Some chocolate bars are scored (split apart) into equal parts to make them easy to break apart and share. Simon wants to share five chocolate bars equally among four people. The chocolate bars are scored in four equal parts. How should Simon share all the chocolate bars so four people each have an equal share? Show all your mathematical thinking.

a) The Z-value corresponding to a confidence level of 95% can be determined as 1.96.

b) To determine the required sample size, we need additional information such as the population size or an estimated proportion. Without this information, we cannot calculate the sample size.

a) The Z-value represents the number of standard deviations a data point is from the mean in a standard normal distribution. For a confidence level of 95%, which corresponds to a 5% significance level, the critical Z-value is approximately 1.96. This value can be obtained from a Z-table or using statistical software.

b) To calculate the required sample size, additional information is needed, such as the population size or an estimated proportion. The sample size formula takes into account factors such as the desired margin of error, confidence level, and variability. Without these details, it is not possible to determine the sample size accurately.

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Answer:

546

Step-by-step explanation:

3 1/2 times 3 equals 10 1/2. 10 1/2 times 52 equals 546.

Answer: 9π≈28.26 squared units

Step-by-step explanation: The distance between the two points, 3 units, is the radius. And then we use that to find the area by squaring and multiplying by pi.

Answer:

7m and 49 m^2

Step-by-step explanation:

i am not sure on the second answer

For a real number x, by using mathematical induction it is shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx for every positive integer n.

To prove the inequality a[tex](1 + x)^{2n}[/tex] > 1 + 2nx  for every positive integer n, we will use mathematical induction.

The inequality holds true for n = 1, and we will assume it is true for some positive integer k.

We will then show that it holds for k + 1, which will complete the proof.

For n = 1, the inequality becomes a[tex](1 + x)^2[/tex] > 1 + 2x.

This can be expanded as a(1 + 2x + [tex]x^2[/tex]) > 1 + 2x, which simplifies to a + 2ax + a[tex]x^2[/tex] > 1 + 2x.

Now, let's assume the inequality holds true for some positive integer k, i.e., a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.

We need to prove that it holds for k + 1, i.e., a[tex](1 + x)^{2(k+1)}[/tex] > 1 + 2(k+1)x.

Using the assumption, we have a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.

Multiplying both sides by [tex](1 + x)^2[/tex], we get a[tex](1 + x)^{2k+2}[/tex] > (1 + 2kx)[tex](1 + x)^2[/tex].

Expanding the right side, we have a[tex](1 + x)^{2k+2}[/tex] > 1 + 2kx + 2x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].

Simplifying further, we get a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].

Since k and x are positive, 2k[tex]x^2[/tex] and 2[tex]x^2[/tex] are positive as well.

Therefore, we can write a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex] > 1 + 2(k+1)x.

This proves that if the inequality holds for some positive integer k, it also holds for k + 1.

Since it holds for n = 1, it holds for all positive integers n by mathematical induction.

Therefore, we have shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx  for every positive integer n.

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Answer:

5 + 4 snice it's inside the circle and when you get your answer you times it with 3

Step-by-step explanation:

( 5 + 4 ) x 3

  9 x 3

27

(5+4) x 3 = 27

Answer:

1,512

Step-by-step explanation:

36x42

Answer:

54 cm²

Step-by-step explanation:

1 cm= 3 m

2 cm= 6 m

3 cm= 9 m

9×6=54

Area of bedroom= 54 cm²

Answer: 98

Step-by-step explanation: According to the corresponding angles theorem m<1=82. Then according to the linear supplements theorem m<2=98. Hope this helps!

Answer:

98°

Step-by-step explanation:

Angle 1 also measures 82° because it is a corresponding angle to the given angle. Angles 1 and 2 are supplementary and therefore must add up to 180°.

Answer: Big rectangle shades 1/4+1/2

Step-by-step explanation:

So have a Big

Answer: 3. Tan; 4. 4.76; 5. 12

Step-by-step explanation: First question: SOH CAH TOA; if you draw a picture with the given information you know the Opposite and Adjacent sides to the upper left angle, or OA which is also Tan according to Soh Cah Toa. Second question: Use inverse tan(1/12) to solve. Third question: Same idea as the last question but use inverse sin(1/5)

Answer:

36%

Step-by-step explanation:

30/2500 x 30/2500=

900/2500=0.36

0.36*100=36%

Answer: 5 + 47 = 108

Step-by-step explanation: dont worry it works

Answer:

pythagoras thoerem

Step-by-step explanation:

y squared = 10 squared - 7 squared

y = 100 - 49= 51

y square root of 51 =7.1

If you made this Very good job. I like it, and its hard to make a song i like. i like about 60 songs total out of the 10000+ ik of

Answer:

grab objects

Step-by-step explanation:

barrels and things like that would most likely grab objects so the fish can have room to swim and stuff

Answer: just simplify condense it then your answer will be log(16)

Answer:

5

Step-by-step explanation:

Answer:

x-intercept

y-intercept

Step-by-step explanation:

Answer:

x-intercept y-intercept

Answer:

[see below]

Step-by-step explanation:

[tex]5(2)=7\\\\10\neq 7[/tex]

No, (2, 7) is not the answer to the equation 5x = y.

[tex]5x=y\\\\5(2)=y\\\\\boxed{10=y}[/tex]

The value of y should be 10.

Hope this helps.

Answer:

72

Step-by-step explanation:

Answer:

72 units

Step-by-step explanation:

The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex] in a right triangle when a and b are the two legs and c is the hypotenuse (the longest side).

[tex]a^2+b^2=c^2[/tex]

In the diagram, 30 measures one of the legs and 78 measures the hypotenuse. Plug these in as a and c.

[tex]30^2+b^2=78^2\\900+b^2=6084[/tex]

Subtract 900 from both sides

[tex]900+b^2-900=6084-900\\b^2=5184[/tex]

Take the square root of both sides

[tex]900+b^2-900=6084-900\\\sqrt{b^2} =\sqrt{5184}\\b=72[/tex]

Therefore, the length of the missing side is 72 units.

I hope this helps!

Based on the results, we can observe that as x approaches 2, the slopes of PQ are getting closer to 4. Therefore, we can guess that the slope of the tangent line to the curve at P(2,12) is approximately 4.

To find the slope of the secant line PQ, we need to determine the coordinates of point Q and then calculate the slope using the formula:

slope = (change in y) / (change in x)

Given that Q is the point (x, x^2 + x + 6), we can substitute the values of x to find the corresponding slopes.

If x = 2.1:

Q = (2.1, (2.1)^2 + 2.1 + 6) = (2.1, 12.51)

Slope of PQ = (12.51 - 12) / (2.1 - 2) = 0.51 / 0.1 = 5.1

If x = 2.01:

Q = (2.01, (2.01)^2 + 2.01 + 6) = (2.01, 12.0601)

Slope of PQ = (12.0601 - 12) / (2.01 - 2) = 0.0601 / 0.01 = 6.01

If x = 1.9:

Q = (1.9, (1.9)^2 + 1.9 + 6) = (1.9, 11.61)

Slope of PQ = (11.61 - 12) / (1.9 - 2) = -0.39 / -0.1 = 3.9

If x = 1.99:

Q = (1.99, (1.99)^2 + 1.99 + 6) = (1.99, 11.9601)

Slope of PQ = (11.9601 - 12) / (1.99 - 2) = -0.0399 / -0.01 = 3.99

Based on the results, we can observe that as x approaches 2, the slopes of PQ are getting closer to 4. Therefore, we can guess that the slope of the tangent line to the curve at P(2,12) is approximately 4.

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Answer:

200

Step-by-step explanation:

happy to help

The lateral area of  square based pyramid is 200 square feet

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The given square base pyramid has four faces of triangles and one square shape base

The lateral surface area of pyramid formula 4 × (1/2)bl,

b = side length of the base, and

l = slant height

Lateral surface area =2 bl

=2×10×10

=200 square feet

Hence,  the lateral area of  square based pyramid is 200 square feet

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Answer:

5.06 years or 60.75 months

Step-by-step explanation:

Compound interest formula:

[tex]AV=PV(1+\frac{i}{n})^{n*t}\\4045=3355(1+\frac{.037}{12})^{12t}\\1.025=(1.003)^{12t}\\log1.025_{1.003}=12t\\60.75=12t\\5.062[/tex]

5.06 years or 60.75 months

It will take Andrew  5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for compound interest to solve this problem:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

where:

A is the amount of money at the end of the investment period

P is the principal amount (initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time (in years) of the investment period

In this case, we want to solve for t. We know that:

P = $3355

r = 0.037 (3.7% as a decimal)

n = 12 (compounded monthly)

A = $4045

Substituting these values into the formula, we get:

[tex]4045 = $3355(1 + 0.037/12)^(^1^2^t^)[/tex]

ln(1.206) = 12t ln(1 + 0.037/12)

ln(1.206) = 12t ln(1 + 0.0031)

ln(1.206) = 12t ln(1.0031)

0.187=12t 0.0031

0.187=0.0372t

t=5.02

Therefore, it will take Andrew approximately 5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.

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Answer:

1.6 unit^2 (dec. form) or 1 3/5 unit^2 (frac. form)

Step-by-step explanation:

(1 1/5)(1 1/3)

(6/5)(4/3)

1.6 unit^2 (dec. form) or 1 3/5 unit^2 (frac. form)

The mean of the finishers in the New York City 10-km run is 60 minutes and standard deviation is 9 minutes.

To determine the percentage of finishers who have times between 55 and 75 minutes, we need to find the Z-scores for both of these values as follows:

Z1 = (55 - 60) / 9 = -0.56Z2 = (75 - 60) / 9 = 1.67

Now, we need to find the area under the standard normal distribution curve between these two Z-scores as follows:

P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56) Using a standard normal distribution table,

we can find the probabilities as:

P(Z < 1.67) = 0.9525P(Z < -0.56) = 0.2881

Therefore , P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56)= 0.9525 - 0.2881= 0.6644Therefore, the percentage of finishers who have times between 55 and 75 minutes is 66.44%.

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Answer:

(x1, y1) = (1, 3)

(x2, y2) = (4, 12)

Step-by-step explanation:

y= x^2 - 4

y= 5x - 8

(substitute the value for y)

x^2 - 4 = 5x - 8

(solve the equation)

x = 1

x = 4

(substitute the values)

y = 5 × 1 - 8

y = 5 × 4 - 8

(solve the equations)

y = -3

y = 12

( the possible solutions are)

x1, y1 = 1, -3

x2, y2 = 4, 12

(check the solutions)

-3 = 1^2 - 4

-3 = 5 × 1 - 8

12 = 4^2 - 4

12 = 5 × 4 - 8

(simplify)

-3 = -3

-3 = -3

12 = 12

12 = 12

(the ordered pairs are the solutions)

Answer:

5a - 3

Step-by-step explanation:

3a + 2a = 5a

1 - 4 = -3

5a + (-3) or 5a - 3

(a) The complete graph K41 has 820 edges. This can be calculated using the formula for the number of edges in a complete graph, which is given by the expression (n(n-1))/2, where n is the number of vertices. Substituting n = 41, we get (41(41-1))/2 = 820.

(b) The number of isomorphisms from K41 to itself is equal to the number of permutations of the vertices. This can be calculated as 41!, which represents the number of ways to arrange the vertices of K41.

(c) The graph C41 is not isomorphic to itself because it has a specific edge pattern. Thus, there are no isomorphisms from C41 to itself.

(d) The chromatic number of K41 is equal to its number of vertices, which is 41. This is because each vertex can be assigned a unique color, and no two adjacent vertices share the same color in a complete graph.

(e) The chromatic number of C41 is 2. This is because C41 contains a Hamiltonian cycle, which is a cycle that visits each vertex exactly once. A Hamiltonian cycle can be colored with only two colors, where adjacent vertices are assigned different colors.

(f) A spanning tree of K41 is a connected acyclic subgraph that includes all the vertices of K41. The number of edges in a spanning tree of K41 is equal to the number of vertices minus 1, which is 41 - 1 = 40.

(g) If a single edge is added between nonadjacent vertices of a tree with 41 vertices, the largest number of cycles the graph might have is 41. This can occur when the new edge connects two vertices that are at maximum distance from each other in the original tree, resulting in a new cycle.

(h) The smallest number of leaves possible in a spanning tree of K41 is 1. This can be achieved by removing all but one edge from K41, resulting in a single leaf node.

(i) The largest number of leaves possible in a spanning tree of K41 is 40. This can be achieved by removing all but one vertex from K41, resulting in a single vertex connected to 40 leaf nodes.

(g) The number of spanning trees that C41 has can be calculated using Cayley's formula, which states that a complete graph with n vertices has nn-2 spanning trees. Substituting n = 41, we get 4141-2 = 240 spanning trees for C41.

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Answer:

28.27 rounded orrrr 28.27433388 not rounded.

Step-by-step explanation:

area of circle=πr^2

radius=3 km

3^2=9

9*π

Step-by-step explanation:

Area of a circle = πr²

Radius (r) =1/2 Diameter

=60/2

=30km

Area = π x (30)²

= π x 900

= 2027km²

Step-by-step explanation:

From the table, let's extract a set of data.

let's take x = 3, y = -9.

Let's substitute x into each of the equation to check.

A.

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

From here we can see the calculated y is not equal to the y in the table, therefore this cannot be the answer.

B.

[tex]y = x \\ y = - 3[/tex]

From here we also can see the calculated y is not equal to the y in the table, therefore this also cannot be the answer.

C.

[tex]y = 3x \\ = 3( - 3) \\ = - 9[/tex]

From here we can see the calculated y is equal to the y in the table , therefore this is the answer.

D.

[tex]y = - 3x \\ = - 3( - 3) \\ = 9[/tex]

From here we can see the calculated y is not equal to the y in the table, therefore this is not the answer.