Suppose 50% of the registered voters in a country are Republican. If a sample of 629 voters is selected, what is the probability that the sample proportion of Republicans will differ from the population proportion by more than 4%? Round your answer to four decimal places.

The range, median and mode of the data-set are given as follows:

Considering the stem-and-leaf plot, the data-set is given as follows:

54, 55, 60, 66, 69, 72, 73, 74, 75, 75, 81, 82, 88, 89, 95, 96.

The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus:

96 - 54 = 52.

The data-set has an even cardinality of 16, hence the median is calculated as the mean of the two middle elements as follows:

Median = (74 + 75)/2

Median = 74.5.

The mode of a data-set is the observation that appears the most times in the data-set, hence it is of 75, which is the only observation that appears twice in the data-set.

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An Annual is not an example of an agreement.

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{-5})\qquad \qquad \stackrel{slope}{m}\implies - \cfrac{20}{11} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{-\cfrac{20}{11}}(x-\stackrel{x_1}{8})\implies y+5=-\cfrac{20}{11}x+\cfrac{160}{11} \\\\\\ y=-\cfrac{20}{11}x+\cfrac{160}{11}-5\implies y=-\cfrac{20}{11}x+\cfrac{105}{11}\)

Answer:

Anwer is 426.4.

Step-by-step explanation:

HOPE ITS HELP YOU.

Answer:

A and C

Step-by-step explanation:

Normal distribution is characterized by a symmetrical mean and two tails (_/\_ like this but a bit more curvy)

Answer:

Hence, the relation R is a reflexive, symmetric and transitive relation.

Given :

A be the set of all lines in the plane and R is a relation on set A.

\(R=\{l_1,l_2\in A|l_1 \;\text{is parallel to}\; l_2\}\)

To find :

Which type of relation R on set A.

Explanation :

A relation R on a set A is called reflexive relation if every \(a\in A\) then \((a,a)\in R\).

So, the relation R is a reflexive relation because a line always parallels to itself.

A relation R on a set A is called Symmetric relation if \((a,b)\in R\) then \((b,a)\in R\) for all \(a,b\in A\).

So, the relation R is a symmetric relation because if a line \(l_1\) is parallel to the line \(l_2\) the always the line \(l_2\) is parallel to the line \(l_1\).

A relation R on a set A is called transitive relation if \((a,b)\in R\) and \((b,c)\in R\) then \((a,c)\in R\) for all \(a,b,c\in A\).

So, the relation R is a transitive relation because if a line \(l_1\) s parallel to the line \(l_2\) and the line \(l_2\) is parallel to the line \(l_3\) then the always line \(l_1\) is parallel to the line \(l_3\).

Therefore the relation R is a reflexive, symmetric and transitive relation.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Step-by-step explanation:

f(g(13)) = \(\sqrt{g(13)}\) =\(\sqrt{13-9}\)=\(\sqrt{4}\)=2

Answer:

12

Step-by-step explanation:

You simply add the coefficients together.
3 + 4 + 5 = 12

Answer:

To solve this trigonometric equation, we can use the following trigonometric identity:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Applying this identity, we get:

sin(65° - 25°) = sin(65°)cos(25°) - cos(65°)sin(25°)

simplifying this expression, we get:

sin(40°) = (sin(65°) / 2) - (sin(25°) * √3 / 2)

Now, we can use another trigonometric identity:

sin(2a) = 2sin(a)cos(a)

to simplify the expression on the right side of the equation. We have:

sin(65°) = 2sin(32.5°)cos(32.5°)

and

sin(25°) = 2sin(12.5°)cos(12.5°)

Substituting these into our original equation, we get:

sin(40°) = (sin(32.5°)cos(32.5°) - sin(12.5°)cos(12.5°)) * √2

Using the same trigonometric identity, we can simplify the expression on the right side of the equation:

sin(32.5°)cos(32.5°) - sin(12.5°)cos(12.5°) = 1/2(sin(65° - 25°) - sin(65° + 25°))

= 1/2(sin(40°) - sin(90°))

= 1/2(sin(40°) - 1)

Substituting this back into our original equation, we get:

sin(40°) = 1/2(sin(40°) - 1) * √2

Multiplying both sides by 2/√2, we get:

2sin(40°) / √2 = sin(40°) - 1

Adding 1 to both sides, we get:

sin(40°) + 1 = 2sin(40°) / √2

Simplifying the right side of the equation, we get:

2sin(40°) / √2 = sin(40°) * √2

Substituting this back into our equation, we get:

sin(40°) + 1 = sin(40°) * √2

Subtracting sin(40°) from both sides, we get:

1 = sin(40°) * (√2 - 1)

Dividing both sides by (√2 - 1), we get:

sin(40°) = 1 / (√2 - 1)

Multiplying the numerator and denominator by (√2 + 1), we get:

sin(40°) = (√2 + 1) / 1

Therefore, sin65° - sin25º = √2.sin20⁰ is not correct, and the correct value of sin(65°) - sin(25°) is (√2 + 1) / 2.

Step-by-step explanation:

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From LHS

Sin65 - Sin25

*Using SinC - SinD formula*

= 2Cos[(65+25)/2]×Sin[(65-25)/2]

=2cos90/2 × sin40/2

=2cos45sin20

=2 × (1/square root 2) sin20

=square root 2 × sin20

=RHS ( look photo to be more clear)

Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

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

Let's simplify left sides of each statement and compare with right sides:

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

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Step-by-step explanation:

mean = sum of observation/ no. of observation

mean = 3+5+6+4+7+3+9+8/ 8

Answer:

3+5+6+4+7+3+9+8/8

45/8

5.625

Answer:

a = \(\frac{d}{b+c}\)

Step-by-step explanation:

a(b + c) = d

isolate a by dividing both sides by b + c

a = \(\frac{d}{b+c}\)

Answer:

Step-by-step explanation:

The bell boy added $270 and $20 incorrectly. The $20 bill was something that was returned due to overcharching. On the other hand, $270 was the amount that they paid for their room. This only means that $20 should be deducted from $270 and that's the amount that they paid for their room while $30 and $20 are the amount that the bell boy received as a tip

Total money of the three men: 3($100) = $300

They paid $270 for the room: $300 - $270 = $30

Tip for the bell boy: $30 - $30 = $0

Amount overcharged to them: $0 + $20 = $20

Tip to the bell boy: $20 - $20 = $0

They were left with no more money from the original $300.

The simplified form of 6 log₃x - 7 log₃y + 4 log₃z is  log₃{(x⁶z⁴)/y⁷}.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself. For instance, the number 6 is multiplied by itself four times, yielding 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

The simplification of the provided logarithmic expression can be done as follows:-

6 log₃x - 7 log₃y + 4 log₃z,

= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law}

= log₃x⁶ + log₃z⁴ - log₃y⁷

= log₃x⁶z⁴ - log₃y⁷ {Using the Product law}

= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law}.

Hence, the simplified form of 6 log₃x - 7 log₃y + 4 log₃z is  log₃{(x⁶z⁴)/y⁷}.

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Answer:

a) 10.40

b) 62.40

Step-by-step explanation:

im smart

Answer: 25% of 40 or 0.25 of 40 is 10.

Step-by-step explanation:

Basically you have to divide 40 by 10 because 1/4 of 100 is 25. 25 is 1/4 of 100.

So knowing this 40/0.25 is equal to 10. This is why 0.25 of 40 is 10.

The man's daily wage is given as follows:

$42.

The wages are obtained applying the proportions in the context of the problem.

The woman receives $24 for 8 hours of work, hence her hourly wage is given as follows:

24/8 = $3 per hour.

(Hourly wage = Total wages/total hours).

Their wages per hour are in the ratio 7:5, hence the man's hourly wage is obtained multiplying the woman's hourly wage by 7/5, hence:

7/5 x 3 = 21/5 = $4.2 per hour.

The man works 10 hours a day, hence the daily wage is given as follows, multiplying the hourly wage by 10:

10 x 4.2 = $42.

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Answer: I think the greatest common factor is 4x^2

Step-by-step explanation:

Find the numerical common factors. Which are 8, -12, and 20. Find the variable common factors for x^4, x^3, and x^2. Multiply them together. Then break down the factors on both sides and pick the biggest one. Finally multiply them together. (I’m sorry, I’m very bad at explaining things.)

Using Proportion the table value is,

Cheese   Number of Pizzas

3 pounds          8

18 pounds        48

22.5 pounds    60

27 pounds        72

What is a proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

We have,

3 pounds bag of cheese makes 8 pizzas.

This means,

3 pounds = 8 pizzas

1 pound = 8/3 pizzas

Now,

1 pound = 8/3 pizzas

Multiply 18 on both sides.

18 pounds = 18 x 8/3

18 pounds = 48 pizzas

1 pound = 8/3 pizzas

Multiply 22.5 on both sides.

22.5 pounds = 22.5 x 8/3

22.5 pounds = 60 pizzas

1 pound = 8/3 pizzas

Multiply 27 on both sides.

27 pounds = 27 x 8/3

27 pounds = 72 pizzas

Thus,

The number of Pizzas for 3 pounds is 8.

The number of Pizzas for 18 pounds is 48.

The number of Pizzas for 22.5 pounds is 60.

The number of Pizzas for 27 pounds is 71.

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Answer:

The prime number 2.

Step-by-step explanation:

Odd number + Odd number = Even number

An odd number plus another odd number equals an even number. And most prime numbers are odd, so you might think this is true. Is it?

Wrong. The prime number 2 is an even number and

Even number + Odd number = Odd number

Odd number + Even number = Odd number

So, there is a number that can make the sum of two prime numbers odd.

Answer:

2r3

Step-by-step explanation:

15÷6

6 can go into 15 two times without going over the number 15. 6 times 2 is 12. So 15-12 = 3 so 2r3 or 5/2 or 2.5 or 2 1/2

Answer:

C. 5 inches

Step-by-step explanation:

I’m area you have to multiply L • W

But since we don’t know the width we can divide the length by the area.

40/8 = 5

So the answer would be 5.

Another way to solve this problem is with using guess and check.

I hope it helps! Have a great day!

Anygays~

Answer:

C. 5 inches

Step-by-step explanation:

Use the numbers we have in the word problem, so you´d divide 40 by 8 since you´re trying to find the width. 40 is the area and 8 is the length so divide it tofind the width.

40/8 = 5

ANSWER: 5 inches

I hope it helps! Have a great day!

Answer:

The distance traveled in one revolution is 282.6 cm.

Step-by-step explanation:

Diameter of wheel, d = 90 cm

The distance traveled by the wheel in one revolution is circumference.

The circumference of the wheel is

\(C = \pi\times d\\C =3.14\times 90\\C = 282.6cm\)

Answer:

b & c

Step-by-step explanation:

Answer:

\( - 8(45) + 482 = - 360 + 482 = 122\)