangle given.

In Triangle BOH

[tex]Tan 60^0=\dfrac{h}{x}\\h=xTan 60^0[/tex]

Similarly, In Triangle BOL

[tex]Tan 50^0=\dfrac{h}{x+60}\\h=(x+60)Tan 50^0[/tex]

Equating the Value of h

[tex]xTan 60^0=(x+60)Tan 50^0\\xTan 60^0=xTan 50^0+60Tan 50^0\\xTan 60^0-xTan 50^0=60Tan 50^0\\x(Tan 60^0-Tan 50^0)=60Tan 50^0\\x=\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0} ft[/tex]

Since we have found the value of x, we can now determine the height, h of the tree.

[tex]h=\left(\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0}\right)\cdotTan 60^0\\h=229.23 feet[/tex]

The height of the tree is 229.23 feet.

Answer:

28

Step-by-step explanation:

3/4x= 21

x= 21(4/3)

x= 28

Check! (optional)

28 x 3/4 = 21

Check correct!!!!!!

Answer:

the number is 28

Step-by-step explanation:

I know this because 21 is 3/4 of a number. 21 divided by 3 is 7, you do this to find what 1/4 of the number is. so then you add 7 to 22 and you get 28!

Step-by-step explanation:

[tex] - 18 - \frac{3}{4v} = 3[/tex]

[tex] - \frac{3}{4v} = 3 + 18[/tex]

[tex] - \frac{3}{4v} = 21[/tex]

Now doing cross multiply

-3 = 21 * 4v

[tex]v = - \frac{3}{21 \times 4} [/tex]

Therefore

[tex]v \: = \frac{1}{28} [/tex]

Hope this helps.

Answer:

A)  (33/5, 0, 44/5)

B) - 11

C) (28/5, 2, - 54/5)

D) 11, 12.83

Step-by-step explanation:

A)

Given the vectors

b= (1, 2,-2)

a= (-3, 0, 4)

Projection of the vector b onto the line along vector a as p=ˆxa

Calculating ab,

ab= a1b1 + a2b2 + a3b3

a1= - 3, a2=0, a3=4, b1=1, b2=2, b3= - 2

ab= (-3)(1) + (0)(2) +(4)(-2)

ab= - 3 + 0 +(-8)

ab= - 11

Vector projection which is

( ab÷ /vector a/^2) × vector a

= - 11/√(-3)^2 + (0)^2 + (4)^2

= - 11/ √9 +16

=-11/√25

= - 11/5× (-3, 0, - 4)

= (33/5, 0, 44/5)

B) When p= pb

It will be a scalar projection and will be written as:

ab÷ /a/

-11/√1

= - 11

C) Given the vector that form P to b in

e= b - p

=b- ˆxa

e= (1, 2,-2) - (33/5, 0, 44/5)

= (1 - 33/5, 2- 0, -2 - 44/5)

=(5-33/5, 2, - 10- 44/5)

= (28/5, 2, - 54/5)

D.

Length of the projection vector:

/e/ = √(33/5^2 + 0 + 44/5^2)

/e/= √33^2/25 + 0 + 44^2/25

/e/= √33^2/25 +44^2/25

/e/= √121

/e/= 11

Length of error vector

/e/ = √(28/5)^2 + 2^2 + (-54/5)^2

/e/= √28^2/25 +4 +(-54^2/25)

/e/= 12.83

Answer:

a) and b) p= (33/25, 0, -44/25)

c) e = (-8/25, 2, -6/25)

d) p = 11/5 = 2.2

e) e = (2/5)√26 = 2.039

Step-by-step explanation:

Given

b = (1, 2, −2)

a = (−3, 0, 4)

a)  and b) We use the formula

p = (at*b)/(at*a)*a

⇒ p = ((−3, 0, 4)*(1, 2, −2)/((−3, 0, 4)*(−3, 0, 4)))*(−3, 0, 4)

[tex]p=\frac{at*b}{at*a}*a\\ p=\frac{(-3, 0, 4)*(1, 2,-2)}{(-3, 0, 4)*(-3, 0, 4)} *(-3, 0, 4)\\ p=\frac{-3+0-8}{9+0+16}*(-3, 0, 4)\\ p=-\frac{11}{25} *(-3, 0, 4)\\ p=(\frac{33}{25} ,0,-\frac{44}{25})[/tex]

c)

 [tex]e=b-p\\ e=(1, 2, -2)-(\frac{33}{25} ,0,-\frac{44}{25})\\ e=(-\frac{8}{25} ,2,-\frac{6}{25} )[/tex]

d) We use the formula

[tex]p=\sqrt{(\frac{33}{25} )^{2} +(0)^{2} +(\frac{-44}{25} )^{2}} =\frac{11}{5}[/tex]

e) Applying the same formula we have

[tex]e=\sqrt{(\frac{-8}{25} )^{2} +(2)^{2} +(\frac{-6}{25} )^{2}} =\frac{2}{5}\sqrt{26} =2.039[/tex]

Answer:

a) Yes, it is a linear combination.

b) Impossible to write as a linear combination.

Step-by-step explanation:

Recall that given vectors u,v,w we say that w is a linear combination of u and v if there exists real numbers a,b such that

[tex]w=au+bv[/tex]

a) [tex] u = (2,19,-16, -4)[/tex]. So, we have the following

[tex] (2,19,-16, -4)=a(6,-7,8,6)+b(4,6,-4,1)[/tex]. Which give us the following equations

[tex]6a+4b = 2[/tex]

[tex]-7a+6b = 19[/tex]

[tex]8a-4b = -16[/tex]

[tex]6a+b =-4[/tex]

Note that if we add the first and the third equation, we get that [tex]14a = -14[/tex] which implies that a=-1. In the first equation, if a=-1, then [tex]4b=2+6[/tex] which implies that b=2. We must check that when (a,b) =(-1,2) the four equations are still valid.

So

[tex]6(-1)+4(2) = -6+8 = 2[/tex]

[tex]-7(-1)+6(2) = 7+12 = 19[/tex]

[tex]8(-1)-4(2) = -8-8 = -16[/tex]

[tex]6(-1)+(2) =-6+2 = -4[/tex]

Since all equations are met, we have written the desired vector u as the linear combination of the initial vectors.

b) Repeating the same analysis, we get

[tex](432 , 1134 , −18, 132)=a(6,-7,8,6)+b(4,6,-4,1)[/tex]

[tex]6a+4b = 432[/tex]

[tex]-7a+6b = 1134[/tex]

[tex]8a-4b = -18[/tex]

[tex]6a+b =132[/tex]

adding the first and third equation we get [tex]14a = 414[/tex] so a = 207/7. Replacing this value will give us that b=891/14.

However,

note that

[tex]-7\frac{207}{7}+6\frac{891}{14} = \frac{1124}{7}\neq 1134[/tex]. Then, it is impossible to write the linear combination.

The question seeks a linear combination of vectors from a given set 'S' that matches specified vectors. Using vector addition and scalar multiplication, it is possible to find a unique combination for each specified vector. If no combination can provide the required vector, 'IMPOSSIBLE' is the answer.

In this problem, you're asked to express a given vector as a linear combination of other vectors from the set 'S'. This involves using the properties of vector addition and scalar multiplication to define a unique way to represent each given vector. A linear combination of vectors involves adding or subtracting multiples of these vectors.

For instance, if we have the set S = {(6, -7, 8, 6), (4, 6, -4, 1)}, and we're asked to write the vector u = (2, 19, -16, -4), the correct linear combination would be -1 times the first vector in S plus 2 times the second vector (-1*(6,-7,8,6) + 2*(4,6,-4,1) = (2, 19, -16, -4)). This means vector 'u' would be expressed as u = -1 * S1 + 2 * S2. If no such combination is possible, the answer would be 'IMPOSSIBLE'.

Other important concepts related to this problem include vector addition, scalar multiplication, and the distributive property. Vector addition is both associative and commutative and vector multiplication by a sum of scalars is distributive. The direction and magnitude of vectors are also significant elements to consider while solving such problems.

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Answer:

There is no sufficient evidence

Step-by-step explanation:

See attached files

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

µ = 75

For the alternative hypothesis,

µ ≠ 75

Since the number of samples is 20 and no population standard deviation is given, the distribution is a student's t.

Since n = 20,

Degrees of freedom, df = n - 1 = 20 - 1 = 19

t = (x - µ)/(s/√n)

Where

x = sample mean = $69.46

µ = population mean = $75

s = samples standard deviation = $9.78

t = (69.46 - 75)/(9.78/√20) = - 2.53

We would determine the p value using the t test calculator. It becomes

p = 0.01

Since alpha, 0.05 > than the p value, 0.01, then the null hypothesis is rejected.

Therefore,

The value of the test statistic is -2.53; therefore, the null hypothesis is rejected for level of significance = 0.05

Answer:

Over the boundary: maximum:13, minimum:12

Over D: maximum:13, minimum:0

Step-by-step explanation:

We are given that [tex]f(x,y) = 12x^2+13y^2[/tex] and D is the disc of radius one. Namely, [tex]x^2+y^2\leq 1[/tex].

First, we want to find a critical point of the function f. To do so, we want to find the values(x,y) such that

[tex] \nabla f (x,y) =0[/tex].

Recall that [tex] \nabla f (x,y) = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})[/tex].

So, let us calculate [tex] \nabla f (x,y)[/tex] (the detailed calculation of the derivatives is beyond the scope of the answer.

[tex]\frac{\partial f}{\partial x} = 24x[/tex]

[tex]\frac{\partial f}{\partial y} = 26y[/tex]

When equalling it to 0, we get that the critical point is (0,0), which is in our region D. Note that the function f is the sum of the square of two real numbers multiplied by some constants. Hence, the function f fulfills that [tex]f(x,y)\geq 0[/tex]. Note that f(0,0)=0, so without further analysis we know that the point (0,0) is a minimum of f over D.

If we restrict to the boundary, we have the following equation [tex] x^2+y^2=1[/tex]. Main idea is to replace the value of one of the variables n the function f, so it becomes a function of a single variable. Then, we can find the critical values by using differential calculus:

Case 1:

Let us replace y. So, we have that [tex]y^2=1-x^2[/tex]. So, [tex]f(x,y) = 12x^2+13(1-x^2) = -x^2+13[/tex].

So, we will find the derivative with respect to x and find the critical values. That is

[tex] \frac{df}{dx} = -2x=0[/tex]

Which implies that x =0. Then, [tex] y =\pm 1[/tex]. So we have the following critical points (0,1), (0,-1). Notice that for both points, the value of f is f(0,1) = f(0,-1) = 13.  If we calculate the second derivative, we have that at x=0

[tex] \frac{d^2f}{dx^2} = -2<0[/tex]. By the second derivative criteria, we know that this points are local maximums of the function f.

Case 2:

Let us replace x. So, we have that [tex]x^2=1-y^2[/tex]. So, [tex]f(x,y) = 12(1-y^2)+13y^2 = y^2+12[/tex].

So, we will find the derivative with respect to y and find the critical values. That is

[tex] \frac{df}{dx} = 2y=0[/tex]

Which implies that y =0. Then, [tex] x =\pm 1[/tex]. So we have the following critical points (-1,0), (1,0). Notice that for both points, the value of f is f(1,0) = f(-1,0) = 12.  If we calculate the second derivative, we have that at y=0

[tex] \frac{d^2f}{dx^2} = 2>0[/tex]. By the second derivative criteria, we know that this points are local minimums of the function f.

So, over the boundary D, the maximum value of f is 13 and the minimum value is 12. Over all D, the maximum value of f is 13 and the minimum value is 0.

Final answer:

The critical point of f(x, y) on the disk D is (0, 0). f(x) restricted to the boundary of D is f(x) = 12x^2 + 13(1 - x^2) with the domain [-1, 1]. The absolute maximum and minimum values of f(x, y) over all of D are 25 and 0, respectively.

Explanation:

To find the critical point of the function f(x, y) = 12x2 + 13y2 on the disk D: x2+y2 ≤ 1, we need to set the partial derivatives of f with respect to x and y equal to zero.

The partial derivative with respect to x is 24x, and setting it to zero gives x = 0. Similarly, the partial derivative with respect to y is 26y, which implies y = 0. Therefore, the critical point is (0, 0).

On the boundary of D, where x2+y2 = 1, we can solve for y2 as y2 = 1 - x2. Substituting into f, we get a function of a single variable x: f(x) = 12x2 + 13(1 - x2) with the closed interval domain [-1, 1].

The maximum value on the boundary occurs at x = ±1, giving a maximum of f(±1) = 25. The minimum on the boundary is at x = 0, which gives f(0) = 13.

Across the entire disk D, the absolute minimum is at the critical point (0,0), with f(0, 0) = 0, and the absolute maximum is the same as the boundary maximum, f(x) = 25.

Answer:

They will accept the $50,000 maximum offered by your insurance company

In this scenario, with $50,000 liability insurance, if you cause a $75,000 accident, the other party is likely to accept the $50,000 from your insurance (Option C) but could also sue you for the remaining $25,000 (Option D).

In this scenario, if you cause an accident resulting in $75,000 in damage to the passengers in another car, your liability insurance has a maximum coverage limit of $50,000 per accident. Typically, insurance policies cover up to the policy limits, and the insurance company would pay out up to $50,000 to the injured parties.

The most likely outcome in this situation would be that the injured parties may initially pursue a claim with your insurance company, and the insurance company would pay up to its policy limit of $50,000. However, since the damages exceed the policy limit, the injured parties may still have the option to sue you personally for the remaining $25,000 to cover their damages.

So, the answer could be a combination of options C and D: They may accept the $50,000 maximum offered by your insurance company but could also potentially sue you for the remaining $25,000 if they believe it's necessary to cover their damages. The actual outcome may vary depending on the specific circumstances, local laws, and the decisions made by the injured parties and their legal advisors. It's crucial to notify your insurance company as soon as an accident occurs so they can handle the situation accordingly.

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Let U={a,b,c,d,e,f,g,h}

A={a,c,d}

B={b,c,d}

C={b,e,f,g,h}

Answer:

a) [tex]P(R<95)=P(\frac{R-\mu}{\sigma}<\frac{95-\mu}{\sigma})=P(Z<\frac{95-100}{3.606})=P(Z<-1.387)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-1.387)=0.0827[/tex]

b) [tex]P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)[/tex]

And we can find this probability using the complement rule and the normal standard table or excel and we got:

[tex]P(z>2.774)=1-P(Z<2.774) = 1-0.9972 = 0.0028[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the time for the step 1 and Y the time for the step 2, we define the random variable R= X+Y for the total time and the distribution for R assuming independence between X and Y is:

[tex]R \sim N(40+60 = 100,\sqrt{2^2 +3^2}= 3.606 s)[/tex]  

Where [tex]\mu=65.5[/tex] and [tex]\sigma=2.6[/tex]

We are interested on this probability

[tex]P(R<95)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{R-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(R<95)=P(\frac{R-\mu}{\sigma}<\frac{95-\mu}{\sigma})=P(Z<\frac{95-100}{3.606})=P(Z<-1.387)[/tex]

And we can find this probability using the normal standard table or excel and we got:

[tex]P(z<-1.387)=0.0827[/tex]

Part b

[tex]P(R>110)=P(\frac{R-\mu}{\sigma}>\frac{110-\mu}{\sigma})=P(Z>\frac{110-100}{3.606})=P(Z>2.774)[/tex]

And we can find this probability using the complement rule and the normal standard table or excel and we got:

[tex]P(z>2.774)=1-P(Z<2.774) = 1-0.9972 = 0.0028[/tex]

Given Information:  

Mean = μ = 40 + 60 = 100 minutes  

Standard deviation = σ = 2² + 3² = 13 minutes  

Required Information:  

a. P(X < 95) = ?

b. P(X > 110) = ?

Answer:  

a. P(X < 95) = 0.0823

b. P(X > 110) = 0 .0028

Explanation:  

a)

Let random variable X represents the time in minutes of wheel throwing and firing.

The probability that a piece of pottery will be finished within 95 minutes means,

P(X < 95) = P(Z < (x - μ)/√σ)  

P(X < 95) = P(Z < (95 - 100)/√13)  

P(X < 95) = P(Z < -1.39)  

The z-score corresponding to -1.39 is 0.0823

P(X < 95) = 0.0823

Therefore, there is 8.23%  probability that a piece of pottery will be finished within 95 minutes.

b)

P(X > 110) = 1 - P(X < 110)  

P(X > 110) = 1 - P(X < (x - μ)/√σ)

P(X > 110) = 1 - P(X < (110 - 100)/√13)

P(X > 110) = 1 - P(X < 2.77)

The z-score corresponding to 2.77 is 0.9972

P(X > 110) = 1 - 0.9972

P(X > 110) = 0 .0028

Therefore, there is 0.28%  probability that a piece of pottery will take longer than 110 minutes.

Answer:

The correct explanation is:

D. Statistical significance means that the result observed in a sample is unusual when the null hypothesis is assumed to be true.

Step-by-step explanation:

The statistical significance gives a threshold to measure if a sample result or observed effect is due only to a sampling or it really reflects a characteristics of the population we are studying.

The level of statistical significance is usually 0.05 or 5%, depending on how strong the evidence needs to be and the consequences of the conclusions of the study, taking into account the Type I and Type II errors.

Thus the response above i.e., "option D" is appropriate.

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Answer:

0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 990 kWh

Standard Deviation, σ = 198 kWh

We are given that the distribution of energy consumption levels is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(September energy consumption level is between 1100 kWh and 1250 kWh)

[tex]P(1100 \leq x \leq 1250)\\\\ = P(\displaystyle\frac{1100 - 990}{198} \leq z \leq \displaystyle\frac{1250 -990}{198}) \\\\= P(0.5556 \leq z \leq 1.3131)\\\\= P(z \leq 1.3131) - P(z < 0.5556)\\\\= 0.9054- 0.7108= 0.1946[/tex]

0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

Answer:

256 m2

Step-by-step explanation:

- First, know the formula A = (a+b/2)h

- Using this, we will fill the equation in with our variables. For example...

A = ((13+19)/2)16

A = (32/2)16

A = (16)(16)

A = 256 m2

- Hope this helps! If you need a further explanation or step by step practice please let me know.

Answer:

The maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight is of 3.46 ounces.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this problem:

[tex]\sigma = 13.3, n = 40[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.645*\frac{13.3}{\sqrt{40}}[/tex]

[tex]M = 3.46[/tex]

The maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight is of 3.46 ounces.

Final answer:

The maximal margin of error for a 90% confidence interval for the mean watermelon weight is calculated using the z-score for the confidence level, the known population standard deviation, and the sample size, resulting in 3.463 ounces.

Explanation:

To find the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight when the mean weight of the watermelons is 66 ounces, the population standard deviation is 13.3 ounces, and the sample size is 40, we use the formula for the margin of error E = z * (σ / sqrt(n)), where z is the z-score corresponding to the confidence level, σ is the population standard deviation, and n is the sample size.

For a 90% confidence interval, the z-score is approximately 1.645. Plugging in the values, we get:

E = 1.645 * (13.3 / sqrt(40))
= 1.645 * (2.105)
= 3.463 ounces.

The maximal margin of error is therefore 3.463 ounces, which means the interval is 66 ± 3.463 ounces for the true population mean weight of watermelons with 90% confidence.

Answer:

Check the explanation

Step-by-step explanation:

Period, X  Actual , Y

1                        6

2                       11

3                       9

4                       16

5                       17

Y= intercept + slope*x

Answer a and b:

INTERCEPT(known Y's,known X's)          Slope(known Y's,known X's)

                      3.7                                                           2.7

Simple linear regression equation is

Forecast, Y= 3.7+ 2.7*x

Period, X  Actual , Y  linear          Absolute           squared

                                   trend         deviation=         deviation=

                                Forecast,      |Forecast -        (absolute          

                            Y= 3.7+ 2.7*x      Actual|            deviation)^2

1                  6            6.40                  0.4                      0.2

2                 11            9.10                   1.9                       3.6

3                 9            11.80                  2.8                       7.8

4                16           14.50                  1.5                       2.3

5                17           17.20                  0.2                       0.0

6                              19.90  

                                                                                      2.78

                                                                                      MSE

Answer c: MSE= 2.78

Answer d: Forecast for x= 6= 19.90

Answer:

C

Step-by-step explanation:

The correct option is option C , that is the rule which describes the translation is (x, y) → (x + 4, y - 3).

What do you mean by translation ?

The modification of an existing diagram to create a different version of the following diagram is known as translation.

The translated triangle is moved along the x-axis by 4 units, to the right. The numbers get more positive as one moves to the right along the x-axis, hence an additional 4 units should be added to the x-coordinate. So , the coordinate would be x + 4.

Along the y-axis, the triangle is also pushed downward by 3 units. More negative numbers are produced as the axis moves below, hence 3 should be subtracted. So , the coordinate should be y - 3.

Based on the above information, we can conclude that another way to write the given rule by translation is (x, y) → (x + 4, y - 3) .

Therefore , the correct option is option C , that is the rule which describes the translation is (x, y) → (x + 4, y - 3).

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Answer:

2/9

Step-by-step explanation:

The ratio is 12/54 which can be simplified by dividing the numerator and denominator by 6 to get 2/9

Complete Question:

A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with ? = 0.001 millimeters. A random sample of 15 rings has a mean diameter of \bar{X}= 74.106. Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter.

(Round your answers to 3 decimal places.)

(Calculate the 99% two-sided confidence interval on the true mean piston diameter.

Answer:

99% true sided confidence Interval on the true mean Piston diameter = (74.105, 74.107)

Step-by-step explanation:

Check the attached file for the complete solution

Answer:

42.86%

Step-by-step explanation:

3/7 as a decimal is 0.4286... and to convert that into a decimal, you move the decimal point right twice.

0.4286 = 42.86%

I hope this helped!

Final answer:

To convert the fraction 3/7 into a percent, divide 3 by 7 to get the decimal 0.4286, then multiply by 100 to get 42.86%.

Explanation:

Converting a Fraction to a Percent

To convert a fraction like 3/7 into a percent, follow these steps:

Therefore, 3/7 as a percent is 42.86%.

A percent (or per cent) is a way of expressing a number as a fraction of 100. The term "percent" comes from the Latin per centum, which means "by the hundred." It is often represented by the symbol "%."

Answer:

A. 24024

B. 364

Step-by-step explanation:

(a) There are 14*13*12*11 = 24024 ways to select the officers...

(b) Since the officers can also serve on the committee, the sampling

    is with replacement, so then there are (14 choose 3) ways to

    select the committee members... 364 ways to be exact

Answer:

1. 564 tractor trailers

2. (0.2919, 0.4339)

3. It should be noted that there is 90% confidence that the true population proportion lies between 0.2919 and 0.4339.

Step-by-step explanation:

1)

Proportion= P = 0.8333333333333 (1/12)

Margin error= 0.06/2 = 0.03

Confidence level= 99

Significance level = α= (100 - 99)%= 1%= 0.01

α/2 = 0.01/2 = 0.0005

Sample size= n

= p(1 - p) (Z*/E)

=0.8333333333333 x (2.576/0.03)^2

=563.15

Approximately

=564

2) Sample size n= 124

Sample number of event x =45

Sample proportion = p= x/n

=45/124

= 0.3629

Standard error =√p(1 - p) /n

√(0.3629× (1 - 0.3629)/ 124

= 0.0432

Confidence level= 90

Significance level α= (100-90)% =0.01

Critical value Z* = 1.645

Margin of error = Z×Standard error= 1.645 × 0.0432= 0.07103

Lower limit = p- margin error= 0.3629 - 0.07103= 0.2919

Upper limit = p+margin error= 0.3629 + 0.07103= 0.4339

The answer is (0.2919, 0.4339)

3) It should be noted that there is 90% confidence that the true population proportion lies between 0.2919 and 0.4339.

Answer:

Hi Gabbie,

   The answer to your question that was what is the expected value for the "under 21 and regularly use text messaging" cell is 82.

Please rate me good  :)

Step-by-step explanation:

The answer is 82 because the table that clearly defines the result  was in the question.

Answer:

C(x)=16600+63x

R(x)=160x

Break-even Point, x=172

Step-by-step explanation:

Let x be the number of Toilets Produced.

Fixed cost = $16,600

Variable costs = $63 per toilet.

Total Cost, C(x)=16600+63x

The company expects to sell the toilets for $160.

Selling Price Per Toilet=160

Total Revenue for x Toilets, R(x)=160x

Next, we determine the break-even point.

The break-even point is the point where the Cost of Production equals Revenue generated.

i.e. C(x)=R(x)

16600+63x=160x

16600=160x-63x

16600=97x

x=171.13

The company needs to sell at least 172 Toilets to break even.

To formulate the functions C(x) and R(x) for the total cost and revenue of producing and selling x toilets, we can use the given information about fixed costs, variable costs, and selling price. By setting the total cost equal to the total revenue, we can find the number of toilets needed to break even, which is approximately 171.

To formulate the function C(x) for the total cost of producing x new toilets, we need to consider the fixed cost and the variable cost. The fixed cost is $16,600, which remains constant regardless of the number of toilets produced. The variable cost is $63 per toilet, so we multiply it by x to account for the number of toilets produced. Therefore, the function C(x) can be expressed as:

C(x) = 16,600 + 63x

The function R(x) for the total revenue generated from the sales of x toilets can be found by multiplying the selling price of each toilet by the number of toilets sold. Since each toilet is sold for $160, the function is:

R(x) = 160x

To find the number of toilets needed to break even, we need to determine the value of x when the total cost is equal to the total revenue. In other words, we set C(x) = R(x) and solve for x:

16,600 + 63x = 160x

Subtracting 63x from both sides:

16,600 = 97x

Dividing both sides by 97:

x = 170.10

Therefore, the company needs to sell approximately 171 toilets to break even.

https://brainly.com/question/35114770

#SPJ3

Alternate angles in a transversal are congruent.

The value of x is 13

See attachment for the image of the transversal,

Where [tex](9x + 2)[/tex] and [tex]119[/tex] are alternate angles

This means that:

[tex]9x + 2 = 119[/tex] ---- alternate angles are equal

Collect like terms

[tex]9x = 119 - 2[/tex]

[tex]9x = 117[/tex]

Divide both sides by 9

[tex]x = 13[/tex]

Hence, the value of x is 13

Read more about alternate angles at:

https://brainly.com/question/22580956

Step-by-step explanation:

[tex] {5}^{17} \times {5}^{2} [/tex]

Now adding powers

[tex] {5}^{17 + 2} [/tex]

[tex] {5}^{19} [/tex]

Hope it will help :)

Answer:

5x1^19

Step-by-step explanation:

Basically, the only way to have the 5 be to the power of 1 in this equation is to put it in scientific notation, or in other words, multiply 5 by 1 to the power of 19.

Answer:

[tex]y=\frac{x}{6.4}[/tex]

Step-by-step explanation:

The complete question in the attached figure

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem, we have a proportional relationship between the average speed (x) and the time (y)

Find the constant of proportionality k

Fox =32, y=5

[tex]k=\frac{5}{32}[/tex]

substitute

[tex]y=\frac{5}{32}x[/tex]

we have

[tex]\frac{5}{32}=\frac{1}{6.4}[/tex]

therefore

[tex]y=\frac{x}{6.4}[/tex]

Answer:

1/3

Step-by-step explanation:

For the 1st fraction, since 4 × 3 = 12,

3 /4  =  3 × 3/  4 × 3 =  9/ 12

Likewise, for the 2nd fraction, since 12 × 1 = 12,

5 /12  =  5 × 1 /12 × 1  =  5 /12

Subtract the two fractions: 9 /12  -  5 /12  =  9 - 5 /12  =  4 /12

So next you simplify the answer how many 4 go in 4 and how many go in 12 the simplified answer is the answer is  1/3

Hope this helps

Answer:

The expected value is 0.87.

Step-by-step explanation:

a) To calculate the expected value X we will first see the posible outcomes. So could take value of 0,1,2,3. We will calculate the probability of each outcome. To do so, we will introduce the following notation. Consider the following tuple (A,B,C) where A is the number of butterflies found by Alice, B the number found for by Bob and C the number found by C. To calculate the probability of the tuple (A,B,C) we will do as follows. If the entry of the tuple is 1, then we will multiply by the probability of the person that found the butterfly. So, if A =1, we will multiply by 0.17(Alice finds a butterfly with probability 0.17). On the other side, if the entry of the tuple is 0, we will multiply by (1-p) where p is the probability of the person that found the butterly. So, if A=0, we will multiply by 0.83. So, for example, consider the tuple (1,0,1). The probability of having this result is 0.17*0.75*0.45 (Alice and Charlotte found a butterfly, but Bob didn't). We can do this since we are said that their probabilities of success don't affect others' probabilities.

We will see the total number of butterflies and the tuples associated to that number. That is

X number of butterflies - tuples

0 butterflies - (0,0,0)

1 butterfly - (1,0,0) or (0,1,0) or (0,0,1)

2 butterflies - (1,1,0) or (1,0,1) or (0,1,1)

3 butterflies - (1,1,1)

To find the probability of the value of X, we will sum up the probability of the associated tuples. The values of the probabilities are as follows

(0, 0, 0) =  0.342375

(0, 0, 1 ) = 0.280125

(0, 1, 0)  = 0.114125

(0, 1, 1 ) = 0.093375

(1, 0, 0)  = 0.070125

(1, 0, 1 ) = 0.057375  = 0.17*0.75*0.45

(1, 1, 0)  = 0.023375

(1, 1, 1)  = 0.019125

In this case,

P(X=0) =  0.342375 ,

P(X=1) = 0.464375  = 0.280125 +0.114125+ 0.070125

P(X=2) = 0.174125

P(X =3 ) = 0.019125

So, the expected value of X is given by

0*  0.342375 +1 * 0.464375 +2* 0.174125+3*0.019125 = 0.87

b)Let X1 be the number of butterflies found by Alice, X2 the number found by Bob and X3 the number found by Charlotte. Then X = X1+X2+X3. Using the expected value properties and the independence of X1, X2 and X3 we have that E(X) = E(X1)+E(X2)+E(X3).

Recall that each variable is as follows. Xi is equal to 1 with probability p and it is 0 with probability (1-p). Then, the expected value of Xi is

[tex]1\cdot p + 0\codt (1-p)=p[/tex]. Note that the value of p for X1,X2 and X3 is 17%, 25% and 45% respectively.

Then E(X) = 17%+25%+45%= 0.87.

So the expected number of butterflies is 0.87.

Final answer:

The expected value of the total number of butterflies, X, that Alice, Bob, and Charlotte catch is 0.87. This is found by summing their independent probabilities of catching a butterfly (0.17 for Alice, 0.25 for Bob, and 0.45 for Charlotte). X is also represented as the sum of three indicator random variables X1, X2, and X3, leading to the same expected value.

Explanation:

Expected Value of the Number of Butterflies Caught

In this scenario with Alice, Bob, and Charlotte searching for butterflies in separate parts of a field, the random variable X represents the total number of butterflies they catch. The expected value of X, or E(X), is calculated by adding the individual probabilities of finding a butterfly, since their probabilities are independent.

To find the expected value of X:

Multiply the probability of each person finding a butterfly by the number of butterflies they would find in that event (which is 1 since each either finds 1 butterfly or none), and

Add these products together.

The expected value is thus 0.17 + 0.25 + 0.45 = 0.87 butterflies. We can also express X as X1 + X2 + X3, where each Xi is an indicator random variable for whether Alice (X1), Bob (X2), or Charlotte (X3) found a butterfly.

The expected value for each indicator variable is the same as the person's probability of success. So, E(X1) = 0.17, E(X2) = 0.25, and E(X3) = 0.45. By the linearity of expectation, E(X) = E(X1) + E(X2) + E(X3), which also equals 0.87 butterflies.