Write the decimal expansion for 6 1/3

Thus, we can be 90% confident that the true proportion of men in the college is between 8.8% and 14.0%.

Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. For example, 50% is equivalent to the fraction 50/100, which can be simplified to 1/2. Percentages are commonly used to express ratios, proportions, or rates in various contexts such as finance, statistics, and everyday life. For instance, an interest rate of 3% means that for every $100 borrowed, the borrower will be charged $3 per year. Similarly, a score of 80% on an exam means that the student has answered 80 out of 100 questions correctly.

by the question.

To find the confidence interval of the true proportion of men in the college, we need to use the formula:

\(CI = p ± z\sqrt((p(1-p))/n)\)

where p is the sample proportion (80/700 = 0.114), z is the z-score associated with the confidence level (90% in this case), and n is the sample size (700).

To find the z-score, we can use a standard normal distribution table or a calculator. For a 90% confidence level, the z-score is approximately 1.645.

Plugging in the values, we get:

\(CI = 0.114 ± 1.645\sqrt((0.114(1-0.114))/700)\)

Simplifying, we get:

\(CI = 0.114 ± 0.026\)

Therefore, the 90% confidence interval for the true proportion of men in the college is:

\(CI = 0.114 ± 0.026\)

Rounding to the nearest tenth of a percent, we get:

CI = (8.8%, 14.0%)

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Given a discount of 20% and a manufacturer's coupon of $200, the price after the discount and coupon, (C ∘ D)(x), is 0.8x - 200.

A discount is an amount that reduces the price of a retail item.

Discounts are offered as rates and the discounted price is computed by multiplying the discount factor and the price.

Discount rate on offer = 20%

Discounting factor = 80% or 0.8 (100 - 20%)

Manufacturer's coupon off the price = $200

Let the price of the bureau = x

The price after the discount (discounted price) is given by D(x)

D(x) = 0.8x

The price after the coupon = C(x) = x - 200

The price after applying the discount and the coupon, (C ∘ D)(x) = 0.8x - 200

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Wilson's Warehouse sells a certain brand's bureau. They are offering a 20% discount in addition to accepting a manufacturer's coupon for $200 off. Let the price of the bureau be x. If the price after the discount is given by D(x) and the price after the coupon is C(x), find (C ∘ D)(x).

Answer:

Answer:

1.11111=111111100000

Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator

1.11111=1.111111

Multiply to remove 5 decimal places. Here, you multiply top and bottom by 105 = 100000

1.111111×100000100000=111111100000

Simplify the improper fraction,

=111111100000

In conclusion,

1.11111=111111100000

Step-by-step explanation:

The fraction equivalent of the repeating decimal 1.11111 is 10/9. This means that 1.11111 is equivalent to 10/9, indicating a ratio of 10 parts to 9 parts. Simplifying the fraction ensures that it is in its simplest form with no common factors between the numerator and the denominator other than 1.

To express the decimal 1.11111 as a fraction, we can use algebraic manipulation. Let's denote the repeating decimal as x:

x = 1.11111...

To eliminate the repeating part, we can multiply x by 10:

10x = 11.11111...

Now, we can subtract the original equation from the multiplied equation to eliminate the repeating part:

10x - x = 11.11111... - 1.11111...

Simplifying the equation:

9x = 10

Dividing both sides by 9:

x = 10/9

Therefore, the fraction equivalent of the repeating decimal 1.11111 is 10/9. This means that 1.11111 is equivalent to 10/9, indicating a ratio of 10 parts to 9 parts. Simplifying the fraction ensures that it is in its simplest form with no common factors between the numerator and the denominator other than 1.

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Answer:

B

Step-by-step explanation:

According to the theorem, equal sides have equal angles opposite to them so AB AND AC are equal so x and y are also equal

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

csc θ = 13/12

Step-by-step explanation:

cos θ = 12/13

Formula: cos θ = 1/cscθ

Its just the reciprocal.

solve:

1/csc θ = 12/13

csc θ = 13/12

Answer:

\(\textsf{a)} \quad \text{cosec}\:\theta=\dfrac{13}{12}\)

Step-by-step explanation:

Given cosine trigonometric identity:

\(\boxed{\cos\theta=\dfrac{12}{13}}\)

To find the value of cosec θ, use the trigonometric identity:

\(\boxed{\text{cosec}\; \theta=\dfrac{1}{\cos\theta}}\)

Substitute the given value of cos θ into the cosec θ identity:

\(\implies \text{cosec}\:\theta=\dfrac{1}{\frac{12}{13}}\)

\(\implies \text{cosec}\:\theta=1 \div \dfrac{12}{13}\)

\(\implies \text{cosec}\:\theta=1 \times \dfrac{13}{12}\)

\(\implies \text{cosec}\:\theta=\dfrac{13}{12}\)

Therefore, the value of cosec θ is:

\(\boxed{\text{cosec}\:\theta=\dfrac{13}{12}}\)

Answer: A

Step-by-step explanation:

Area of a triangle is base times height

We have a base made by point m and n with a length of 6

now the third point has to form a height which when put with the base, gets you 18

area of triangle is bh/2

so lets set height as h, 6x/2 = 18 6x = 36 x = 6

This means the point has to be 6 apart either left or right. Only point that matches this is a.

Answer:

\(b\ge \:5\)

Step-by-step explanation:

\(-138\ge \:-6\left(6b-7\right)\\\\\)

Switch sides

\(-6\left(6b-7\right)\le \:-138\\\)

Multiply both sides by -1

\(\left(-6\left(6b-7\right)\right)\left(-1\right)\ge \left(-138\right)\left(-1\right)\)

Simplify

\(6\left(6b-7\right)\ge \:138\)

Divide both sides by 6

\(\frac{6\left(6b-7\right)}{6}\ge \frac{138}{6}\)

Simplify

\(6b-7\ge \:23\)

Add 7 to both sides

\(6b-7+7\ge \:23+7\)

Simplify

\(6b\ge \:30\)

Divide both sides by 6

\(\frac{6b}{6}\ge \frac{30}{6}\)

Simplify

\(b\ge \:5\)

Answer:

x = 8

measure of each side = 27 units

Step-by-step explanation:

Properties of an equilateral triangle:

If ΔGHJ is an equilateral triangle, the side measures are equal.

\(\implies \sf GH = HJ = GJ\)

\(\implies (5x-13)=(11x-61)=(7x-29)\)

To solve for x, choose 2 side lengths, equate them, and solve for x:

\(\implies \sf GH=HJ\)

\(\implies 5x-13=11x-61\)

\(\implies 5x-13 - 5x =11x-61 - 5x\)

\(\implies -13=6x-61\)

\(\implies -13+61=6x-61+61\)

\(\implies 48=6x\)

\(\implies 48 \div 6=6x \div 6\)

\(\implies x=8\)

To find the measure of each side, substitute the found value of x into one of the side expressions:

\(\begin{aligned}\implies \textsf{GH}&=5(8)-13\\& =40-13\\& =27\end{aligned}\)

Therefore, x = 8 and the measure of each side is 27 units.

Equilateral triangles have same sides

Length of each side

Answer:

21 inches

Step-by-step explanation:

1 inch = 6 miles

126/6 = 21

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

its D

Step-by-step explanation:

calculator

Answer:

n1=0 n2=4 n3=8 n4=12

Step-by-step explanation:

tn=4(n-1) is the formula to determine the value of the nth term, so all you have to do is plug in what term you want for the variable and solve.

for example

n1=4(1-1)=0

n2=4(2-1)=4

n3=4(3-1)=8

n4=4(4-1)=12

Hope you understand and have a great day.

Answer:

where??

Step-by-step explanation:

Answer:

Step-by-step explanation:

nth term = 3*(2n - 1 )

n =1  ;    first term = 3*( 2*1 - 1) = 3* (2-1)  = 3*1 = 3

n = 2 ; second term = 3*( 2*2 - 1) = 3* (4-1)  = 3*3 = 9

n = 3 ;  third term = 3*( 2*3 - 1) = 3* (6-1)  = 3*5 = 15

To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

The fastest time in the obstacle course is 260 seconds.

In statistics, a quartile is a type of quantile that divides a data set into four equal parts, or quarters, each representing 25% of the dataset. The first quartile (Q1) marks the 25th percentile, the second quartile (Q2) marks the 50th percentile, and the third quartile (Q3) marks the 75th percentile. The difference between the third and first quartiles is called the interquartile range (IQR), which is used to measure the spread of the data.

Here,

According to the box plot.

The minimum value = 260 sec

The maximum value = 360 sec

The quartile = 300 sec and 340 sec

The median = 330 sec

The fastest time in the obstacle course = 260 sec

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Answer:

mutlaply all of them then davide by 18 then u got ur answer

Step-by-step explanation:

Answer:

The zero 1 has a multiplicity of 1.

The zero -2 has a multiplicity of 2.

Hope this clears up any confusion :)

Step-by-step explanation:

Answer:

The zero  1  has a multiplicity of 1.

The zero −2 has a multiplicity of  2 .

Step-by-step explanation:

All customers, with the exception of customer 4, should receive coupons due to the probability that different consumers may use them.

Given that,

Probability of Customer Using Coupon

1- 0.47

2- 0.35

3- 0.27

4- 0.03

5- 0.08

We have to identify the anticipated profit for each client. Answers should be rounded to the closest cent. If applicable, enter a negative value as a negative number.

If users use the coupons, Honey will profit as follows:

= Revenue - Cost

= 1 - 0.05

= $0.95

If the coupon is not used, the cost of $0.05 becomes the profit.

Customer 1 expected profit:

= P(coupon used) × Profit if coupon used + (1 - P(coupon used)) × Profit if coupon not used

= (0.47 x 0.95) + ( (1 - 0.47) x -0.05)

= $0.42

Customer 2 expected profit:

= (0.35 x 0.95) + ( (1 - 0.35) x -0.05)

= $0.30

Customer 3 expected profit:

= (0.27 x 0.95) + ( (1 - 0.27) x -0.05)

= $0.22

Customer 4 expected profit:

= (0.03 x 0.95) + ( (1 - 0.03) x -0.05)

= -$0.02

Customer 5 expected profit:

= (0.08 x 0.95) + ( (1 - 0.08) x -0.05)

= $0.03

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Answer:

E. When the sample size​ increases, because the standard deviation of the distribution of sample means better estimates the population standard deviation for larger sample sizes.

Step-by-step explanation:

Answer:

c.) 8/3

Step-by-step explanation:

the two sides must weigh the same, or 12 grams.

the weights labelled x combined with the 4 grams weight should equal 12 grams.

the equation solved for x would be:

3x + 4 = 12

3x = 8

x = 8/3

50

Step-by-step explanation:

180=65+65+x

180=130+x

-130 -130

x=50

Answer:

x=50°

Step-by-step explanation:

at first base angle of isosceles triangle are equal

so

65°+65°+x=180 sum of all angle of triangle

x=150°

Answer:

D

Step-by-step explanation:

For each triangle, you are given two sides and the included angle (the one between those 2 sides). That's side-angle-side, so it is S-A-S.

The SAS Rule for Similar Triangles says that for 2 triangles X and Y, if you have the SAS of one and the SAS of the other, then X and Y are similar (same shape and proportions) if

(a) the angle in X is congruent (same) as the angle in Y

(b) the ratio between the two given sides in X is the same as the ratio between the two given sides in Y

For this particular problem, the ratio PR/PQ = 18/21 = 6/7 if you simplify by dividing both top and bottom by 3.

So we are looking for another triangle where we have the same ratio. (Put the smaller number on top, in the fraction.)

Answer A:  12/15 simplifies to 4/5, wrong answer

Answer B:  9/12 simplifies to 3/4, wrong answer

Answer C:  6/10 simplifies to 3/5, wrong answer

Answer D: 15/17.5 looks harder, because there is a decimal in it. But we know 17.5 is just 17 and a half, so I would first multiply top and bottom by 2

We get 30/35. That looks a lot better. Now it is easier to see we can divide both top and bottom by 5.

We get 6/7! That is the correct answer, so D is the triangle similar to PQR.

Carson can line up his textbooks on his bookshelf in 24 different ways

What is Permutation?

Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.

What is Combination?

The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.

According to the given information:

Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:

n! / (n - r)!

where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).

On substituting the values in the formula,

4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24

Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.

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Answer:

a) common difference = 5

b) common difference =  - 2

c) not an arithmetic sequence

last question:
nth term: aₙ = 3n - 1

a₅₀ = 149

a₄₀₀ = 899

Step-by-step explanation:

Common difference d = difference between successive terms
For a)
d = 9 -4 = 14 - 9 = 5

For b)
d = 8 - 10 = 6 - 8 = -2

For c) 5, 5, 2, 0
5  -5 = 0
which is not equal to
2 - 5 = 3
So this is not an arithmetic sequence
(unless of course the series numbers have been copied wrong)

For the last question

Sequence = 2, 5, 8, 11, 14, ...

d = 5 - 2 = 8 -5 =  3

The nth term of an arithmetic sequence is given by the formula:

aₙ = a₁ + d(n-1)

where a₁ = first term = 2

d = 3

So
aₙ = 2 + 3(n- 1)
aₙ = 2 + 3n - 3
aₙ  = 2 -3 + 3n

aₙ = -1 + 3n
aₙ = 3n - 1

Check:

a₂ = 3(2) - 1 = 5
a₃ = 3(3) - 1 = 8
a₄ = 3(4) - 1 = 11

a₅₀ = 3(50) - 1 = 150 - 1 = 149

a₃₀₀ = 3(300) - 1 = 900 - 1 = 899

The probability that either event A or B will occur is 43/60

Using the parameters given

n(A) = 29

n(B) = 14

Total number of events = 29+17+14 = 60

The probability of each event :

P(A) = 29/60

P(B) = 14/60

P(A or B ) = P(A) + P(B)

P(A or B ) = 29/60 + 14/60

P(A or B ) = 43/60

Therefore, the probability of A or B is 43/60

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Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720