If AD=2/3AB, the ratio of the length of BC to the length of DE is A. 1/6 B. 1/4 C. 3/2 D. 3/4

Answer:

(a) 2,162,160

(b) 3,003

Step-by-step explanation:

(a) order matters

You can choose from 14 for the first pick. Then you have 13 left for the second pick. Then you have 12 left for the third pick. Keep going until you have 9 left for the 6th pick. The number when order matters is:

total = 14 * 13 * 12 * 11 * 10 * 9 = 2,162,160

(b) Order does not matter

Start with the same number as above for picking 6 out of 14. Since order does not matter, we divide by the number of ways you can arrange 6 items.

Since there are 6! ways of arranging 6 items,

total = 2,162,160/6! = 3,003

The number of ways when the order matters are 121080960.

The number of ways when order does not matters are 3003.

Given,

Choose 6 colors, without replacement, from 14 distinct colors.

We have to find:

- How many ways can this be done, if the order of the choices matters.

- How many ways can this be done if the order of the choices does not matter.

We use permutation when the order of the arrangements matters.

It is given by:

[tex]^ nP_r[/tex] = n! / r!

We use combination when order does not matter.

It is given by:

[tex]^nC_{r}[/tex] = n! / r! (n-r)!

Find the number of ways when order matters.

We have,

n = 14 and r = 6

[tex]^{14}P_{6}[/tex]

= 14! / 6!

= (14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6!) / 6!

= 4 x 13 x 12 x 11 x 10 x 9 x 8 x 7

= 121080960

Find the number of ways when order does not matter.

We have,

n = 14 and r = 6

[tex]^{14}C_{6}[/tex]

= 14! / 6! 8!

= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2

= 7 x 13 x 11  x 3  

= 3003

Thus,

The number of ways when the order matters are 121080960.

The number of ways when order does not matters are 3003.

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Answer:

slope = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, 2)

m = [tex]\frac{2-1}{4-0}[/tex] = [tex]\frac{1}{4}[/tex]

Answer:

the answer would be 1/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

Answer:

$91

Step-by-step explanation:

If a jacket is on sale for 35% off, that means that the price of the jacket is [tex]100-35=65[/tex]% of its original price.

We can find 65% of 140 by making 65% into a decimal - 0.65, then multiply it by 140.

[tex]140\cdot0.65=91[/tex]

Hope this helped!

Answer:

$91.00

Step-by-step explanation:

The jacket is on sale for 35%. Usually, you pay for 100% of the jacket's price. Since it is on sale, we can subtract 35% from 100%.

100%-35%=65%

With the sale, you only pay for 65% of the price.

Now, we can multiply 65% and 140.

65% * 140

Convert 65% to a decimal. Divide 65 by 100 or move the decimal place 2 spots to the left.

65/100=0.65

65.0 --> 6.5 --> 0.65

0.65 * 140

Multiply

91

$91

The sale price for the sports jacket is $91.00

Answer:

Those ratios could be 3:1

Step-by-step explanation:

cot x / (1 + csc x)

Multiply by conjugate:

cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)

Distribute the denominator:

cot x (1 − csc x) / (1 − csc²x)

Use Pythagorean identity:

cot x (1 − csc x) / (-cot²x)

Divide:

(csc x − 1) / cot x

[tex]p^2 - 10pq + 16q^2=\\p^2-2pq-8pq+16q^2=\\p(p-2q)-8q(p-2q)=\\(p-8q)(p-2q)[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of a line given two points first find the slope of the line and use the formula

y - y1 = m( x - x1) to find the Equation of the line using any of the points given

Slope of the line using points

(3,2) and (4,6) is

[tex]m = \frac{6 - 2}{4 - 3} = \frac{4}{1} = 4[/tex]

So the equation of the line using point

( 3 , 2 ) and slope 4 is

Hope this helps you

Answer:

84 beads

Step-by-step explanation:

She had 98 beads and lost all but fourteen. So it would be 98 - 14 which would get you 84 beads that the girl has lost

Answer:

answer below

Step-by-step explanation:

1. price per gallon of gasoline and total cost of gasoline

2. distance from a door and height of a wheelchair ramp

perfect positive linear relationship:

this is a relation that exists between two variables. The pearson correlation is used to check this relationship and if the relationship is 1.0 then it is established that a positive linear relationship exists

negative linear relationship

this is a relationship between variables where the pearson correlation is less than 0. if the value is -1.0 then a negative linear relatioship exists.

price per gallon of gasoline and total cost of gasoline move in the same direction so it is positive.

distance from a door and height of a wheelchair ramp are negative because they do not move in the same direction.

Answer: Find answers in the attachment files

Step-by-step explanation:

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The correct option is  D

Step-by-step explanation:

From the question the question we are told that

    The researchers were able to state that they are 95% confident that between 52.5% and 59.5% of all U.S. adults believe that the U.S. federal government is not doing enough to keep U.S. elections safe.

Generally a confidence interval states to what extent the chances of the true population is within the a given range

 So the 95% confidence interval given in the question as 52.5% and 59.5%  means that the chances of the true population mean being with this given range is 95%

 So given that the the true population mean is within this range then it means that the population mean will be greater than 50%

   So  the statement that best describe and interprets this result is

The results show significant statistical support that most U.S. adults (over 50%) believe that the U. S. Federal government is not doing enough to keep U.S. election safe.

Using concepts of circles, it is found that the angle measure of each slice is of 72º.

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

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

5 equal slices, thus:

[tex]\frac{360}{5} = 72[/tex]

The angle measure of each slice is of 72º.

A similar problem is given at https://brainly.com/question/16746988

Answer:

3

Step-by-step explanation:

[tex] \sqrt[4] {27} \cdot \sqrt[4] {3} = [/tex]

[tex] = \sqrt[4] {27 \cdot 3} [/tex]

[tex] = \sqrt[4] {3^3 \cdot 3^1} [/tex]

[tex] = \sqrt[4] {3^4} [/tex]

[tex] = 3 [/tex]

Answer:

x could be 3 or 1

Step-by-step explanation:

x²+3=4x

x²-4x+3=0

(x-3)(x-1)

x could be 3 or 1

The values could be 1 or 3.

In this exercise, you're required to write a mathematical (algebraic) expression for the given word problem and determine which values could be the unknown number.

Translating the word problem into an algebraic expression, we have;

[tex]n^{2} = 4n - 3\\\\n^{2} - 4n + 3 = 0[/tex]

We would solve the quadratic equation by using the factorization method;

[tex]n^{2} - 3n -n + 3 = 0\\\\n(n - 3) - 1(n - 3) = 0\\\\(n - 1)(n - 3) = 0[/tex]

Therefore, the values could be 1 or 3.

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Answer:

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....[/tex]

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

[tex]fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}[/tex]

In this exercise we must calculate the Taylor series for the given function in this way;

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

The Taylor series of f(x) around the point a, can be written as:

[tex]f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....[/tex]

Here we have:

[tex]f(x) = 4cos(x)\\a = 7\pi[/tex]

Then, let's calculate each part:

[tex]f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4[/tex]

Here we already can see two things:

1) The odd derivatives will have a sin(x) function that is zero when evaluated in [tex]x=7\pi[/tex].

2) We also can see that the sign will alternate between consecutive terms.

So we only will work with the even powers of the series:

[tex]f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....[/tex]

So we can write it as:

[tex]f(x)=\sum f_n[/tex]

Such that the n-th term can written as:

[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]

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Answer:

Since 1 cm represents 6 km

2 cm will represent 12 km

Hence Adam's house is 12 km away

Answer:

The answer is  C. 3

Step-by-step explanation:

If u divide 6 divided by 2 it will get you 3

i also got it right bc i took the quiz.

Answer

Is it C I may have done my math wrong lol

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

If we have 4 integers that have an average of 9, then all the numbers will add up to [tex]9\cdot4=36[/tex].

If we want the greatest number possible, the other 3 need to be the lowest possible.

Since they are all different, the lowest possible values of the first 3 numbers are 1, 2, and 3.

[tex]1 + 2 + 3 = 6[/tex]

[tex]36 - 6 = 30[/tex]

So 30 is the greatest value of one of the integers.

Hope this helped!

Answer:

Reject H₀.

Step-by-step explanation:

In this case, we need to test whether the average student spent less than the recommended amount of time doing homework in statistics.

The provided data is:

S = {20, 29, 28, 22, 26, 22, 22, 18, 23, 21, 20, 27}

Compute the sample mean:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{12}\cdot [20+29+...+27]=23.167[/tex]

The population standard deviation is σ = 7.

The hypothesis for the test is:

H₀: The average student does not spent less than the recommended amount of time doing homework, i.e. μ ≥ 24.

Hₐ: The average student spent less than the recommended amount of time doing homework, i.e. μ < 24.

(A)

Compute the standardized test statistic value as follows:

[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]

  [tex]=\frac{23.167-24}{7/\sqrt{12}}\\\\=-0.412[/tex]

Thus, the standardized test statistic value is -0.412.

(B)

The significance level of the test is:

α = 0.07

The critical value of z is:

z₀.₀₇ = -1.476

The rejection region is:

(-∞, -0.1476)

(C)

Compute the p-value as follows:

[tex]p-value=P(Z<-0.412)=0.34[/tex]

*Use a z-table.

Thus, the p-value is 0.34.

(D)

Since, p-value = 0.34 > α = 0.07, the null hypothesis was failed to be rejected at 7% level of significance.

Thus, the correct option is (A).

Answer:

[tex]\boxed{2y^{2} - y - 15}[/tex]

Step-by-step explanation:

Use the FOIL technique in order to distribute the terms properly. FOIL stands for First Terms, Outside Terms, Inside Terms, and Last Terms. In order to properly distribute, multiply the common terms based on the steps in the FOIL technique. So, in this case:

Therefore, multiply the terms:

Then, add or subtract based on the signs:

2y² - 6y + 5y - 15

Then, add like terms to finish simplifying the expression. This leaves you with 2y² - y - 15.

Answer:

2y2 – y – 15

Step-by-step explanation:

(2y + 5)(y – 3)

= 2y(y – 3) + 5(y – 3)

= 2y2 – 6y + 5y – 15

= 2y2 – y –15

Answer: No, the orders are not independent.

Step-by-step explanation:

If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)

Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.

P = P1*P2.

In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.

Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.

If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:

P = 0.55*0.72 = 0.396 (or 39.6%)

But we know that the actual probability is 48%.

So this is larger, which means that the outcomes are not independent.

Answer:

Hey there!

True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.

Let me know if this helps :)

Answer:

well all of these look like a way so we have to use elimination method

A : random number tables : well it has random numbers so X out

B: PHONE NUMBERS: well phone numbers are random so X out

C: USing the internet : totally X out

D: books of random numbers: X out

so none of the above i guess

The only way that might not be used in generating random numbers is : (B). using phone numbers selected at random in a local phone book

Random numbers are numbers that occurs randomly without prediction. these numbers are impossible to predict using past values.

Random numbers are important for computer encryption and lotteries.

In conclusion, The only way that might not be used in generating random numbers is using phone numbers selected at random in a local phone book

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Answer:

x - 3y = 12

Step-by-step explanation:

Find the point-slope form of this equation and then convert the point-slope form into standard form (ax + by = c):

y - k = m(x - h) becomes y - 2 = (1/9)(x + 6).

Multiplying all three terms by 9 removes the fraction:

3y - 6 = x + 6, or x - 3y = 12

Answer:

Exact Form:

283 /11

Decimal Form:

25.  72

Mixed Number Form:

25  8 /11

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

= - 54

Step-by-step explanation:

- 99 + 3^2•5

- 99 + 9 × 5

- 99 + 45

= - 54

Answer:

1.649 approximately 2

Step-by-step explanation:

S.d = standard deviation = 0.5

Time taken = lead time = 2 weeks

Mean = demand for week = 5 boxes

We are required to find the safety stock to maintain at 99% service level.

At 99% level, the Z value is equal to 2.326.

Therefore,

Safety stock = z × s.d × √Lt

= 2.326 × 0.5 x √2

= 1.649

Which is approximately 2.

Answer:

x = ±2

Step-by-step explanation:

log 7 (x^2 + 11) = log 7 15

We know that log a ( b) = log a(c)   means b =c

x^2 + 11 = 15

Subtract 11 from each side

x^2 = 15-11

x^2 =4

Take the square root of each side

sqrt(x^2) =±sqrt(4)

x = ±2