100 POINTS IF CORRECT!!! NEED WORK

1. Let X be a binomial random variable with n = 20 and p =. 3.

А.

p)"-* , then

evaluate it using your calculator. (1 point)

B. Using probability notation, P(X = x), write out all the probabilities yould need to add

up in order to calculate P(X < 6), and then evaluate it using your calculator. (1 point)

c. For part B, why did you choose the upper bound that you did? If you were using the

normal approximation could you choose a different upper bound? Why or why not?

(1 point)

Answer:

1:3

Step-by-step explanation:

To simplify the ratio 16:32, we find the greatest common divisor of 16 and 32, and then we divide 16 and 32 by the greatest common divisor.

The greatest common divisor that you can use to simplify 16:32 is 16. Which means the answer to ratio 16:32 simplified is: 1:2

Hope it helps

Answer:

74

Step-by-step explanation:

All the angles of a triangle add up to 180

66+40 = 106

To find the missing angle...

180-106 = 74

Answer:

ANGLE A=74

Step-by-step explanation:

LET ANGLE A BE X

ANGLE B=40°

ANGLE C=66°

SUM OF ADJACENT ANGLE IS 180°

SO, WHEN:

40+66+X=180

X=180-106

ANGLE A=74°

HAVE A NICE DAY!!

The pairwise comparisons that need to be made for this anova result will be b.3

In order to determine the number of pairwise comparisons needed for a one-way between-subjects ANOVA with three groups, we can use the formula:

N = (k * (k-1)) / 2

Where N represents the number of pairwise comparisons and k represents the number of groups. In this case, k = 3.

Plugging in the values:

N = (3 * (3-1)) / 2

N = (3 * 2) / 2

N = 6 / 2

N = 3

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To solve the problem we must know about the formula of the length of the Arc.

\(\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}\)

The angle made by the arc in the center is 2.7 radians.

Given to us

Let the angle be θ.

Substituting the values in the formula of Length of Arc,

\(\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}\\\\ \)

\(8\ in. = \dfrac{2\pi \times 3 \times \theta}{360^o}\)

\(\theta = \dfrac{360^o\times 8\ in.}{2\pi \times 3 }\\\\ \theta = 152.788^o \approx 152.79^o\)

\(\theta = 152.79^o\\\\ \)

   \(=\dfrac{\theta \times \pi}{180^o}\)

   \(\rm{=2.6666667 \approx 2.7\ radians\)

Hence, the angle made by the arc in the center is 2.7 radians.

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Answer:

B' (7, 0)

C' (4, -1)

Step-by-step explanation:

The rule for translating is given by <3, 2>, which means that we add 3 to every x-coordinate and 2 to every y-coordinate.

Step 1:  Add 3 to the x coordinate of B

The coordinates for B are (4, -2)

4 + 3 = 7

Step 2:  Add 2 to the y coordinate of B:

-2 + 2 = 0

Thus, the coordinates for B' are (7, 0)

Step 3:  Add 3 to the x coordinate of C:

The coordinates of C are (1, -3)

1 + 3 = 4

Step 4:  Add 2 to the y coordinate of C:

-3 + 2 = -1

Thus, the coordinates for C' are (4, -1)

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:

2 7/12

Step-by-step explanation:

Simple fraction problem

Answer:

D

Step-by-step explanation:

f(x)=(3/5)x-10

f(5)=(3/5)(5)-10=

3-10=

-7

Hope this helps!

Answer: The area of the small inner circle is 1/3 of the area of the outer annulus if and only if the ratio of the radii of the circles is 2:1

Step-by-step explanation: The area of the small inner circle is 1/3 of the area of the outer annulus if and only if the ratio of the radii of the circles is 2:1. In that case, the reason is very simple. The inner circle has an area of πr^2, and the outer circle has an area of π(2r)^2 = 4πr^2, where r is the radius of the inner circle.

Answer:  A  8\(\pi\)

Step-by-step explanation:

A=\(\pi r^{2}\)  so for larger  \(16\pi =\pi r^{2}\)   and r=4  therefore d=8

To find the length of square I use the diameter of the larger circle as the diagonal of the square.  Use pythagorean:

\(d^{2} =x^{2}+ x^{2} \\8^{2} =2x^{2} \\64/2 = x^{2} \\x=\sqrt{32} =4\sqrt{2}\)     this is the length of the square side which is also the diameter of the inner circle

so the radius is x/2   r=2\(\sqrt{2}\)

\(A=\pi r^{2} =\pi (2\sqrt{2} )^{2} = \pi (2^{2} *2} )=8\pi\)

Answer:

he has 1/6 of a piza left

Step-by-step explanation:

becuase if you take the left over pizza, 3/4 it is bacially only a quarter of the piza gone, if image a pizza half of the circle is there, and half of the half circle is also there, and that is 3 sections, 6 d 3 get along, so ecaily each of the 3 section are wroth 2 slices and he ate 5, so 1 is left.

In a genetic algorithm for the Traveling Salesman Problem (TSP), a chromosome represents a potential solution or a route through the cities. The chromosome typically consists of a sequence of genes, where each gene represents a city.

In this case, if we have 10 cities, the chromosome could be represented as a string of 10 genes, where each gene represents a city. For example, if the cities are labeled A, B, C, ..., J, a chromosome could look like:

Chromosome: ABCDEFGHIJ

This chromosome represents a potential route where the salesperson starts at city A, visits cities B, C, D, and so on, in the given order, and finally returns to city A.

It's important to note that the specific representation of the chromosome may vary depending on the implementation details of the genetic algorithm and the specific requirements of the problem. Different representations and encoding schemes can be used, such as permutations or binary representations, but a simple string-based representation as shown above is commonly used for small-scale TSP instances.

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Answer:

Plan A

The formula is

A=p (1+r)^t

A=2,000×(1+0.06)^(4)

A=2,524.95 ( future value )

Interest earned=A-p

Interest earned=2524.95-2000

Interest earned=524.95

Plan B

Use the simple interest formula

I=prt

I interest earned?

P principle 2000

R interest rate 0.13

T time 4years

I=2,000×0.13×4

I=1,040

The Answer is

Plan B; $1,040

Step-by-step explanation:

Answer:

t = -3

Step-by-step explanation:

Given: -8t = 27 + t, we must isolate the variable; in this case, the variable is t.

So, to isolate the variable, we will move all terms containing t to the left side of the equation.

Therefore,

-9t = 27

Then, we divide each term by -9 and simplify.

We get:

t = -3

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

-3≤x<2

Step-by-step explanation:

Answer: 1 1/2

Step-by-step explanation:

3/4+3/4=6/4=1 2/4=1 1/2

Answer:

1 1/2

Step-by-step explanation:

3/4+3/4 = 6/4 = 1 2/4 = 1 1/2

The volume of the cube with the shortest possible side lengths is 216 cubic inches.

If a steel sphere with a 3-inch radius is made by removing metal from the corners of a cube that has the shortest possible side lengths, then the side lengths of the cube must be equal to the diameter of the sphere.

side length of cube = diameter of sphere

side length of cube = 2 x radius of sphere

side length of cube = 2 x 3 inches

side length of cube = 6 inches

The volume of the cube can be calculated using the formula below.

V = s³

where V = volume and s = side length of cube

V = (6 inches)³

V = 216 cubic inches

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The system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store are;

y = 50x + 100    ------(eq 1)

y = 75x + 50    ------(eq 2)

A) Let the total cost of the cat tree be y

Let each additional piece added be x.

Since basic tree is $100 and each additional platform costs $50, then we can say that;

y = 50x + 100    ------(eq 1)

Now, their basic cat tree starts at $50 and each additional piece costs $75. Thus;

y = 75x + 50    ------(eq 2)

B) Subtract eq 1 from eq 2 to gte;

25x - 50 = 0

25x = 50

x = 50/25

x = 2

y = 75(2) - 50

y = $100

C) The Store that would be cheaper depending on the add - ons is Puuur Place because as x increases, it's y-value increases at a lesser rate than that of Meow.

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Answer:

C The Item cost more than mona was able to pay

Step-by-step explanation:

I took the test

The simple event among the given options is "You get exactly 1 head."

Probability can be defined as the measure of the likelihood of a particular event occurring. Probability ranges between 0 and 1,

The sample space is a set of all possible outcomes of an experiment. In this case, the sample space for flipping a coin 3 times is (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT).

Now the probability of each event by dividing the number of favorable outcomes by the total number of possible outcomes.

A simple event is one that consists of only one outcome. Out of the given options, the only simple event is "You get exactly 1 head," which has the favorable outcome

Therefore, the probability of getting exactly one head is:

P(exactly 1 head) = Number of favorable outcomes / Total number of possible outcomes

P(exactly 1 head) = 3 / 8

P(exactly 1 head) = 0.375 or 37.5%

Thus, the correct answer is: You get exactly 1 head.

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The system has a bifurcation at k = -4 and k = 1.(a) To find the determinant and trace of matrix A in terms of k: A = [k 1; 4 -1]

The determinant of A is given by: det(A) = k*(-1) - (4*1) = -k - 4. The trace of A is the sum of the diagonal elements: tr(A) = k + (-1) = k - 1. To find the values of k where the system has a bifurcation, we need to find the values of k for which the determinant or trace changes sign. This occurs when the determinant or trace is equal to zero. Setting det(A) = 0: -k - 4 = 0, k = -4. Setting tr(A) = 0: k - 1 = 0, k = 1. Therefore, the system has a bifurcation at k = -4 and k = 1. (b) To determine the type of equilibrium at the origin (0, 0) for values of k that are not the bifurcating values, we need to analyze the eigenvalues of matrix A.

For k ≠ -4 and k ≠ 1, the eigenvalues of A can be found by solving the characteristic equation: det(A - λI) = 0 where I is the identity matrix and λ is the eigenvalue. Substituting the values of matrix A into the characteristic equation, we have: |k - λ 1| = 0, |4 -1 - λ| = 0. Expanding the determinants: (k - λ)(-1 - λ) - (4)(1) = 0, λ² - (k + 1)λ + (k + 4) = 0. The eigenvalues of A are the roots of this quadratic equation. By analyzing the discriminant of the quadratic equation, we can determine the type of equilibrium: If the discriminant (D) is positive, the eigenvalues are real and distinct, indicating a saddle point. If D is zero, the eigenvalues are real and repeated, indicating a center. If D is negative, the eigenvalues are complex conjugates, indicating a spiral point.

(c) Now, let's analyze the cases for specific values of k: i. k = 0: In this case, the matrix A becomes: A = [0 1; 4 -1]. To find the eigenvalues, we solve the characteristic equation: λ² + λ - 4 = 0. Using the quadratic formula, the eigenvalues are: λ = (-1 ± sqrt(1 - 4*(-4)))/2. λ = (-1 ± sqrt(17))/2. The general solution in terms of real-valued functions can be expressed as: y₁(t) = C₁ * exp((-1 + sqrt(17))/2 * t), y₂(t) = C₂ * exp((-1 - sqrt(17))/2 * t). Since the eigenvalues are real and distinct, the phase portrait will consist of two real-valued curves with different exponential growth/decay rates.

ii. k = 1: In this case, the matrix A becomes: A = [1 1; 4 -1]. To find the eigenvalues, we solve the characteristic equation: λ² - 1λ - 5 = 0. Using the quadratic formula, the eigenvalues are: λ = (1 ± sqrt(1 + 4*5))/2, λ = (1 ± sqrt(21))/2. The general solution in terms of real-valued functions can be expressed as: y₁(t) = C₁ * exp((1 + sqrt(21))/2 * t), y₂(t) = C₂ * exp((1 - sqrt(21))/2 * t). Again, since the eigenvalues are real and distinct, the phase portrait will consist of two real-valued curves with different exponential growth/decay rates.

iii. k = 2: In this case, the matrix A becomes: A = [2 1; 4 -1]. To find the eigenvalues, we solve the characteristic equation: λ² - λ - 9 = 0. Using the quadratic formula, the eigenvalues are: λ = (1 ± sqrt(1 + 4*9))/2, λ = (1 ± sqrt(37))/2. The general solution in terms of real-valued functions can be expressed as: y₁(t) = C₁ * exp((1 + sqrt(37))/2 * t), y₂(t) = C₂ * exp((1 - sqrt(37))/2 * t). Again, since the eigenvalues are real and distinct, the phase portrait will consist of two real-valued curves with different exponential growth/decay rates. (d) To show that the two functions obtained in part (c)i. are linearly independent, we can consider the linear combination of the two functions: C₁ * exp((-1 + sqrt(17))/2 * t) + C₂ * exp((-1 - sqrt(17))/2 * t)

If this linear combination is equal to zero for all values of t, then the only solution is when C₁ = C₂ = 0. In other words, the functions are linearly independent. To verify this, we can assume the linear combination is equal to zero and solve for C₁ and C₂: C₁ * exp((-1 + sqrt(17))/2 * t) + C₂ * exp((-1 - sqrt(17))/2 * t) = 0. This equation holds for all t if and only if C₁ = C₂ = 0. Therefore, the functions are linearly independent.

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Answer:

I hope this helps :)        

If angle 1 and angle 2 supplementary, angle 2 and angle 3 are supplementary, The measure of  ∠2 = 47° and  ∠3 = 133°.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are supplementary  angles as the total of these two angles is 180°. The sum of complimentary angles is 90 degrees.

Given,

the measure of angle 1 = 133°

As, ∠1 + ∠2 are supplementary angles,

⇒  ∠1 + ∠2 = 180°                                        ......(1)

∠2 + ∠3 are supplementary angles,

⇒  ∠2 + ∠3 = 180°                                       .......(2)

From (1),

⇒ 133° + ∠2 = 180°

⇒ ∠2 = 47°

From (2),

47° + ∠3 = 180°

∠3 = 133°

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The value of perimeter of the quadrilateral is,

⇒ 6x² + x - 1

We have to given that;

The quadrilateral is shown in figure.

All sides of quadrilateral are, (2x + 5) , (x² - 3x) , (4x² + 2x) , (x² - 6)

Now, We can formulate;

The value of perimeter of the quadrilateral is,

⇒ (2x + 5) + (x² - 3x) + (4x² + 2x) + (x² - 6)

⇒ 6x² + x - 1

Thus, The value of perimeter of the quadrilateral is,

⇒ 6x² + x - 1

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The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).

In other words, it tells us how much the information values are scattered around the mean.

When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.

This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.

This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.

For case, let's consider two sets of information:

Set A and Set B.

Set A:

2, 3, 4, 5, 6

Set B:

1, 3, 5, 7, 9

Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).

This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.

Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.

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