Determine the five-number summary for this data set, taking into account any outliers. 10 13 15 12 12 4 12 17 12 13 15 18 10 11 20 19 Tiles 11.5 13 16 20 10 12.5 17

Answer:

13. Answer: 0

17. Answer: 3

19. Answer: 2

Step-by-step explanation:

13. f(g(3))

First find g(3) on the right graph.

We see that at x = 3, g(x) = 4

So g(3) = 4

Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer

17.f(f(5))

f(5) = 1

f(f(5)) = f(1) = 3 answer

19. g(g(2))

g(2) = 0

g(g(2)) = g(0) = 2 answer

a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).

a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).

b.i) The Hare runs 31,680 inches per minute (1,900,800/60).

b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).

c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).

In this exercise, the following equivalent values are used for computing the distance and speed:

Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)

Speed of Hare = 30mph

30 miles = 52,800 yards (30 x 1,760)

52,800 yards = 1,900,800 inches (52,800 x 36)

= 880 yards per minute (52,800/60)

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El volumen que queda entre la esfera y el cubo es:  30.49cm^3

El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.

Para el cubo que tiene una arista de 4cm, el volumen es:

V = (4cm)^3 = 64 cm^3

Para la esfera con un diametro de 4cm, el radio es:

R = 4cm/2 = 2cm

Y el volumen será:

V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3

El volumen que queda entre la esfera y el cubo es:

V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3

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Since there is only one value of x, hence the equation given has only one solution

Equations are expressions separated using mathematical operations. Given the equation below;

2x+5+2x+3x = x

Collect the like terms

2x+2x+3x -x = -2

7x -x = -2

Simplify

6x = -2

x = -2/6

x = -1/3

Since there is only one value of x, hence the equation given has only one solution

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Answer: 60

Step-by-step explanation:

Almost everything in this picture is irrelevant to finding the measure of x.

x = 180 - 90 - 30 = 60

Answer:

y = 2x² − 12x + 8

Step-by-step explanation:

FIRST METHOD :

y = 2x² − 12x + 8

  = (2x² − 12x) + 8

  = 2 (x² − 6x) + 8

  = 2 (x² − 6x + 9 − 9 ) + 8

  = 2 (x² − 6x + 9) − 2×9 + 8

  = 2 (x² − 6x + 9) − 18 + 8

  = 2 (x² − 6x + 9) − 10

  = 2 (x − 3)² − 10

Then ,the equation has a extremum value of (3,-10)

Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0

(2 > 0) , the graph (parabola) opens upward

Therefore ,the extremum (3,-10) is a minimum.

SECOND METHOD :

the graph of a function of the form f(x) = ax² + bx + c

has an extremum at the point :

[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]

in the equation : f(x) = 2x² − 12x + 8

a = 2  ; b = -12  ; c = 8

Then

[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]

Then

[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]

the graph of a function f(x) = 2x² − 12x + 8

has an extremum at the point (3 , -10)

Since the parabola opens up ,then the extremum (3,-10) is a minimum.

The dependent variable here is task performance. The independent variable in the question is musical genres.

This is the term that is used to refer tp the variable that is of interest. It is the variable that one is trying to determine.

The independent variable is the x variable. It is the variable that helps us check the impact that it has on the dependent variable.

The task performance is what we want to know here. To do so we want to use the genre of music.

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Answer:

slope is 4

Step-by-step explanation:

Slope is rise/run

for every 4 units it rises it runs 1 unit

4/1=4

Using the normal distribution, the value of z is of z = 1.5.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

For this problem, considering the symmetry of the normal distribution, the area above the mean is given by:

0.8664/2 = 0.4332.

Hence z has a p-value of 0.5  + 0.4332 = 0.9332, hence the value of z is z = 1.5.

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The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

Herein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:

dy / dt = 3 · y · (1 - y / 14)

dy / [3 · y · (1 - y / 14)] = dt

dy / [- (3  / 14) · y · (y - 14)] = dt

By partial fractions we find the following expression:

- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt

- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.

y = 14 / [1 - C · tⁿ], where n = - 14² / 3.

If y(0) = 10, then the particular solution is:

y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.

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Answer:

I think it's 120 dollars sorry if i get it wrong but I am sure it is right tell me when you get the right answer byeeee.

Answer:

the price of one pound of trail mix is $3

the price of one pound of jelly beans is $2.5

Step-by-step explanation :

let t be the price of one pound of trail mix.

and b be the price of one pound of jelly beans.

This statement:

“For 3 pounds of trail mix and 8 pounds of jelly beans,

the total cost is $29”

Can be translated mathematically like this :

3t + 8b = 29

This statement:

“For 5 pounds of trail mix and 2 pounds of jelly beans,

the total cost is $20”

Can be translated mathematically like this :

5t + 2b = 20

We obtain a system of two equations :

3t + 8b = 29

5t + 2b = 20

Solving the system:

3t + 8b = 29  (equation 1)

5t + 2b = 20. (equation 2)

3t + 8b = 29

20t + 8b = 80   [4×(equation 2)]

3t + 8b = 29

17t = 51  [4×(equation 2) - equation 1]

3t + 8b = 29

t = 51/17 = 3

9 + 8b = 29

t = 3

8b = 20

t = 3

b = 20/8 = 5/2

t = 3

b = 5/2

t = 3

Therefore ,the solution to our system is (3 , 2.5)

Step-by-step explanation:

the probability of 1 tested insect is killed is 60% or 0.6.

the probability that it is not killed is then 1-0.6 = 0.4.

when we test 7 insects and exactly 4 survive is the event that

3 insects are killed, 4 insects survive.

the probability for one such case is

0.6×0.6×0.6 × 0.4×0.4×0.4×0.4

how many such cases do we have ?

as many as ways we can select 4 insects out of the given 7.

these are 7 over 4 combinations :

7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35

so, the probability that exactly 4 out of 7 tested insects survive is

35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935

If y = 3 cot x/8, the double differentiation of y gives,

y'' = (3/32) (cosec x/8)(cot x/8)

Given value of y is,

y = 3 cot x/8

Differentiation of the above equation will give us the following,

y' = d(3 cot x/8) / dx

y' = 3d(cot x/8) / dx ........... (1)

Now, we know that the differentiation of cot x is -cosec²x

Therefore, d(cot x/8) / dx = -(cosec²x/8)/8

Thus, equation (1) transforms as follows,

y' = -3(cosec²x/8)/8

Taking differentiation of the above equation, we get,

y'' = -3d((cosec²x/8)/ 8dx

y'' = -6d(cosec x/8) / 8dx   [Using chain rule] .......... (2)

As we know, the differentiation of cosec x is -(cosec x)(cot x),

d(cosec x/8) / dx = -(cosec x/8)(cot x/8) / 8 [Using chain rule]

Therefore, equation (2) can be written as,

y'' = -(-6(cosec x/8)(cot x/8) / (8×8)

∴ y '' = 3(cosec x/8)(cot x/8) / 32

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Answer:

9 Sahil has a fish tank in the shape of a cuboid, as shown in the diagram-- Diagram is NOT accurately drawn The tank is

55 cm long

28cm wide

cm 33 high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the tank. What is the greatest number of neon tetra fish Sahil can put in his tank?

Step-by-step explanation:

Answer:

(a+b)² - 11(a+b) -42

Step-by-step explanation:

Thoughtfully split the expression at hand into groups, each group having two terms,

Group 1:  -11b-11a 

Group 2:  a2+2ab 

Group 3:  b2-42 

Pull out from each group separately :

Group 1:   (a+b) (-11)

Group 2:   (a+2b) (a)

Group 3:   (b2-42) (1)

Looking for common sub-expressions :

Group 1:   (a+b) (-11)

Group 3:   (b2-42) (1)

Group 2:   (a+2b) (a)

final answer:(a+b)² - 11(a+b) -42

Answer:

(a+b+3)(a+b-14)

Step-by-step explanation:

let a+b be x,

= x²-11x-42

=x²-(14-3)x-42

=x²-14x+3x-42

=x(x-14)+3(x-14)

=(x+3)(x-14))

replacing x by a+b,

=(a+b+3)(a+b-14)

Based on the cost and revenue functions to the company for selling x items, the domain of C(x) is [0, 100].

The range of C(x) is (200, 4,200).

The domain would be the lowest capacity and the maximum capacity. As these are physical units to sell, the lowest unit would be 0 units as units can't be negative.

The maximum capacity is given as 100 items so the domain is:

= [0, 100]

The range is:

When x is 0, the function gives C(x) as:

= 40(0) + 200

= 200

When x is the maximum of 100, the C(x) is:

= 40(100) + 200

= 4,200

Range is:

(200, 4,200)

Full question is:

What is the domain and range of C(x)?

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From the 2 selected employees, the probability that they will both be females is; C: 4/15

We are given;

Number of male employees = 7

Number of female employees = 8

Total number of employees = 8 + 7 = 15

Now, 2 random employees are chosen and so the number of ways of selecting this is; 15C2

Now, out of the 2 selected employees, the probability that they will be female = 8C2/15C2 = 28/105 = 4/15

Thus, we can conclude that from the 2 selected employees, the probability that they will both be females is; C: 4/15

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The probability that the student plays football is 20/33.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the student plays football = total number of students who play football / total number of students

The probability that the student plays football = 40/66 = 20/33

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Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.

The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.

Given that angle ADE ≅ angle ABC, we also know that:

Angle EAD ≅ CAB.

Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.

Thus, the ratios that are equal to each other would be:

AE/EC = AD/DB.

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there are 12 months in a year, so then 4 months is really 4/12 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\to \frac{4}{12}years\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (1200)(0.05)(\frac{1}{3})\implies I=20~GHC[/tex]

The period of [tex]f(x)[/tex] is [tex]\boxed{2\pi}[/tex].

Recall that [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] both have periods of [tex]2\pi[/tex]. This means

[tex]\sin(x + 2\pi) = \sin(x)[/tex]

[tex]\cos(x + 2\pi) = \cos(x)[/tex]

Replacing [tex]x[/tex] with [tex]3x[/tex], we have

[tex]\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)[/tex]

In other words, if we change [tex]x[/tex] by some multiple of [tex]\frac{2\pi}3[/tex], we end up with the same output. So [tex]\sin(3x)[/tex] has period [tex]\frac{2\pi}3[/tex].

Similarly, [tex]\cos(5x)[/tex] has a period of [tex]\frac{2\pi}5[/tex],

[tex]\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)[/tex]

We want to find the period [tex]p[/tex] of [tex]f(x)[/tex], such that

[tex]f(x + p) = f(x)[/tex]

[tex] \implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)[/tex]

On the left side, we have

[tex]\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)[/tex]

and

[tex]\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)[/tex]

So, in terms of its period, we have

[tex]f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)[/tex]

and we need to find the smallest positive [tex]p[/tex] such that

[tex]\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}[/tex]

which points to [tex]p=2\pi[/tex], since

[tex]\cos(2\pi-2\pi) = \cos(0) = 1[/tex]

[tex]\sin(2\pi - 2\pi) = \sin(0) = 0[/tex]

This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.

The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.

It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.

The yearly interest rate must be divided by 12.

Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).

Additionally, you'll add 12 to the number of years remaining on your loan term.

The total amount of interest that is paid for the term loan is $383,385.54

Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.

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Answer:

40°, 50°, and 90°

Step-by-step explanation:

Let the smallest angle be x.

Then, the other small angle is x+10.

The acute angles of a right triangle are complementary, so x+x+10=90, and thus x=40.

So, the acute angles measure 40° and 50°.

Therefore, the three angles are 40°, 50°, and 90°.

Answer:

[tex]h = \bf 28.3 \space\ m[/tex]

Step-by-step explanation:

• We are given:

○ Volume = 36 m³,

○ Circumference = 4 m

• Let's find the radius of the cylinder first:

[tex]\mathrm{Circumference} = 2 \pi r[/tex]

Solving for [tex]r[/tex] :

⇒ [tex]4 = 2 \pi r[/tex]

⇒ [tex]r = \frac{4}{2\pi}[/tex]

⇒ [tex]r = \bf \frac{2}{\pi}[/tex]

• Now we can calculate the height using the formula for volume of a cylinder:

[tex]\mathrm{Volume} = \boxed{\pi r^2 h}[/tex]

Solving for [tex]h[/tex] :

⇒ [tex]36 = \pi \cdot (\frac{2}{\pi}) ^2 \cdot h[/tex]

⇒ [tex]h = \frac{36 \pi^2}{4 \pi}[/tex]

⇒ [tex]h = 9 \pi[/tex]

⇒ [tex]h = \bf 28.3 \space\ m[/tex]

Answer:

9π m ≈ 28.27m

Step-by-step explanation:

The volume of a right cylinder is given by the formula

πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder

Circumference of base of cylinder is given by the formula 2πr

Given,

2πr = 4m

r = 2/π m

Volume given as 36 m³

So πr²h = 36
π (2/π)² h = 36

π x 4/π² h = 36

(4/π) h = 36

h = 36π/4 = 9π ≈ 28.27m

The focal length of the given ellipse is given as (±6, 0)

An ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.

The standard equation of an ellipse is expressed as;

x^2/a^2 + y^2/b^2 = 1

The formula for calculating the focus of the ellipse is given as:

c^2 = b^2 - a^2

Given the equation of an ellipse

(x-7)^2/64 + (y-5)^2/100 = 1

This can also be expressed as:

(x-7)^2/8^2 + (y-5)^2/10^2 = 1

Comparing with the general equation

a = 8 and b = 10

Substitute

c^2 = 10^2 - 8^2

c^2 = 100 - 64

c^2 = 36

c = 6

Hence the focal length of the given ellipse is given as (±6, 0)

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Answer:

The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.

'25' above sigma is the upper bound.

In general it means adding 42 from 1 to 25 times.

so 42(25).

Answer:

C. 42(25)

Step-by-step explanation:

Took the unit test review and this was the correct option choice.

Goodluck on your unit test, I am sure that you will do good :)

Answer:

Point C will be at (3,1), Point B will be at (7,1) and Point A will be at (7,5)

Step-by-step explanation:

[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]

[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]

[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787