Draw the function
[tex]y = \tan(x) [/tex]
on the interval [-pi, pi]​

Answer:

Mean age: 48

Standard deviation: 4

Step-by-step explanation:

a) Mean

The formula for Mean = Sum of terms/ Number of terms

Number of terms

= 42 + 54 + 50 + 54 + 50 + 42 + 46 + 46 + 48+ 48/ 10

= 480/10

= 48

The mean age is 48

b) Standard deviation

The formula for Standard deviation =

√(x - Mean)²/n

Where n = number of terms

Standard deviation =

√[(42 - 48)² + (54 - 48)² + (50 - 48)² +(54 - 48)² + (50 - 48)² +(42 - 48)² + (46 - 48)² + (46 - 48)² + (48 - 48)² + (48 - 48)² / 10]

= √-6² + 6² + 2² + 6² + 2² + -6² + -2² + -2² + 0² + 0²/10

=√36 + 36 + 4 + 36 + 4 + 36 + 4 + 4 + 0 + 0/ 10

=√160/10

= √16

= 4

The standard deviation of the ages is 4

Answer:

A) C1 = 0.00187 m = 0.187 cm,  C2 = 0.0062 m = 0.62 cm

B)  A sample of how the graph looks like is attached below ( periodic sine wave )

C) w = [tex]\sqrt[4]{3}[/tex] is when the amplitude of the forced response is maximum

Step-by-step explanation:

Given data :

mass = 5kg

length of spring = 10 cm = 0.1 m

f(t) = 10sin(t) N

viscous force = 2 N

speed of mass = 4 cm/s = 0.04 m/s

initial velocity = 3 cm/s = 0.03 m/s

Formulating initial value problem

y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m

spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m

f(t) = 10sin(t/2) N

using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion

the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)

A) finding the solution of the initial value

attached below is the solution and

B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like

C attached below

Complete Question

On the uploaded image is a similar question that will explain the given question

Answer:

The value of k is  [tex]k = 214285.7[/tex]

The percentage  of the oil that will be cleaned is [tex]x = 80.77\%[/tex]

Step-by-step explanation:

From the question we are told that

   The  cost of cleaning up the spillage is  [tex]C = \frac{ k x }{100 - x }[/tex]  [tex]x \le x \le 100[/tex]

     The  cost of cleaning x =  70% of the oil is  [tex]C = \$500,000[/tex]

Now at  [tex]C = \$500,000[/tex] we have  

       [tex]\$ 500000 = \frac{ k * 70 }{100 - 70 }[/tex]

       [tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]

      [tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]

      [tex]k = 214285.7[/tex]

Now  When  [tex]C = \$900,000[/tex]

       [tex]x = 80.77\%[/tex]

volume of a cone

.

.

.

volume of sphere

.

.

number of spheres that can be made......

.

.

hence a hemisphere can be formed

Answer:

The upper bound of the confidence interval is 0.34

Step-by-step explanation:

Here in this question, we want to calculate the upper bound of the confidence interval.

We start by calculating the margin of error.

Mathematically, the margin of error = 0.29 -0.24 = 0.05

So to get the upper bound of the confidence interval, we simply add this margin of error to the mean

That would be 0.05 + 0.29 = 0.34

Answer:

0.4207149;0.7271136; 0.3063987; 0.04979 ; 0.01832

Step-by-step explanation:

For an exponential distribution:

IF Mean time until failure = 23100

λ = 1/ 23100 = 0.0000432900

What is the probability that a randomly selected fan will last at least 20,000 hours

x ≥ 20000

P(X ≥ 20000) = 1 - P(X ≤ 20000)

1 - P(X ≤ 20000) = [1 - (1 - e^(-λx))]

1 - P(X ≤ 20000) = [1 - (1 - e^(-0.0000432900*20000)

1 - P(X ≤ 20000) = [1 - (1 - 0.4207148)]

1 - P(X ≤ 20000) = 1 - 0.5792851

1 - P(X ≤ 20000) = 0.4207149

11) What is the probability that a randomly selected fan will last at most 30,000 hours?

x ≤ 30000

P(X ≤ 30000) = 1 - e^(-λx)

P(X ≤ 20000) = 1 - e^(-0.0000432900*30000)

= 1 - e^(−1.2987)

= 1 - 0.2728863

= 0.7271136

111) What is the probability that a randomly selected fan will last between 20,000 hours and 30,000 hours?

0.7271136 - 0.4207149 = 0.3063987

B) What is the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations?

More than two standard deviation

X = 23100 + 2(23100) = 23100 + 46200 = 69300

Using the online exponential probability calculator :

P(X > 69300) = 0.04979

C) What is the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations?

X = 23100 + 3(23100) = 23100 + 69300 = 92400

P(X > 92400) = 0.01832

Answer:

the answer to the question is "C"

Answer:

mean=87

median=87

Step-by-step explanation:

mean=sum of test score/number of subject

mean=79+91+93+85+86+88/6

mean=522/6

mean=87

Literal meaning of median is medium.

To find the number which lies in the medium, we must rearrange the number in ascending.

79, 91, 93, 85, 86, 88

79, 85, 86, 88, 91, 93

86+88/2=87

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer.

Answer:

At 3 hours, the trains will be equidistant from the station.

Step-by-step explanation:

The first train leaves at 75 miles per hour and has a 2 hour head start.  This will put the first train at mile marker 150 (75 * 2) when the second train leaves the station at 125 mph.

To solve when they will be near each other, we set up an equation to solve for t.

150 + 75t = 125t

150 = 50t

3 = t

So given this value, we know the trains will be equidistant from the train station on parallel tracks after 3 hours.

Cheers.

Answer: $2750

Step-by-step explanation:

Formula to calculate interest : I = Prt , where P = Principal amount , r = rate of interest ( in decimal) , t= time.

Given:  I= $495

t= 3 years

r= 6% = 0.06

Then, according to the above formula:

[tex]495 = P (0.06\times3)\\\\\Rightarrow\ P=\dfrac{495}{0.18}\\\\\Rightarrow\ P=2750[/tex]

Hence, the principal invested = $2750

Greetings from Brasil...

In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.

The translations are established as follows:

→ Horizontal

F(X + k) ⇒ k units to the left

F(X - k) ⇒ k units to the right

→ Vertical

F(X) + k ⇒ k units up

F(X) - k ⇒ k units down

In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.

F(X) = X³

4 units horizontal to the left: F(X + 4)

3 units vertical to the bottom: F(X + 4) - 3

So,

F(X) = X³

The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted

Every modification may be a part of a function's transformation.

Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).

If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:

Vertical shift, often known as phase shift:

Y=f(x+c) with a left shift of c units (same output, but c units earlier)

Y=f(x-c) with a right shift of c units (same output, but c units late)

Vertical movement:

Y = f(x) + d units higher, up

Y = f(x) - d units lower, d

Stretching:

Stretching vertically by a factor of k: y = k f (x)

Stretching horizontally by a factor of k: y = f(x/k)

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) = x³

And , the transformed function has coordinates as A ( -4 , -3 )

So , when function is shifted 4 units to the left , we get

g' ( x ) = ( x + 4 )³

And , when the function is shifted vertically by 3 units down , we get

f ( x ) = ( x + 4 )³ - 3

Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3

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Answer:

  x = 1.00995066776

  x = 2.52925492433

Step-by-step explanation:

This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...

  [tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]

The attached graph shows zeros at

  x = 1.00995066776 and 2.52925492433

_____

Comment on the equation

Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068

Comment on the answer refinement

We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2[/tex]

Step-by-step explanation:

utilise the formula a+(n-1)d

a is the first number while d is common difference

Answer:

22

Step-by-step explanation:

Using the formular, Un = a + (n - 1)d

Where n = 10; a = -23; d = 5

U10 = -23 + (9)* 5

U10 = -23 + 45 = 22

[tex]10[/tex] divisions between $389$ and $390$ so each division is $\frac{390-389}{10}=0.1$

A is 8 division from $389$, so, A is $389+8\times 0.1=389.8$

similarly, C is one division behind $389$ so it is $389-1\times 0.1=388.9$

and B is $390.3$

Answer:

[tex]x = \frac{1}{3} [/tex]

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒([tex]\frac{1}{3x}[/tex])

*rewrite to solve for x :

10⁰ = [tex]\frac{1}{3x}[/tex]

1 = [tex]\frac{1}{3x}[/tex]

1 · x = [tex]\frac{1}{3x}[/tex] · x

1x = [tex]\frac{1}{3}[/tex]

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = [tex]\frac{1}{3}[/tex]

Answer:

$3

Step-by-step explanation:

Given

Total Cost Price: $12,000

Unit Cost Price= $6

Total Selling Price = $18,000

Required

Determine the profit on each share

First, we need to determine the units of share bought;

Units = Total cost price / Unit Cost Price

[tex]Units = \frac{\$12000}{\$6}[/tex]

[tex]Units = 2000[/tex]

Next is to determine the selling price of each share; This is calculated as follows;

Unit Selling Price = Total Selling Price / Units Sold

[tex]Unit\ Selling\ Price = \frac{\$18000}{\$2000}[/tex]

[tex]Unit\ Selling\ Price = \$9[/tex]

The profit is the difference between the unit cost price and unit selling price

[tex]Profit = Unit\ Selling\ Price - Unit\ Cost\ Price[/tex]

[tex]Profit = \$9 - \$6[/tex]

[tex]Profit = \$3[/tex]

it was all about equating some values

to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

Let's determine the number of cooks required to bake the required number of cakes during the available time.

We have the following information:

- Each cook can bake either 5 large cakes or 14 small cakes per hour.

- The kitchen is available for 3 hours.

- We need to bake 29 large cakes and 260 cakes in total.

First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:

1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.

Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:

1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.

Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:

Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours

We need to bake 29 large cakes, so:

29 = Number of cooks × 15

Number of cooks = 29 / 15 ≈ 1.93

Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.

Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:

Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours

We need to bake 260 small cakes, so:

260 = Number of cooks × 42

Number of cooks = 260 / 42 ≈ 6.19

Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.

Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.

Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

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Answer:

D

Step-by-step explanation:

Option D is correct. Slope of the line shown in the graph is 3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=(y₂-y₁)/(x₂-x₁)

The line is passing through point (2, 2) and (4, 8).

Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.

Plug in the values in slope formula:

Slope = (8-2)/(4-2)  

=6/2

=3

Hence, slope of the line shown in the graph is 3. Option D is correct.

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Answer:

n + 1

Step-by-step explanation:

Starting with the integer 'n,' we represent the "next integer" by n + 1.

Answer:

2x^2 + x - 6 = rectangular garden: length = 2x – 3 feet; width = x + 2 feet

Step-by-step explanation:

(2x - 3)(x + 2) = 2x^2 + x - 6 =

2x^2 + 4x - 3x - 6 = 2x^2 + x - 6 =

2x^2 + x - 6

You get the original equation from the two sides multiplied. :)

Hope this helps, have a good day.

The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The area is 2x² + x – 6 square feet. Then the factor of the equation is given as,

A = 2x² + x – 6

A = 2x² + 4x – 3x – 6

A = 2x(x + 2) – 3(x + 2)

L × W = (2x – 3)(x + 2)

The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.

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Answer:

Yes it can be concluded that state employees earn on average less than federal employees

  The critical value is  [tex]Z_{\alpha } = - 2.33[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = \$ 59593[/tex]

   The sample size is  n =  30

    The  sample mean is [tex]\= x = \$ 58800[/tex]

     The  standard deviation is  [tex]\sigma = \$ 1500[/tex]

     The significance level is  [tex]\alpha = 0.01[/tex]

The null hypothesis is  [tex]H_o : \mu = \$ 59593[/tex]

 The  alternative hypothesis is  [tex]H_a : \mu < \$ 59593[/tex]

The critical value of [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_{\alpha } = - 2.33[/tex]

 Generally the test statistics is  mathematically evaluated as

            [tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]

=>         [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]  

=>          [tex]t = -2.896[/tex]

The  p-value is obtained from the z-table

   [tex]p-value = P(t < -2.896) = 0.0018898[/tex]

Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees  

Answer:

0.16

Step-by-step explanation:

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

Answer is 0.16

Answer: ABCD is a parallelogram.

Step-by-step explanation:

First we plot these point on a graph as given in attachment.

From the attachment we can observe that AD || BC || x-axis .

also, AB ||CD, that will make ABCD a parallelogram ,  but to confirm we check the property of parallelogram "diagonals bisect each other" , i.e . "Mid point of both diagonals are equal".

Mid point of AC= [tex](\dfrac{-5+4}{2},\dfrac{2+5}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]

Mid point of BD= [tex](\dfrac{-3+2}{2},\dfrac{5+2}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]

Thus, Mid point of AC=Mid point of BD

i.e. diagonals bisect each other.

That means ABCD is a parallelogram.

Answer: ABCD is a parallelogram.

Step-by-step explanation:

First, we plot these points on a graph as given in the attachment. From the attachment, we can observe that AD || BC || x-axis. Also, AB ||CD, which will make ABCD a parallelogram, but to confirm, we check the parallelogram property "diagonals bisect each other," i.e., "Midpoint of both diagonals is equal."

The midpoint of AC=. The midpoint of BD=. Thus, the Midpoint of AC=Mid point of BD diagonals bisects each other. That means ABCD is a parallelogram.

Answer:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The answer is C.

Step-by-step explanation:

We are given the rational function:

[tex]\displaystyle f(x) = \frac{x-3}{4x-1}[/tex]

In rational functions, the domain is always all real numbers except for the values when the denominator equals zero. In other words, we need to find the zeros of the denominator:

[tex]\displaystyle \begin{aligned}4x -1 & = 0 \\ \\ 4x & = 1 \\ \\ x & = \frac{1}{4} \end{aligned}[/tex]

Therefore, the domain is all real number except for x = 1/4.

In interval notation, this is:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The left interval represents all the values to the left of 1/4.The right interval represents all the values to the right of 1/4. The union symbol is needed to combine the two. Note that we use parentheses instead of brackets because we do not include the 1/4 nor the infinities.  

In conclusion, our answer is C.

Answer:

The third one

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

there is 100 candies. That means we can easily turn the amount of each type of candy into a percent. there was 30 butterscotch which means that is 30 percent. There was 15 strawberry which means that is 15 percent. add that and you get 45. This is a shortcut and i advise you use the way your teacher taught you.

[tex]|\Omega|=100\\|A|=30+15=45\\\\P(A)=\dfrac{45}{100}=0.45[/tex]

So TRUE

Answer:

this? hope it helps ........

Answer:

The answer is area=32pi-64 and the perimeter is 8pi

Step-by-step explanation:

Answer:

It sold 14 cans boxes of food and 12 cans of food.

Step-by-step explanation:

The factor for the food cans depend upon every seven food boxes .So, the same no. of sets of food cans will be sold.

Let the no. of sets of food boxes be x.

According to the question,

6x+7x=26

13x=26

x=26/13

x=2

No. of food cans =6x=6×2=12 cans

No. of food boxes=7x=7×2=14 boxes

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Answer:

[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]

Step-by-step explanation:

The domain is the set of all possible x values.

The range is the set of all possible y values.

For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.

[tex]\mathrm{D= (-7,3] }[/tex]

For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.

[tex]\mathrm{R= (-10,9.2] }[/tex]

Answer: 2 years

Step-by-step explanation:

The exponential growth function is given by :-

[tex]y=A(1+r)^x[/tex] (i)

, where A = initial value , r = rate of growth and  x= time period.

As per given ,

A= 242

r= 12% = 0.12

To find : t when y= 300.

Put all the values in (i)

[tex]300=242(1+0.12)^x\\\\\Rightarrow\ \dfrac{300}{242}=(1.12)^x\\\\\Rightarrow\ 1.23967=(1.12)^x[/tex]

Taking log on both sides , we get

[tex]\log (1.2396) = t \log (1.12)\\\\\Rightarrow\ 0.09328=t(0.049218)\\\\\Rightarrow t=\dfrac{0.09328}{0.049218}=\approx2[/tex]

hence, it will take 2 years.