3. (6 Points). Solve the initial value problem y'-y.cosx=0, y(pi/2)=2e

Answer: The probability that the batch is accepted is 0.812.

Step-by-step explanation:

Since we have given that

Number of defective cars = 5

Total number of cars = 100

Probability of getting first car non defective = [tex]\dfrac{95}{100}[/tex]

probability of getting second car non defective = [tex]\dfrac{94}{99}[/tex]

Probability of getting third car non defective =  [tex]\dfrac{93}{98}[/tex]

Probability of getting fourth car non defective = [tex]\dfrac{92}{97}[/tex]

Using the multiplication rule, probability that the batch is accepted is given by

[tex]\dfrac{95}{100}\times \dfrac{94}{99}\times \dfrac{93}{98}\times \dfrac{92}{97}\\\\=0.812[/tex]

Hence, the probability that the batch is accepted is 0.812.

Answer with explanation:

→Total number of people in the committee=6

→Number of votes in the system represented by q ,

      =6+ 4+4+ 3+ 2+ 1=20

a.→Value of q would represent a simple majority if , q>10 that is it would be greater than 50% of votes, means 11 votes.

b.→Value of q that would represent two-thirds majority

        [tex]=\frac{2}{3}\times 20\\\\=\frac{40}{3}\\\\=13.33[/tex]

Approximately 14 votes.

Answer:

angular moment is 0.25 kg.m²/s

Step-by-step explanation:

given data in question

mass (m) = 0.25 kg

length of string i.e. radius (r) = 0.5 m

velocity = 2 m/s

to find out

angular momentum before mass release

solution

we know angular moment formula i.e.

angular moment = mass × velocity × radius   ................1

put the value mass velocity and radius in equation 1 we get angular moment i.e.

angular moment = mass × velocity × radius

angular moment = 0.25 × 2 × 0.5

angular moment = 0.25

so the angular moment is 0.25 kg.m²/s before release and 0.25 kg.m²/s after release because angular momentum is always conserved

The question deals with angular momentum and its conservation in rotational motion. The angular momentum before the mass is released remains constant and is carried by the mass upon release. Supplementary problems discuss changes in angular momentum and the effects of pulling in a spinning mass on its rotational dynamics.

The question regards the concept of angular momentum in classical mechanics, specifically within the realm of rotational motion. Angular momentum, denoted by L, is a physical quantity that represents the rotational inertia of a spinning object multiplied by its angular velocity, and it's given by the formula L = Iω, where I is the moment of inertia and ω is the angular velocity.

For the case where a mass is spinning over your head and then released, the angular momentum just before the release is conserved. This means that if we calculate the angular momentum while the mass is attached to the string and spinning, the same amount of angular momentum will be present in the mass's linear motion after it is released along the tangent. If we assume that the mass travels in a circular path while attached to the string, the angular momentum can be related to the linear momentum by L = mvr, where m is the mass, v is the linear velocity just before release, and r is the radius of the circular path.

Upon release, because angular momentum is conserved, the mass carries this angular momentum into its linear motion, causing it to move off on a tangent at a velocity that reflects this conservation. If there are no external torques acting on the system, the angular momentum will not change; therefore, it 'moves' with the mass as linear momentum.

Regarding the supplementary problems provided, when angular velocity is increased, the tendency for a spinning object is to move outward due to centrifugal force. Consequently, the string's angle with respect to the vertical will increase. To calculate the initial and final angular momenta, one would use the same conservation principle, taking into account the changes in angular velocity and the moment of inertia. A scenario where the rod spins fast enough to make the ball horizontal suggests an infinitely large angular velocity, which is not practically achievable. Therefore, the ball cannot be truly horizontal as it would require an infinite amount of energy.

Concerning the rock on a string example, as you pull the string in and reduce the radius, the angular momentum remains constant assuming no external torques are acting on the system. This leads to an increase in the angular velocity since L = Iω and I decreases with a smaller radius (I for a point mass is mr²). The increased speed will result in a shorter time required for one revolution (higher frequency of rotation) and a greater centripetal acceleration. The string is under more tension as a result of the increased centripetal force, which might lead to it breaking.

For the collision problem with the spinner and the rod spinning at different rates, conservation of energy or momentum principles would be employed to find the corresponding change in angular velocity. The initial and final angular momenta or energies are equated, considering that all the energy transferred is mechanical and that the rotational inertia of the spinner is required to calculate the angular velocity post-collision.

Answer:  The equation, in "slope-intercept form" ; is:

________________________________________________

                   →   " y  =   x  +  4  " .

________________________________________________

Step-by-step explanation:

________________________________________________

Use the formula for linear equations;  written in "point-slope format" ;

which is:

      y −  y₁  = m( x −  x₁ )  ;

We are given the slope, "m" ;  has a value of:  "1 " ;  

           that is;  " m = 2 " .

________________________________________________

  We are given the coordinates to 1 (one) point on the line; in which the coordinates are in the form of :

    " ( x₁ , y₁ ) " ;  

→   that given point is:  "(10, 6)" ;  

            in which:  x₁ =  10 ;

                             y₁  =  6 .

→ Given:  The slope, "m" equals "1" ;  ________________________________________________

Let's plug our known values into the formula:

    →  "  y  −  y₁  = m( x − x₁ ) "  ;

_______________________________________________

    →   As follows:

    →   " y  −  10  = 1(x − 6) ;

______________________________________________

Now, focus on the "right-hand side of the equation" ;

    →    1(x  −  6) = ? ;   Simplify.

______________________________________________

Note the "distributive property" of multiplication:

            →  a(b + c) =  ab   +   ac ;

As such:  " 1(x  −  6) =  (1*x)  +  (1 * -6) " ;

                             =  1x   + (-6) ;

                             =   x  −  6 ;

[Note that:  " 1 x = 1 * x = x " ;

[Note that   " + (-6) "  =  " ( " − 6 " ) .] ;  

                 →  {since:  "Adding a negative" is the same as:

                                  "subtracting a positive."} ;

________________________________________________

          Now, let us bring down the "left-hand side of the equation" ; &

rewrite the entire equation; as follows:

________________________________________________

                           →   "  y  −  10  =   x  −  6 " ;  

________________________________________________

Note:  We want to rewrite the equation in "slope-intercept form" ;

           that is;  " y = mx + b "  ;

                 in which:  "y" ; stands alone as a single variable on the "left-hand side" of the equation;  with "no coefficients" [except for the "implied coefficient" of " 1 "} ;

                                 "m" is the coefficient of "x" ;

                                 and the "slope of the line" ;  

          Note that "m" may be a "fraction or decimal" ; and may be "positive or negative.

            If the slope is "1" ; (that is "1 over 1" ; or: "[tex]\frac1}{1}[/tex]" ;

then,  " m = 1 " ;  and we can write " 1x " as simply "x" ; since the implied coefficient is "1" ;  

               →  since " 1" , multiplied by any value {in our case, any value for "x"} , equals that same value.

________________________________________________

       "b"  refers to the "y-intercept" of the graph of the equation;  

           that is; the "y-value" of the point at which the graphed line of the equation crosses the "y-axis" ;  

           that is, the "y-value" of the coordinates of the point at which the graphed line of the equation crosses the "y-axis" ;

           that is, the ["y-value" of the]  y-intercept" .  

Note that the value of "b" may be positive or negative, and may be a decimal or fraction.

  If the value for "b" is negative, the equation can be written in the form:

          " y = mx - b " ;

    {since:  " y = mx + (-b) "  is a bit tedious .}

          If the y-intercept is "0" ; (i.e. the line crosses the y-axis at the origin, at point:  " (0,0) " ;  

then we simply write the equation as:  "y = mx " ;  

                                ________________________________________________

So;  we have:              →   " y  − 10  =  x  −  6 " ;  

________________________________________________

       →   We want to rewrite our equation in slope-intercept form,

that is;  " y = mx + b " ;  as explained above.

We can add "10" to each side of the equation ; to isolation the "y" on the "left-hand side" of the equation:

           →  " y  −  10  + 10  =  x  − 6  +  10 " ;

to get:

           →  " y  =  x  +  4 " ;

________________________________________________

          →  which is our answer.

________________________________________________

Note:  This answer:  " y = x + 4 " ;

                  →  is written in the "slope-intercept format";  

                     →   " y = mx +  b "  ;

  in which:  "y" is isolated as a single variable on the "left-hand side of the equation" ;

                   The slope of the equation is "1" ; or an implied value of "1" ;

    that is;   " m  = 1 " ;  

                   "b  =  4 " ;  

         →  {that is;  the "y-value" of the  "y-intercept" —  "(0, 4)" — of the graph of the equation is:  "4 ".} .

________________________________________________

Hope this answer is helpful!

          Best wishes to you in your academic pursuits

               —  and within the "Brainly" community!

________________________________________________      

To solve the equation [tex]25^3^k[/tex] = 625, rewrite the base as a power of 5 and use the exponentiation rule. Simplify the equation and equate the exponents to solve for k.

To solve the exponential equation 253k = 625, we need to rewrite the base of 25 as a power of 5. Since 25 = 52, we can rewrite the equation as (52)3k = 625.

Using the rule (ab)c = ab × c, we can simplify the equation to 52 × 3k = 625.

Now, we can rewrite 625 as a power of 5 by realizing that 625 = 54. Therefore, we have 52 × 3k = 54.

Since the bases are the same, we can equate the exponents and solve for k:

2 × 3k = 4

6k = 4

k = 4/6

k = 2/3

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To solve the exponential equation 25^3k = 625, rewrite the base 25 as a power of 5. Simplify the equation and set the exponents equal to each other to solve for k.

To solve the exponential equation 253k = 625, we can rewrite the base 25 as a power of 5, since 52 = 25. So, the equation becomes (52)3k = 625. Using the rule of exponents (am)n = amn , we can simplify it to 56k = 625.

Next, we can rewrite 625 as a power of 5: 625 = 54. So, the equation becomes 56k = 54.

Since the bases are the same, we can set the exponents equal to each other: 6k = 4. Solving for k, we divide both sides by 6 to get k = 4/6 = 2/3.

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Answer:

1/3

Step-by-step explanation:

Once you know there is a 3 in the hand, and only one card is drawn from the cards in the hand, then the probability of drawing the 3 is 1/3.

Answer:

P (chosen card is 3) = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We are given that a 3​-card hand is dealt from a standard​ 52-card deck, and then one of the 3 cards is chosen at random.

Given that only one of the cards is a 3, we are to find the probability that the chosen card is a 3.

Since only one card is a 3 and one card is chosen so:

P (chosen card is 3) = 1 / 3

Answer:

Step-by-step explanation:

Given function is

(a)F(x)=[tex]\left ( x^{3}+5\right )^{0.25}-15e^{x^{3}}[/tex]

[tex]F^{'}\left ( x\right )[/tex]=[tex]0.25\left ( x^{3}+5\right )^{-0.75}\frac{\mathrm{d} x^{3}}{\mathrm{d} x}-15e^{x^{3}}\frac{\mathrm{d} x^{3}}{\mathrm{d} x}[/tex]

[tex]F^{'}\left ( x\right )=0.25\left ( x^{3}+5\right )^{-0.75}\times 3x^{2}-15e^{x^{3}}\times \left ( 3x^{2}\right )[/tex]

(b)F(x)=[tex]\frac{\left ( x-3\right )^2\left ( x-5\right )}{\left ( x-4\right )^2\left ( x^{2}+3\right )^5}[/tex]

[tex]F^{'}\left ( x\right )[/tex]=[tex]\frac{\left [ 2\left ( x-3\right )\right \left ( x-5\right )+\left ( x-3\right )^2]\left [ \left ( x-4\right )^2\left ( x^2+3\right )^5\right ]-\left [ 2\left ( x-4\right )^{3}\left ( x^2+3\right )^5+5\left ( x^2+3\right )^4\left ( 2x\right )\left ( x-4\right )^2\right ]\left [ \left ( x-3\right )^2\left ( x-5\right )\right ]}{\left [\left ( x-4\right )^2\left ( x^2+3\right )^5\right ]^2}[/tex]

Let

[tex]S=23+24+25+\cdots+101+102+103[/tex]

This sum has ___ terms. Its terms form an arithmetic progression starting at 23 with common difference between terms of 1, so that the [tex]n[/tex]-th term is given by the sequence [tex]23+(n-1)\cdot1=22+n[/tex]. The last term is 103, so there are

[tex]103=22+n\implies n=81[/tex]

terms in the sequence.

Now, we also have

[tex]S=103+102+101+\cdots+25+24+23[/tex]

so that adding these two ordered sums together gives

[tex]2S=(23+103)+(24+102)+\cdots+(102+24)+(103+23)[/tex]

[tex]\implies2S=\underbrace{126+126+\cdots+126+126}_{81\text{ times}}=81\cdot126[/tex]

[tex]\implies S=\dfrac{81\cdot126}2\implies\boxed{S=5103}[/tex]

Answer:

98

Step-by-step explanation:

100-65=35

Turn 35 into a percent then a decimal, later multiply it by 280

280 X .35=98

Final answer:

The sale price of the down comforter after a 65% discount is $98. This is found by calculating the discount amount of $182 from the original price of $280, then subtracting it to find the final sale price.

Explanation:

To calculate the sale price of the down comforter after a reduction of 65%, we first find the discount amount and then subtract it from the original price. Here's how:

To calculate the discount amount:

The sale price of the down comforter after a 65% discount is $98.

Answer:  0.0971

Step-by-step explanation:

Given : Sample size : [tex]n=26[/tex]

The percent of people are afraid of flying [tex]=43\%[/tex]

Thus the proportion of people are afraid of flying [tex]P=0.43[/tex]

We know that the formula to find the standard deviation of the distribution of sample proportions is given by :-

[tex]\text{S.E.}=\sqrt{\dfrac{P(1-P)}{n}}\\\\\Rightarrow\text{S.E.}=\sqrt{\dfrac{0.43(1-0.43)}{26}}\\\\\Rightarrow\ \text{S.E.}=0.0970923430396\approx0.0971[/tex]

Hence, the standard deviation of the distribution of sample proportions = 0.0971

The standard error for the distribution of sample proportions is approximately 0.0966 (rounded to four decimal places).

The standard error (SE) for a sample proportion can be calculated using the following formula:

SE = √[p(1 - p) / n]

Where:

p is the population proportion (0.43, or 43% expressed as a decimal).

n is the sample size (26).

Let's calculate the standard error:

SE = √[0.43 * (1 - 0.43) / 26]

SE = √[0.43 * 0.57 / 26]

SE = √(0.009351923076923077)

SE ≈ 0.096645

So, the standard error for the distribution of sample proportions is approximately 0.0966 (rounded to four decimal places).

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Answer: 2.14 %

Step-by-step explanation:

Given : pH measurements of a chemical solutions have

Mean :  [tex]\mu=6.8[/tex]

Standard deviation : [tex]\sigma=0.02[/tex]

Let X be the pH reading of a randomly selected customer chemical solution.

We assume  pH measurements of this solution have a nearly symmetric/bell-curve distribution (i.e. normal distribution).

The z-score for the normal distribution is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x = 6.74

[tex]z=\dfrac{6.74-6.8}{0.02}=-3[/tex]

For x = 6.76

[tex]z=\dfrac{6.76-6.8}{0.02}=-2[/tex]

The p-value =[tex]P(6.74<x<6,76)=P(-3<z<-2)[/tex]

[tex]P(z<-2)-P(z<-3)=0.0227501- 0.0013499=0.0214002\approx0.0214[/tex]

In percent, [tex]0.0214\times=2.14\%[/tex]

Hence, the percent of pH measurements reading below 6.74 OR above 6.76 = 2.14%

None of the given sets A, B, or C is a subspace of Pn. Set A does not always include the zero vector, set B does not contain the zero polynomial, and set C excludes cases where coefficients aren't positive.

In mathematics, a subspace must satisfy three conditions: it must contain the zero vector, it must be closed under addition, and it must be closed under scalar multiplication. Looking at the set A, we see that it does not contain all polynomials of the form p(t) = a + bt2, as it won't include the zero vector when both a and b are not zero. Therefore, set A is not a subspace.

Set B includes all polynomials of exactly degree 4. But it doesn't contain the zero polynomial which is of degree 0, so B isn't a subspace either.

As for set C, although it includes polynomials of degree at most 4, it requires the coefficients to be positive which is problematic in case of scalar multiplication. Hence, C is not a subspace.

Therefore, none of the specified sets is a subspace of Pn for the appropriate value of n.

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[tex]x=7.5\overline{26}\\10x=75.\overline{26}\\1000x=7526.\overline{26}\\1000x-10x=7526.\overline{26}-75.\overline{26}\\990x=7451\\x=\dfrac{7451}{990}[/tex]

It can be expressed as a fraction with integer numerator and denominator, so it's a rational number.

Answer:

  see below

Step-by-step explanation:

Filling the given numbers into the given formulas, you have ...

Line AB:

  x = 1 +(4-1)t, y = 1 +(3-1)t

  x = 1+3t, y = 1+2t . . . . . . simplify

Line BC:

  x = 4 +(1-4)t, y = 3 +(7-3)t

  x = 4 -3t, y = 3 +4t . . . . . simplify

Line AC:

  x = 1 +(1-1)t, y = 1 +(7-1)t

  x = 1, y = 1+6t . . . . . . . . . .simplify

Step-by-step Answer:

Calculating Pi using Archimedes method of polygons.

We know that the definition of pi is the ratio of circumference of a circle divided by the diameter.  Starting with Pythagorean Theorem, and proposition 3 of Euclid’s Elements, Archimedes was able to approximate pi to any precision arithmetically, without further resort to geometry!

He figured that the perimeter of any regular polygon (all sides and vertex angles equal) is an approximation to a circle.  More sides will make closer approximations.

Starting with a hexagon, he bisects the central angles to make polygons 12-, 24-, 48- and 96-sides, whose perimeters approaches that of a circle, and hence the approximation to pi since the diameter remains known and constant.

Proposition 3 is also commonly referred to as the angle bisector theorem, which states that in a triangle, an angle bisector subdivides the opposite sides in the ratio of the two remaining sides.

 Please refer to the attached image for the nomenclature of the geometry.

The accompanying diagram shows that the perimeter of a hexagon is 12 times the length of AB, or 12*(1.0/2) = 6.  With the diameter equal to 2*1.0 = 2, the approximation to pi is 6/2=3.0.

Pi(6) = 3.0

If we divide the central angle by two, we end up with a 12-sided polygon (dodecagon), with the half central angle of 15 degrees (triangle A’BC).  To calculate the new perimeter, we need to calculate the length A’B, which is given by the angle-bisector theorem as

A’B / A’A  = BC / AC

All other sides are known in terms of A’B

A’B / (0.5-A’B) = sqrt(3)/2 / 1

Solve for A’B by cross-multiplication and solving for A’B, we get

A’B = sqrt(3)/(2sqrt(3)+4) = 0.2320508 (to 7 decimals)

At the same time, the radius has been reduced to  

A’C = sqrt(A’B^2+BC^2) = 0.896575

That brings the approximation of pi as 12*A’B/A’C

P(12) = 3.1058285 (7 decimals)

Continuing bisecting, now using a polygon of 24 sides, we only have to replace

AB by A’B, AC by A’C, and 12 by 24 to get

Pi(24) = 3.132629 (7 decimals)

Repeating again for a polygon of 48 sides,  

Pi(48) = 3.1393502

Pi(96) = 3.1410320

Pi(192) = 3.1414525

Pi(384) = 3.1415576

Etc.

The accurate value of pi to 10 digits is 3.1415926536

And we conclude that Pi(48) is the first approximation the provides 2 decimal places of accuracy.

Note: What was calculated was actually the lower bound value of pi.

We can obtain the upper bound value of pi using the length of BC as the radius, which gives the upper bound.  The average of the two bounds for a 384-sided polygon gives P_mean(384) = 3.1416102, which is accurate to 2 units in the 5th decimal place.

The Archimedes exhaustion method is a geometric approach to estimate the value of pi. By inscribing and circumscribing regular polygons within and around a circle, Archimedes determined lower and upper bounds for the value of pi.

As the number of sides for the polygons increased, the approximation of pi became more accurate. With a 96-sided polygon, Archimedes found that pi was greater than 3.1408 and less than 3.1429. By taking the average of these bounds, a more precise estimation of pi accurate to two decimal places is achieved.

Thus, using the Archimedes exhaustion method, we can estimate pi to be approximately 3.14, making it precise to two decimal places.

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We have [tex]17\equiv-9\pmod{26}[/tex], so that [tex]x\equiv-1\pmod{26}[/tex], so [tex]x\equiv25\pmod{26}[/tex], and any solution of the form [tex]x=25+26n[/tex] satisfies the congruence, where [tex]n[/tex] is any integer.

The question involves solving a congruence equation. Given the equation 9x + 17 ≡ 0 (mod 26), we would typically isolate x to find the solution. However, the question seems to be missing an operator. Hence, an explicit answer cannot be provided.

The question involves solving a congruence. To solve the accord 9x ≡ 17 (mod 26), you must find an integer x such that 9x leaves a remainder of 17 when divided by 26.

This unity can be rewritten as 9x - 17 = 26k, where k is an integer. Our task is to solve for x given these parameters.

Given the nature of the question, I cannot provide a direct solution because it is missing an operator between 9x and 17. Assuming the operator is '+', the congruence will be 9x + 17 ≡ 0 (mod 26).

The steps to solve a congruence equation can vary, but generally, the goal is to isolate x on one side of the equation. However, it's easier to proceed with this congruence with explicit details.

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Answer:

x (smallest to largest) = 0,45 ,55

y (smallest to largest) = 0,10,40

Step-by-step explanation:

(hours)        Dinghy Rowboat        Labor Available

Metal Work 2             3                       120

Painting         2              2                        110

Let x represent the number of dinghies the company can manufacture and y represent the number of rowboats.

So, total hours for metal work = [tex]2x+3y[/tex]

So, total hours for Painting = [tex]2x+2y[/tex]

So, equation becomes:

[tex]2x+3y\leq 120[/tex]

[tex]2x+2y\leq 110[/tex]

[tex]x\geq 0[/tex]

[tex]y\geq 0[/tex]

Plot the inequalities

Refer the attached figure

So, the vertices of the feasible region are (0,40),(45,10) and (55,0)

So, x values are 0 , 45 and 55

x represents the number of dinghies

So, x (smallest to largest) = 0,45 ,55

y values are 40,10,0

y represent the number of rowboats.

So, y (smallest to largest) = 0,10,40

Answer:

Data warehouse

Step-by-step explanation:

Data warehouse  is a technology that combines data from one or more sources so it can be compared for making business decisions.

Moreover, Data warehouse can be explained as  a technology that combines from one or more sources so it can be prepared for making business decisions. A data warehouse is constructed by Integrating data from multiple heterogeneous sources that support analytical reporting, and decision making.

Answer:

The basic quadratic function is f(x) = x²

The equation of the graph is y = (x - 3)² - 1

Step-by-step explanation:

* Lets explain how to solve the problem

- The graph is a parabola which oped upward

∵ The function is represented by a parabola

∴ The graph is a quadratic function

∴ The basic quadratic function is f(x) = x²

- The vertex of the basic quadratic function is (0 , 0)

∵ From the graph the vertex of the parabola is (3 , -1)

∵ The x coordinate of the basic function change from 0 to 3

∴ The basic function translate 3 units to the right

- If the function f(x) translated horizontally to the right  by h units,

 then the new function g(x) = f(x - h)

∵ f(x) = x²

∴ The new function g(x) = (x - 3)²

∵ The y-coordinate of the basic function change from 0 to -1

∴ The basic function translate 1 unit down

- If the function f(x) translated vertically down  by k units, then the

 new function g(x) = f(x) - k

∵ g(x) = (x - 3)²

∴ The new function h(x) = (x - 3)² - 1

∵ h(x) = y

∴ The equation of the graph is y = (x - 3)² - 1

# Note: you can write the equation in general form by solve the

  bracket of power 2

∵ (x - 3)² - 1 = (x)(x) - (2)(3)(x) + (3)(3) - 1 = x² - 6x + 9 - 1 = x² - 6x + 8

∴ y = x² - 6x + 8

Answer:

42 gtt/min

Step-by-step explanation:

Amount of fluid to be infused = 500 mL

Time = 3 hours = 3×60 = 180 minutes

Tubing drop factor/mL = 15 gtt/mL

Fussion rate = (Amount of fluid to be infused / time in minutes)

Fussion rate = 500/180 = 2.78 mL/min

gtt/min = Tubing drop factor/mL× Fusion rate

⇒gtt/min = 15×(500/180)

⇒gtt/min = 15×(25/9)

⇒gtt/min = 125/3

⇒gtt/min = 41.67

⇒gtt/min = 42

∴42 drops/min (gtt/min) should be given.

A stem-and-leaf plot of the chemistry exam scores is created by dividing each score into a tens digit (the stem) and a ones digit (the leaf). We then group the data by stem and list the leaves for each stem, giving us a distribution of the exam scores.

To construct a stem-and-leaf plot, you can follow this process:

So, our stem-and-leaf plot would look like this:

5 | 0
7 | 6 7 9 9
8 | 1 2 3 6
9 | 9

In this plot, for example, '7 | 6 7 9 9' means there are scores of 76, 77, 79, and 79.

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The position of the particle when t equals 6 is equal to -27 feet.

The total distance this particle travels during the 6-s time interval is equal to 69 feet.

Based on the information provided above, we can logically deduce the following polynomial function that models the position of a particle along a straight line;

[tex]s = 1.5t^3 - 13.5t^2 + 22.5t[/tex]

In order to determine the position of the particle when t is equal to 6, we would substitute 6 for t in the polynomial function as follows;

[tex]s(6) = 1.5(6)^3 - 13.5(6)^2 + 22.5(6)[/tex]

s(6) = 324 - 486 + 135

s(6) = -27 feet.

In order to determine the total distance this particle travels during the 6-s time interval, we would have to plot a graph of the velocity of the particle. Also, the velocity of the particle can be determined by taking the first derivative of the position with respect to time;

[tex]s = 1.5t^3 - 13.5t^2 + 22.5t\\\\s' = 4.5t^2 - 27t + 22.5[/tex]

Based on the graph, the particle changes directions at t equal 1 seconds and again t equal 5 seconds. Hence, the velocity of the particle drops to zero at these positions.

In this context, we would find the distance between these intervals;

Distance (0 ≤ t ≤ 1) = 10.5 - 0 = 10.5 feet.

Distance (1 ≤ t ≤ 5) = 10.5 - (-37.5) = 48 feet.

Distance (5 ≤ t ≤ 6) = -27 - (-37.5) = 10.5 feet.

For the total distance, we have;

Total distance = 10.5 + 48 + 10.5

Total distance = 69 feet.

Complete Question:

The position of a particle along a straight line is given by [tex]s = 1.5t^3 - 13.5t^2 + 22.5t[/tex] ft, where t is in seconds. Determine the position of the particle when t = 6 s and the total distance it travels during the 6-s time interval. Hint: Plot the path to determine the total distance traveled.

Answer:

no of success deemed to be usual 5

that is more than 5 success unusual

Step-by-step explanation:

Given data

number of successes  = less than μ − 2.5σ

number of successes  = greater than μ + 2.5σ

trials n  = 10

probability single trial = 0.2

to find out

is it unusual to have more than five successes

solution

we can say that

mean of the binomial, distribution that is

mean =  probability single trial × trials n

mean =  10 × .2

mean = 2

and standard deviation = √(mean× (1-probability))

standard deviation = √2× (1-0.2))

standard deviation = 1.2649

so no of successes are

= μ − 2.5σ                 and           = μ + 2.5σ

= 2 − 2.5(1.2649)      and           = 2 + 2.5(1.2649)

= -0.16225                and           = 5.16225

so now we say no of success deemed to be usual 5

that is more than 5 success unusual here

To determine whether it is unusual to have more than five successes in a binomial experiment with 10 trials and a probability of success of 0.2, we can use the mean and standard deviation of the binomial distribution. The probability of having six or more successes in this experiment is quite low (less than 0.05), so it would be considered unusual.

To determine whether it is unusual to have more than five successes in a binomial experiment with 10 trials and a probability of success of 0.2, we can use the mean and standard deviation of the binomial distribution. The mean is found by multiplying the number of trials by the probability of success (10 * 0.2 = 2), and the standard deviation is found using the formula √(npq) (where q = 1 - p). For this experiment, the standard deviation would be √(10 * 0.2 * 0.8) = 1.26.

To determine whether it is unusual to have more than five successes, we need to find the probability of having six or more successes. We can use the cumulative binomial distribution to find this probability. Using a calculator or a statistical software, we can find that the probability is approximately 0.003.

Since the probability is quite low (less than 0.05), we can consider it unusual to have more than five successes in this particular binomial experiment.

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Answer:

B. (8π + 12) in²

Step-by-step explanation:

1. Identify the formula for the area of both a triangle and a circle.

    Triangle: 1/2(b)(h)

       b = base

       h = height

    Circle: πr²

      r = radius

2. Start by finding the area of the circle, since we already have all the needed information for the variables in the equation.

     π(4)² → π(16) → 16π

3. Half the answer we just got as the area of the circle. We are doing this because we only have half a circle in the diagram, and we solved for the area of a full circle.

    (16π)/2 → 8π

4. Next find the base of the triangle, since this is the only information we do not yet have for the triangle. We will find this by doubling the 4, since 4 inches is only half the length of the base.

    4 × 2 = 8

5. Plug all the information of the triangle into the area of a triangle formula and solve.

    1/2(8)(3) → 1/2(24) → 12

6. Add both the area of the semi-circle and triangle together because they are one shape that we are finding the area for.

     8π + 12  

7. Label answer with units of measurement

    (8π + 12) in²            

ANSWER

The correct option is B

EXPLANATION

The composite figure is made up of a semicircle and an isosceles triangle.

The area of a semicircle is

[tex] \frac{1}{2}\pi {r}^{2} [/tex]

From the diagram, the radius is

[tex]r = 4 \: in[/tex]

When we substitute, area of the semicircle is

[tex] \frac{1}{2} \times \pi \times {4}^{2} [/tex]

[tex]\frac{1}{2} \times \pi \times 16[/tex]

[tex]8\pi \: \: {in}^{2} [/tex]

The area of the isosceles triangle is

[tex] \frac{1}{2} \times base \times height[/tex]

[tex] = \frac{1}{2} \times (4 + 4) \times 3[/tex]

[tex] = \frac{1}{2} \times 8 \times 3[/tex]

[tex] = 12 \: {in}^{2} [/tex]

We add the two areas to obtain the area of the composite figure to be:

[tex](8\pi + 12) {in}^{2} [/tex]

Answer:

D. 45.71 - 6m

Step-by-step explanation:

     Let m = the cost of a marker

Then 6m = the cost of six markers

Heather is paying for these from her savings account.

After deducting the cost of the markers, the amount in her account will be

45.71 - 6m

Answer:

It should be 314.9

Step-by-step explanation:

In every centimeter, there are about .3937 inches

So if you multiple .3937 by 800 and round to the nearest tenth, you get that answer

Answer:

So y(3)=1

Step-by-step explanation:

Given that

[tex]\dfrac{dy}{dx}=x-y[/tex]

y(0)=1,step size h=1

From Euler's method

[tex]\dfrac{dy}{dx}=f(x,y)=x-y[/tex]

[tex]y_{n+1}=y_n+hf(x_n,y_n),x_n=x_0+nh[/tex]  

[tex]y_1=y_0+hf(x_0,y_0)[/tex]

[tex]y_1=1+1f(0,1)[/tex]

f(0,1)=0-1= -1

[tex]y_1=1-1[/tex]=0

[tex]y_{2}=y_1+hf(x_1,y_1)[/tex]

[tex]y_{2}=0+1f(1,0)[/tex]

f(1,0)=1

[tex]y_{2}=1[/tex]

[tex]y_{3}=y_2+hf(x_2,y_2)[/tex]

[tex]y_{3}=1+1f(2,1)[/tex]

f(2,1)=1

[tex]y_{3}=1+1[/tex]=2

[tex]y_{4}=y_3+hf(x_3,y_3)[/tex]

[tex]y_{4}=2+1f(3,2)[/tex]

f(3,2)= -1

[tex]y_{4}=2-1[/tex]=1

So y(3)=1

Answer: 160

Step-by-step explanation:

Given : The options to fill science requirement =4

The options to fill diversity requirement =2

The options to fill English requirement =5

The options to fill math requirement = 4

The Fundamental Counting Principle say that the number of total outcomes is equal to the product of the number of ways of all the events occur in the problem.

Using Fundamental Counting Principle, we have the total number of possible outcomes for the given situation :-

[tex]4\times2\times5\times4=160[/tex]

Hence, the total number of possible outcomes = 160

Answer:

3/8 , 3/8

Step-by-step explanation:

Assumption: A boy is as likely as a girl

hence P(B)= P(G)= 1/2= 0.5

family has 3 children

find the probability of

A) two girls and a boy.

it can happen in following way

BGG, GGB or GBG

P(BGG)= P(GGB)= P(GBG) = [tex]\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}[/tex]

= 1/8

therefore , probability of two girl and a boy= [tex]\frac{1}{8} +\frac{1}{8} +\frac{1}{8}[/tex] = 3/8

B) At least One boy

it can happen is in

BGG, BBG, BBB

P(BGG)= P(BBG)= P(BBB) = [tex]\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}[/tex]

= 1/8

therefore , probability of at least one boy= [tex]\frac{1}{8} +\frac{1}{8} +\frac{1}{8}[/tex] = 3/8