how do the results compare to your hypothesis? explain why your hypothesis was or was not supported by the results.

The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

Let the number of number of red pencils be 'x'.

Total blue pencils = 5.

Ratio = blue pencils/red pencils

5/x = 1/2

x = 5 x 2

x = 10

Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

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The answer of a) Probability = 0.386 and of b) Probability = 0.017

Explain probability.

Estimating the likelihood that experiments will succeed or fail is one use of probability theory. The likelihood of flipping a coin and getting heads or tails, for example, or the likelihood of making a research error, can all be calculated using probabilities. In order to fully appreciate this area of mathematics, it is crucial to comprehend the formula for computing probabilities in equiprobable sample spaces, as well as the probabilities of the complementary event, etc., as well as the likelihood of two occurrences joining together.

no of seniors = 3

no of juniors = 15

a) probability that a group consist of a senior and two juniors =

[tex]\frac{^{3}C_{1} * ^{15}C_{2}}{^{18}C_{3}} \\= \frac{3*105}{316}=0.386\\[/tex]

b) if the name of a student given then there is only one way to select it

For example = we have to select 1 senior which name is already given means there is only one way to select it, and 2 junior in which one name is given then it can only selected by one way, but still one junior student has to be selected out of remaining 14 student which can be selected by ([tex]^{14}C_{1}=14[/tex]) different ways.

probability = [tex]\frac{1*1*^{14}C_{1} }{^{18}C_{3} }=\frac{14}{316}=0.017[/tex]

Hence the answer of a) is 0.386 and of b) is 0.017

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The number of ways there for the 125 pages to be assigned to the four printers = 5^125 ways.

As per the question,

A 125-page document is being printed by four printers.

Each page will be printed exactly once.

There are no restrictions on how many pages a printer can print.

One of the possible combinations is that printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90 and printer D prints out pages 81-85 and 91-100.

Since, there are no restrictions in printing the pages any printer cannot print even a single page and any printer can print all 125 pages. To print 100 pages we have four printers.

⇒ Number of possible ways a single paper can be assigned to the four printers = 4 ways

⇒ Number of possible ways 125 pages can be assigned to the four printers

=  5 × 5 × 5 × 5 .................... 5 ( a total of 125 terms )

=     ways.

Therefore, In   ways we can assign 125 pages to four printers with no restrictions.

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Answer:

  13.5, 17.5

Step-by-step explanation:

You have two numbers whose sum is 31 and whose difference is 4. The second number is larger.

Let x represent the larger number. Then the smaller is x-4, and their sum is ...

  x +(x -4) = 31

Simplifying the expression gives ...

  2x -4 = 31

  2x = 35 . . . . . add 4

  x = 17.5 . . . . . divide by 2

  x -4 = 13.5

The two numbers are 13.5 and 17.5.

__

Additional comment

As we have seen here, the larger number is half the total of the 'sum' and 'difference'. (31+4)/2 = 17.5. This is the generic solution to any "sum and difference" problem.

w should be equal to 92° to prove that r || s.

To prove whether the two lines are parallel we should know whether

So for the given condition, the diagram is drawn. Mark the angles w, x, y, and z.

From the diagram, by the Corresponding Angles Theorem, ∠w=∠92°.

The answer is w. Therefore, option a is correct.

The complete question is -

Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?

a)w

b)x

c)y

d)z

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Answer:

just telling you but we need to see the image which we cannot but I'm not entirely sure but I think it's 2 although I cannot see the image and the other one is 4 I thinke

Answer:

50%

Step-by-step explanation:

It is a half chance, you could be lucky

The given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable.

Independent, dependent, and controlled variables are typically present in an experiment.

The variable that is altered by the scientist is the independent variable.

A false correlation between two variables indicates that their correlation coefficient is almost zero.

When two variables have a strong correlation, altering the value of one will not affect the other.

Therefore, the given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

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Answer:

94

Step-by-step explanation:

if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pig with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

Answer:

Step-by-step explanation:if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pit with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

Answer:Y=1/2x+2

Step-by-step explanation:

Slope intercept form is y=mx+b

m=slope

b= y intercept

y=1/2x+2

Answer:

B because (16-4)/2=6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 14 degrees.

Step-by-step explanation: The sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, if we know the measures of two of the interior angles of a triangle, we can use this fact to find the measure of the third angle.

In this case, we are given that two of the interior angles of the triangle have measures of 54 and 112 degrees. We can use this information to find the measure of the third angle as follows:

180 degrees = 54 degrees + 112 degrees + x

180 degrees = 166 degrees + x

x = 180 degrees - 166 degrees

x = 14 degrees

Therefore, the measure of the third angle of the triangle is 14 degrees.

The vector (nu) x is an eigenvector of A and corresponds to each nonzero complex scalar (nu) (lambda).

Let x in Cn be an eigenvector of A that corresponds to an eigenvalue. Assume that A is a n x n matrix (lambda). Ax = (lambda)x follows.

Let (nu) now be a complex scalar that is nonzero. A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x)

As a result, (nu)x is an eigenvector of A that corresponds to (nu) (lambda).

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There are a total of 216 ways in which the waiter could serve the meal types.

Let the beef meal be denoted by B, chicken meal by C, and fish meal F. Now say the nine people order meals BBBCCCFFF respectively and say that the person who receives the correct meal is the first person. We will solve for this case and then multiply by 9 to account for the 9 different ways in which the person to receive the correct meal could be picked.

Now, we need to distribute meals BBCCCFFF to orders BBCCCFFF with 0 matches. The two people who ordered B's can either both get C's, both get F's, or get one C and one F.

If the two B people both get C's, then the three F meals left to distribute must all go to the C people. The F people then get BBC in some order, which gives three possibilities.

If the two B people both get F's, the situation is identical to the above and three possibilities arise.

If the two B people get CF in some order, then the C people must get FFB and the F people must get CCB. This gives 2*3*3 = 18 possibilities.

In total, we see there are 24 possibilities, so the answer is 9*24 = 216

Thus, there are a total of 216 ways in which the waiter could serve the meal types.

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Your question was incomplete. Check for missing part below-

Find the number of ways in which the waiter could serve the meal types to the nine people so that exactly one person receives the type of meal ordered by that person.

Solving for x in the equation 7 2/5 = 2/3x −4 1/2 gives   17 17/20

In the given equation, we find the value of x by applying the following operations

7 2/5 = 2/3x −4 1/2

7 2/5 = 2x/3 −4 1/2

collecting like terms

7 2/5  + 4 1/2 =

2x/3 = 119/10

multiplying by 3

2x = 119/10 * 3

2x = 357/10

dividing by 2

x = 357 / 10 * 1/2

x = 357/20

x = 17 17/20

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Using the implicit differentiation, it is found that the water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

The volume of the cone of radius r and height h is given as follows:

V = π r² h / 3

Applying implicit differentiation to find the rate of change of the volume as function of time is given as follows:

[tex]\frac{dV}{dt}[/tex] = 2 π  [tex]\frac{rh}{3}[/tex][tex]\frac{dr}{dt}[/tex]  + [tex]\frac{π r² }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

As the radius is constant, hence:

.[tex]\frac{dr}{dt}[/tex]  = 0

Considering that the radius is half of the diameter, the other parameters are:

r = 3 and [tex]\frac{dV}{dt}[/tex] = 2

Hence:

2 = [tex]\frac{π * 3^{2} }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}[/tex] = 6 / 9 π

dh/dt = 0.21.

The water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

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Answer:

557

Step-by-step explanation:

7,241 divided by 13 = 557

Answer:

y= -2x-4

Step-by-step explanation:

parallel==> a line has the same slope ===> (m = -2)

y= -2x+b

and a line pass through the (-3,2) ===> x=-3, y=2

2= -2(-3)+b

2=6+b (subtract 6 from both sides )

-4=b

y= -2x-4



The area bounded by the sin (100x² + 49y²) dA is calculated by using integration is 2π (1 - cos 1).

An area bounded by the curve: When the two curves intersect then they bound the region is known as the area bounded by the curve.

Evaluate the integral by making an appropriate change of variables.

The equation of the ellipse is 100x² + 49y² = 1

Let cos t = 10x and sin t = 7y. Then we have

or x = 1/10 cost , y = 1/7 sint.

Then

=> 100 (1/10cost)^2 + 49 (1/7 sint)^2 = 1

=> cos^2 t + sin^2t = 1 which suggests a change of variable will be:

[tex]\left \{ {{x(r,t) = r/10cost} \atop {y(r,t)=r/7sint}} \right.[/tex]

where 0≤r≤1 and 0≤t≤2[tex]\pi[/tex]. Then we also have,

100x² + 49y² = r²

So,

=> ∫∫ sin (100x^2 + 49y^2)dA

     R

=> [tex]\\[/tex]2 ∫2[tex]\pi[/tex] ∫[tex]1[/tex]  sinr^2 dr dt

       0     0

=> 4[tex]\pi[/tex] ∫[tex]1[/tex]  rsinr^2 dr

          0    

Now r² is replaced by r, then we get

=> 2[tex]\pi[/tex] ∫[tex]2[/tex]  sinr^2 d(r^2)

          0

=> - 2[tex]\pi[/tex] cos r^2 [tex]\left \{ {{r^2=1} \atop {r^2=0}} \right.[/tex]    

=> -2[tex]\pi[/tex] (cos1-cos0)

=> -2[tex]\pi[/tex] (-1 + cos1)

=> 2[tex]\pi[/tex](1-cos1)

Evaluating the integral by making an appropriate change of variables 2 sin(100x^2 + 49y^2) dA.

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Answer:

Area = 81 pi

circumstance = 18 pi

Step-by-step explanation:

radius = 9

The angle between the two vectors (4,1) and (-8,3) will be 145.4°.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is possible to calculate the angle () between two vectors using the formula

[tex]\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

Calculate dot product:

=a · b

= ax · bx + ay · by

= 4 · (-8) + 1 · 3

= - 32 + 3

= -29

=|a|

= √ax² + ay²

= √4² + 1²

= √16 + 1

= √17

=|b|

=√ bx² + by²

= √(-8)² + 3²

= √64 + 9

= √73

[tex]\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]

α = 145.40771131249005°

Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.

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The linear function y = 3x is used to calculate the cost of 23 balloons as $69

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,

y = 3x

x = number of balloons

The cost of 1 balloon = $3

the cost of 23 balloon = x

x = 23 * 3

x = 69

The cost of 23 balloon is $69

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(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

Given that,

One thousand bacteria make up a culture at the beginning. The number of bacteria is 8000 after an hour.

We have to find

(a) Track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, locate the population.

(c) How long will it take for there to be 15,000 bacteria?

(d) Draw the population function's graph.

We know that,

(a) The initial size of the culture is 1000 bacteria.    

So,  

n₀=500

The size of the culture after one hour (for t =1) is 4000 so we extract the equation:

n(1) = 8000

1000er¹=8000

e to the power of r =8

[taking logarithms both side]    

r ln e  =  ln 8                          

r=2.080

[ln e  =  1]

So, we got  

n₀=1000 and r=2.08

The function will be,

n(t)=1000[tex]e^{2.08t}[/tex]

(b) for t = 1.5

n(1.5)=1000[tex]e^{2.08(1.5)}[/tex]

22646

(c) 15000=1000[tex]e^{2.08t}[/tex]

15=[tex]e^{2.08t}[/tex]

Taking log on both sides

ln15= 2.08(t)lne

t=3.68/2.08

t=1.7

(d) Since we have have the exponential equation therefore our graph should be curve not straight line.

Also at t=1, population of bacteria is 4000

Hence the correct graph will be in picture.

Therefore,

(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

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Answer:

29,028 ft.

Step-by-step:

Consider the following:

Mt. Everest - x

Equation:

We are given that Mt. McKinley is 20,321 ft in elevation, and that it is 8,707 ft. lower than Mt. Everest.

When writing this numerically:

20,321 = x - 8,707

Solve for x:

20,321 = x

+8,707     + 8,707

-------------------------

x = 29,028

Mt. Everest is 29,028 ft. in elevation.

Using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

So, we have -9 - 9√3i:

This quantity has a modulus.

|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18

And argument θ to the effect:

tan(θ) = (-9√3) / (-9) = √3

We anticipate that will be between -π and -π/2 radians since -9-9√3i lies in the third quadrant of the complex plane, so that:

θ = arctan(√3) - π = π/3 - π = -2π/3

The polar form is then:

18 (cos(-2π/3) + i sin(-2π/3))

And since -2π/3 is the same angle as 2π - 2π/3 = 4π/3, the right answer is: 18 (cos(4π/3) + i sin(4π/3))

Therefore, using trigonometry identities, we know that the polar form of  -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).

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Complete question:
What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot?

a. 9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

b. 9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

c. 18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )

d. 18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Answer:

18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )

Step-by-step explanation:

D