A sector with an angle 110° at the centre of a circle is cut away from a circular piece of paper of radius 7cm. the remaining part is folded to forming a cone
1; find the vertical angle
2:the angle of sector​

There is enough proof to indicate that the percentage of newsletter readers who possess a Rolls Royce is less than 69%.

The null hypothesis is that p = 0.69, meaning that 69% of the newsletter readers own a Rolls Royce. The alternative hypothesis is that p < 0.69, meaning that less than 69% of the newsletter readers own a Rolls Royce.

We can use a one-tailed z-test to test the hypothesis. Assuming a sample size of n = 100, if we observe fewer than 69 Rolls Royces in our sample, we can reject the null hypothesis.

Using a z-test, we can calculate the z-score by using the formula:

z = (p' - p) / sqrt(p * (1 - p) / n)

where p' is the sample proportion, p is the hypothesized proportion, and n is the sample size.

At a significance level of 0.10, the critical z-value is -1.28. If the calculated z-score is less than -1.28, we can reject the null hypothesis.

If we conduct a survey of 100 newsletter readers and find that 58 of them own a Rolls Royce, the sample proportion would be p' = 0.58. Calculating the z-score, we get:

z = (0.58 - 0.69) / sqrt(0.69 * 0.31 / 100) = -1.83

Since -1.83 is less than -1.28, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that fewer than 69% of the newsletter readers own a Rolls Royce.

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The function f(x) = -2|x - 3| + 2 involves a horizontal shift of 3 units to the right, a vertical reflection, and a downward stretch. Its domain is all real numbers, and its range is all real numbers less than or equal to 2.

The function f(x) = -2|x - 3| + 2 is a transformation of the basic absolute value function f(x) = |x|. Let's analyze the transformations and then graph both functions.Transformations:

1. Shifting: The function f(x) = -2|x - 3| + 2 involves a horizontal shift of the absolute value function f(x) = |x|. The term (x - 3) inside the absolute value causes a shift of 3 units to the right.

2. Reflecting: The negative sign in front of the absolute value function reflects the graph across the x-axis. It causes the function to be reflected vertically.

3. Compressing or stretching: There is no compression or stretching factor present in this particular function.

Graph of the basic function f(x) = |x|:

The graph of the basic function f(x) = |x| is a V-shaped graph that passes through the origin (0, 0). It has symmetry with respect to the y-axis.Graph of the given function f(x) = -2|x - 3| + 2:

To graph the given function, we start with the basic absolute value function f(x) = |x| and apply the transformations: a horizontal shift of 3 units to the right and a vertical reflection. The negative coefficient (-2) affects the amplitude, making the graph steeper.

Domain of f(x) = -2|x - 3| + 2:

The domain of the given function is all real numbers since there are no restrictions on the input values of x.

Range of f(x) = -2|x - 3| + 2:

The range of the given function is the set of all real numbers less than or equal to 2, as the vertical reflection and the coefficient (-2) cause the graph to be reflected and stretched downward.

Note: Without specific constraints on the values of x, the domain and range of the given function follow the typical domain and range of absolute value functions.

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Answer:36

Step-by-step explanation: 3X4 or 3 rectangles plus tow rectanges that = 12

The statement tells us several important things:

1. Of all the money collected from sales, 8.5% is for sales tax.

2. Of all the money collected from the sales, $125 goes to pay the rent for the space that I am using.

3. After deducting the taxes and the rented space, they divide the remaining money into 7 equal parts, which corresponds to $175.

To find the value of the money collected we first calculate the money that is known, i.e. the $175 for 7 of the growers and the $125 for the rent of the space.

This amount of money corresponds to the percentage remaining after taxes are taken out.

The percentage of this amount of money is 91.5%, the percentage of this amount of money is 91.5%.

In conclusion, the answer is $1476

The amount of brown sugar called for in the recipe is 1134.0 grams, tenths of a gram rounded up. By dividing 40 ounces by the conversion value of 28.35 grams per ounce, you can calculate this and get 1134.0 grams.

Rounding to the closest tenth of a gram is necessary to convert 40 ounces to grams. To do this, multiply the weight in ounces by the conversion factor of 28.35 (1 ounce = 28.35 grams).

Therefore, 40 ounces of brown sugar are equivalent to:

40 ounces x 28.35 grams per ounce = 1134 grams

Because 1 gram only roughly equates to 0.04 ounces, it is vital to keep in mind that this is an estimation. This conversion factor may change based on the situation and the material being measured.

Hence, The amount of brown sugar required for the recipe is roughly 1134 grams.

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Answer:

1. B) x = 12

2.C)  -5

3. A) 4

7. C) -4

8. A) -4x -6 = 16x

9. B) 29x = 0

Step-by-step explanation:

okay, number 7 you have to distribute -3 to 6 to get -18. So you get 4 -(3*2y) - 18 = 10. add 18 to both sides to get 4 -(3*2y) = 28. subtract the 4. -(3*2y) = 24. Rever the negative. (3*2y) = -24. Divid by 3; 2y = -8. And divide by 2; y = -4.

Same with number 8 but keeping the 16x.

4x - 2 (4x + 3) = 16x

4x - 8x + - 6 = 16x

-4x + -6 = 16x

9.

4(3 - 4x) = 12

3 - 4x = 3

-4x = 0

x = 0

Now you know x = 0 so anything multipied

with the x is 0. The answer is B.

I hope this helped :)

Answer:

  undefined

Step-by-step explanation:

You want the value of f(-1), given the piecewise defined function f(x).

The function is defined for values of x greater than 1. The value x=-1 is not part of the domain of the function:

  f(-1) = "undefined"

Answer:

t=-3  t=3 m=2

Step-by-step explanation:

a. 10=4+3(t+5)

3xt      3x5

10=4+3t+15

4+15

10=3t+19

-19    -19

-9=3   -9/3

-3=t

b. 28=4+3(t+5)

3xt  3x5

28=4+3t+15

4+15

28=3t+19

-19       -19

9=3t   9/3

3=t

c. 0=16+4(m-6)

4xm 4x-6

0=16+4m-24

16-24

0=4m-8

+8    +8

8=4m    8/4

2=m

The work done by the force field on the particle moving along the given helix is 60π units of work.

To find the work done by the force field F on the particle that moves along the helix r, we use the formula:

W = ∫ F · dr

where · denotes the dot product, and dr is the differential displacement vector along the path of the particle.

First, we need to calculate dr. Since the particle moves along the helix r, we can write:

dr = dx i + dy j + dz k

where dx, dy, and dz are the differentials of x, y, and z with respect to t, respectively. We have:

dx = -2sin(t) dt

dy = 2cos(t) dt

dz = 5 dt

Therefore, we can write:

dr = (-2sin(t) i + 2cos(t) j + 5k) dt

Next, we need to calculate F · dr. We have:

F · dr = (6x i + 6y j + 2k) · (-2sin(t) i + 2cos(t) j + 5k) dt

= -12sin(t) + 12cos(t) + 10 dt

Finally, we can integrate F · dr over the interval 0 ≤ t ≤ 2π to obtain the work done by the force field F on the particle that moves along the helix r:

W = ∫ F · dr = ∫ (-12sin(t) + 12cos(t) + 10) dt

= [-12cos(t) + 12sin(t) + 10t]0\(^(2π)\)

= (-12cos(2π) + 12sin(2π) + 10(2π)) - (-12cos(0) + 12sin(0) + 10(0))

= 20π

Therefore, the work done by the force field F on the particle that moves along the helix r is 20π.

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The median, Q₁, Q₃, lower fence and upper fence of the given data set are 82, 75, 83, 63 and 95.

What is Inter quartile range?

In a range of values, from lowest to highest, the IQR denotes the median 50% of values. Find the median (middle value) of the lower and higher half of the data first, then use that number to calculate the interquartile range (IQR). The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.

Given data set : 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83

Firstly, we will arrange the data into ascending order.

we get, 54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100.

Here, no. of terms is 11

So, Median = (n+1)/2 th = (11+1)/2 = 6th term

So, Median = 82.

Q₁ = (n+1)/4 th term = (11+1)4 th = 3rd term

                                                 = 75

Q₃ = 3(n+1)/4 th term = 9th term = 83

Inter-quartile range = Q₃ - Q₁

                                  = 83 - 75 = 8.

Now, Lower fence = Q₁ - 1.5*IQR

                              = 75 - 1.5× 8

                              = 75 - 12 = 63

       Upper fence = Q₃ + 1.5*IQR

                              = 83 + 1.5×8

                              = 83 + 12

                              = 95.

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Answer:

11/12

Decimal form: 0.916 (the 6 is continuous)

Step-by-step explanation:

The graph of the parent absolute value function decreases over (–∞, 0) interval.

An absolute value function is a function that contains an algebraic expression within absolute value symbols.

Recall that the absolute value of a number is its distance from 0 on the number line.

The absolute value function is f(x) = |x| is defined as,

\(\rm f(x)= x \ if\ x > 0\\\\f(x)= 0 \ if\ x=0\\\\ f(x)=- x \ if\ x < 0\\\)

Observe that the graph is V-shaped.

Hence, the graph of the parent absolute value function decreases over (–∞, 0) interval.

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f ′ is continuous, and 7 2 f ′(x) dx = 16 . Then the value of f(7) is 27.

To find the value of f(7), we can use the information provided. We know that f'(x) is continuous and that the definite integral of 7^2 f'(x) dx is equal to 16.

The integral of 7^2 f'(x) dx is equal to the antiderivative of f'(x) evaluated from 2 to 7. Since we don't have the explicit form of f'(x), we can't directly evaluate the integral. However, we can apply the Fundamental Theorem of Calculus, which states that the definite integral of a derivative gives the difference of the original function evaluated at the endpoints of the interval.

Given that f(2) = 11, we can use the Fundamental Theorem of Calculus to write:

Integral[2 to 7] of 7^2 f'(x) dx = f(7) - f(2)

Since the integral is equal to 16, we have:

16 = f(7) - 11

Solving for f(7), we find:

f(7) = 27

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Answer:

y = 5

Step-by-step explanation:

y = 0x + b

5 = 0(4) + b

5 = 0 + b

5 = b

Answer:

$16152.5 0

Step-by-step explanation:

Yes, g has a maximum and minimum on the set S.

Since S is a closed and bounded interval, by the Extreme Value Theorem, any continuous function on S will have both a maximum and minimum value. Therefore, g, defined on S, will have both a maximum and minimum value.

To find the global maxima and minima of g on the set S, we need to analyze the function g(x). However, since no specific function is defined for g, we cannot determine the exact maxima and minima values without further information. We can make some general observations about g(x) on S. Firstly, since S includes both negative and positive values, g(x) could be a piecewise function that changes at x = 0. Secondly, the behavior of g(x) will depend on the specific function used to define it. For example, if g(x) = x^2, then g(x) will have a minimum value of 0 at x = 0 and a maximum value of 100 at x = 10 or x = -10. Similarly, if g(x) = -x^3, then g(x) will have a maximum value of 1000 at x = 10 and a minimum value of -1000 at x = -10.

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Answer:

95

Step-by-step explanation:

There is zero or no degree of freedom in  the mean of the differences in a paired t-test.

For the paired t-test, we need two variables. One variable defines the pairs for the observations. The second variable is a measurement. Sometimes, we already have the paired differences for the measurement variable. Other times, we have separate variables for “before” and “after” measurements  for each pair and need to calculate the differences.

We also have an idea, or hypothesis, that the differences between pairs is zero. It is also known as the dependent samples t-test, the paired-difference t-test, the matched pairs t-test and the repeated-samples t-test.

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Answer:

y=4

Step-by-step explanation:

Answer:

Step-by-step explanation:

that should be a triangular prism.

a. AnBn = {anbn | n ≥ 0}

To draw a transition diagram for a Turing machine that accepts the language AnBn, we need to design a machine that reads an 'a', then moves to the right to find a corresponding 'b', and repeats this process for any number of 'a's and 'b's.

The transition diagram for the Turing machine accepting the language AnBn would look like this:

```

 a      a      ε

----> q0 ----> q1 ----> q2

 |      |      |

 b      b      ε

```

Explanation:

- q0 is the initial state and the starting point.

- On reading an 'a' in state q0, the machine moves to state q1 and replaces the 'a' with ε (empty symbol). It moves to the right to find a corresponding 'b'.

- On reading a 'b' in state q1, the machine moves to state q2 and replaces the 'b' with ε. It continues to move to the right, looking for more 'a's and 'b's.

- If the machine finds any symbol other than 'a' or 'b', it rejects the input.

b. {aibj | i < j}

To draw a transition diagram for a Turing machine that accepts the language {aibj | i < j}, we need to design a machine that reads 'a's and 'b's, ensuring that the number of 'a's is less than the number of 'b's.

The transition diagram for the Turing machine accepting the language {aibj | i < j} would look like this:

```

 a        b

----> q0 ----> q1

 |        |

 ε        ε

```

Explanation:

- q0 is the initial state and the starting point.

- On reading an 'a' in state q0, the machine stays in state q0 and reads further 'a's.

- On reading a 'b' in state q0, the machine moves to state q1 and reads further 'b's.

- If the machine finds any more 'a's in state q1, it stays in state q1.

- If the machine finds any more 'b's in state q0, it rejects the input.

Note: The diagram represents a basic concept of the Turing machine for the given languages. Depending on the specific requirements and implementation, the transition diagrams may vary.

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Question has a slight error .we should find n(A\(\cap\)B)

\(\boxed{\sf n(A\cup B)=n(A)+n(B)-n(A\cap B)}\)

\(\\ \rm\longmapsto n(A\cap B)=n(A)+n(B)-n(A\cup B)\)

\(\\ \rm\longmapsto n(A\cap B)=12+9-16\)

\(\\ \rm\longmapsto n(A\cap B)=5\)

Answer:

Answer is D

Step-by-step explanation:

A $560 investment compounded annually at a rate of 9% per year will take approximately 7.97 years to double, resulting in a final amount of $1,120.

To determine how long it will take for the investment to double, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

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 number of years

In this case, the initial investment (P) is $560, the annual interest rate (r) is 9% (0.09 as a decimal), and the final amount (A) is $1,120 (double the initial investment).

Plugging in these values, we have:

1,120 = 560(1 + 0.09/n)^(n*t)

To solve for t, we need to choose a value for n. Since compounding is done annually, we can set n = 1:

1,120 = 560(1 + 0.09/1)^(1*t)

1,120 = 560(1 + 0.09)^t

Dividing both sides by 560:

2 = (1 + 0.09)^t

Taking the logarithm of both sides:

log(2) = t * log(1 + 0.09)

Solving for t:

t = log(2) / log(1.09)

Using a calculator, we find:

t ≈ 7.97 years

Therefore, it will take approximately 7.97 years (rounded to 2 decimal places) for the investment to double.

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Answer:

Step-by-step explanation:

Answer:

b 19

Step-by-step explanation:

Answer:

the answer is 19, B.

Step-by-step explanation:

this is my first time answering a question. i hope this helps you.

Answer + Step-by-step explanation:

10 × 5 × 2

= 10 × (5 × 2)   (associative property)

= 10 × (10)

= 10 × 10

= 100

Answer:

a system of government by the whole population or all the eligible members of a state, typically through elected representatives. The United States is one of the world's developed democracies where third parties have the least political influence. The federal entity created by the U.S. Constitution is the dominant feature of the American governmental system.

Step-by-step explanation: