Researches are conducting a study to determine the effect of caffeine on memory among Americans. A sample of 100 individuals is given a list of 20 words to look at and remember over the course of 24 hours. Which of the following uses correct notation?
a. n = 100 b. N = 100 c. n = 20 d. N = 20

Answer:

Step-by-step explanation:

The sum of the given geometric series is given by 79545.8567

Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³,.....

Given here: The expression  1000(1.02)³⁰+ 1000(1.05)(1.02)²⁹+ 1000(1.05)²(1.02)²⁸ + ......

Clearly we can observe that the given sum is a geometric progression with common ratio =1.05/1.02

The given sum is a sum of first 29 terms of the G.P

Thus Sₙ = a(rⁿ - 1) / (r - 1)

        S₂₉=1000×1.02³⁰(1.029²⁹-1) /1.0294-1

              =1811.36(2.291106-1)/0.0294

              =1811.36(1.2911)/0.0294

              =79545.8567

Hence, The sum of the given geometric series is given by 79545.8567

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The mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.

Standard deviation, denoted by the symbol σ, describes the square root of the mean of the squares of all the values of a series derived from the arithmetic mean which is also called the root-mean-square deviation. 0 is the smallest value of standard deviation since it cannot be negative. When the elements in a series are more isolated from the mean, then the standard deviation is also large

Mean [tex]& =\frac{\text { Sum of all data }}{\text { Total number data }} \\[/tex]

[tex]& =\frac{6+5+10+5+6+9+9+5+9+5+8+7+8+6+9+8+9+6+10+8}{20} \\& =\frac{148}{20} \\\end{aligned}$$[/tex]

= 7.4

Thus, the mean of the number of hours of sleep for the above sample is 7.4.

To find: the variance and standard deviation for the above sample.

Standard Deviation=[tex]\sqrt{\frac{\sum f_i\left(x_i-\mu\right)^2}{n-1}} \\[/tex]

[tex]& \sigma \quad=\sqrt{\left\{\begin{array}{l}(6-7.4)^2+(5-7.4)^2+(10-7.4)^2+(5-7.4)^2+(6-7.4)^2 \\+(9-7.4)^2+(9-7.4)^2+(5-7.4)^2+(9-7.4)^2+(5-7.4)^2 \\+(8-7.4)^2+(7-7.4)^2+(8-7.4)^2+(6-7.4)^2+(9-7.4)^2 \\+(8-7.4)^2+(9-7.4)^2+(6-7.4)^2+(10-7.4)^2+(8-7.4)^2\end{array}\right\}} \[/tex]

[tex]& \sigma=\sqrt{\frac{\left\{4(6-7.4)^2+4(5-7.4)^2+2(10-7.4)^2+5(9-7.4)^2+4(8-7.4)^2+(7-7.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{\left\{4(-1.4)^2+4(-2.4)^2+2(2.6)^2+5(1.6)^2+4(0.6)^2+(-0.4)^2\right\}}{19}} \\& \sigma=\sqrt{\frac{58.8}{19}} \\& \sigma=\sqrt{3.0947} \\[/tex]

[tex]& \sigma \quad=1.759186 \\[/tex]

Variance = 3.0947

Therefore, the mean of the number of hours of sleep for this sample is 7.4, the standard deviation is 1.759186 and the variance is. 3.0947.

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The equation 2(x-3) + 21 = -3 is asking to find the value of x that makes the equation true.

Value is the worth of something in terms of the benefits, importance, or usefulness it provides. It is the relative importance or worth of something, as compared to other things. It is what people deem to be important, and it can vary depending on the individual or context. Value is not equivalent to price, which is the monetary cost of something. Value is an intangible concept and can represent the overall benefit or worth of an item, service, or experience. It can also refer to an individual’s moral or ethical standards. Value is subjective, meaning that it is based on a person’s individual beliefs and values. It is also malleable and can change over time. People can assign value to different objects, experiences, or relationships, based on what they find meaningful and important.

Distribute to get: 2x-6+21=-3

Combine like terms to get: 2x+15=-3

Solve for x: x=-21/2

Explain the problem: The equation 2(x-3) + 21 = -3 is asking to find the value of x that makes the equation true.

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Answer:

Below  

Step-by-step explanation:

Here is the answer for 11pi   DEGREES

( but you may have meant 11pi RADIANS   <====but not what you posted) )

 I do not have cot function on my calculator....so I will use tan and then inverse it

 tan (11pi°) = .68876

 .68876 ^(-1) = 1.452

Answer:

x < -2 or x > 5

Step-by-step explanation:

We want to write the compound inequality.

There is an open circle at -2 and a line going to the left.

x < -2

There is an open circle at 5 and a line going to the right.

x > 5

We use an or since they are not connected.

x < -2 or x > 5

The correct option regarding the given sets is option(b)  which shows that A ∩ B' = {3}.

What is set theory?

The area of mathematical logic known as set theory examines sets, which are essentially collections of objects. Set theory is an area of mathematics that primarily focuses on items that are pertinent to mathematics as a whole, despite the fact that any form of an object can be grouped into a set.

Given,

      U = {a,b,c,1,2,3,4}

      A = {b,2,3}

      B = {a,b,2,4}

      C = {4}

      D = {c,3}

      E = {a,b,1,2,3}

      B' = U - B =  {a,b,c,1,2,3,4} -  {a, b,2,4} = {c,1,3}

     A ∩ B' = {b,2,3} ∩ {c,1,3} = {3}

Therefore the correct option regarding the given sets is option(b).

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Answer:

Step-by-step explanation:

answer is 4x^5y²   answer choice b

solution 12 ÷ 3 = 4

to divide x^6 by x - subtract 6 - 1 (power of x = 1) this equals 5

and y^4 divided by y^2 = y^4-2 = y²

True statements about the procedure implement a linear search, So the correct option is, ii only.

Linear search, also known as sequential search, is a simple search algorithm that iterates through an array or a list of elements one by one, starting from the first element, until the desired element is found.

The basic steps of linear search are:

The time complexity of the linear search is O(n), where n is the number of elements in the array/list.

This means that the algorithm takes n steps in the worst-case scenario to find the desired element in an array/list of n elements. Linear search is generally less efficient than other search algorithms like binary search for large data sets.

Linear search can be used on unsorted arrays/lists as well as on sorted arrays/lists. It is a simple and easy-to-implement algorithm and is suitable for small data sets or when the data is not sorted and the data changes frequently.

In addition, a linear search algorithm can also be used to find the index of the element in the array/list if the element is found.

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Answer: 9,9 miles.

Step-by-step explanation: if he can run 6 miles in 51 minutes, he's running 0,11 miles per minute (calculation down below), therefore in 90 minutes he could run 9,9 miles (0,11.90).

6 mi --- 51

x ---- 1

cross multiplication,

51x = 6

x=6/51

x=0,11

If he runs 0,11 miles in 1 minute, in 90 minutes he'll do

0,11 --- 1

x ---- 90

x= 0,11 . 90

x= 9,9

Answer: 200 pairs

Step-by-step explanation:

The store made a profit of $9,000 - $5,000 = $4,000.

Since they made a profit of $20 per pair of sunglasses, we can divide the total profit by $20 per pair to find out how many pairs of sunglasses were involved.

So, the number of pairs of sunglasses is $4,000 / $20 = 200 pairs.

The value of the other number is 504

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

LCM 1512 and HCF 36 , a number is 108

Represent the other number with x

So, we have the following representation

1512 * 36 = 108 * x

Evaluate

x = 504

Hence, the other number i 504

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Answer:

583,200

Step-by-step explanation:

Hope it helps! =D

Answer:

583200

Step-by-step explanation:

The standard deviation is 71.

To find the standard deviation, first calculate the mean which is the sum of all the observations divided by the total number of observations.

Data is, 20, 40, 31, 7, 15, 29, 25, 20, 17, 32, 28, 12, 34, 29, 20, 17, 33, 23.

Total number of observations are, 18.

Sum of observations, 20+40+31+7+15+29+25+20+17+32+28+12+34+29+20+17+33+23 = 432

Mean = sum of observations/total number of observations

Mean = 432/18

Mean = 24

Standard deviation = [tex]\sigma = \sqrt{\dfrac{(\sum x_i-\mu)^2}{N}}[/tex].

Where, μ is the Mean of the observations.

N is total number of observations.

[tex]x_i[/tex]  is the ith observation.

σ = {(20-24)^2+(40-24)^2+(31-24)^2+(7-24)^2+(15-24)^2+(29-24)^2+(25-24)^2+(20-24)^2+(17-24)^2+(32-24)^2+(28-24)^2+(12-24)^2+(34-24)^2+(29-24)^2+(20-24)^2+(17-24)^2+(33-24)^2+(23-24)^2}/18

σ = {1278}/18

σ = 71

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Answer:

Step-by-step explanation

The probability that the sample proportion will be within +/- .02 of the population proportion for a sample of 1600 households is 0.9945.

a. To calculate σ(p), the standard error of the proportion of households spending more than $100 per week on groceries, we can use the following formula:

Where p is the population proportion and n is the sample size.

In this case, p = .17 and n = 800, so the standard error of the proportion of households spending more than $100 per week on groceries is σ(p) = 0.0126.b.

To calculate the probability that the sample proportion will be within +/- .02 of the population proportion, we can use the following formula:

P(|p – p0| ≤ δ) = 1 – 2α

Where p is the population proportion, p0 is the sample proportion, δ is the margin of error, and α is the level of significance (which is usually set to 0.05).

In this case, p = .17, p0 = .17, δ = .02, and α = 0.05, so the probability that the sample proportion will be within +/- .02 of the population proportion is 0.9000.c. To calculate the probability that the sample proportion will be within +/- .02 of the population proportion for a sample of 1600 households, we can use the same formula as above, but with n = 1600.

In this case, p = .17, p0 = .17, δ = .02, and α = 0.05, so the probability that the sample proportion will be within +/- .02 of the population proportion for a sample of 1600 households is 0.9945.

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Answer:

Step-by-step explanation:

A = B⋅H/2

Base = 10 m

Height = 12m

10⋅12= 120

120/2=60²

Completing the square is a strategy that is sometimes required to complete a quadratic equation, the steps and provide an example as to how it can be used are:

Writing a quadratic expression so that it contains the perfect square is known as "completing the square" in algebra. In plain English, the act of "completing the square" can be described as taking the quadratic equation "ax2 + bx + c = 0" and changing it to "a(x + p)2 + q = 0."

Example: expression is x2 - 7x.

A = 1; B = -7 when the above expression is compared to ax2 + bx + c.

The term that needs to be added, according to the formula, to convert the given expression into a perfect square trinomial is (b/2a)2 = (-7/2(1))2 = 49/4.

The term that needs to be added to make the given expression a perfect square trinomial, then, from both approaches, is 49/4.

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Answer:

The place value of 1 = 1 * 1,000 = 1,000

The place value of 2 = 2 * 100 = 200

The place value of 3 = 3 * 10 = 30

The place value of 0 = 0 * 1 = 0

. (Decimal Point)

The place value of 3 = 3 * 1/10 = 3/10 = 0.3

The place value of 4 = 4 * 1/100 = 4/100 = 0.04

Answer:

To find out how much mixture is needed for each cupcake, we can divide the total amount of mixture (4 kg) by the number of cupcakes (244).

4 kg / 244 cupcakes = 16.393 g/cupcake

To find out how much milk is needed for each cupcake, we can divide the total amount of milk (366 ml) by the number of cupcakes (244).

366 ml / 244 cupcakes = 1.496 ml/cupcake

So, for each cupcake we need 16.393g of mixture and 1.496ml of milk

Step-by-step explanation:

Answer:

x = -3 & 3

Step-by-step explanation:

∣5xI = 15

divide both sides by 5:

(∣5xI)/5 = 15/5

∣xI = 3

I-3I = 3 AND I3I = 3

so:

x = -3 & 3

V is a vector space with the operations of addition and scalar multiplication.

Since f(t) and g(t) are real numbers, you're utilizing the fact that the real numbers themselves are commutative in that step, which truly confused me when I first learned about it and after.

Let V denote the set of all differentiable real-valued functions defined on the real line.

You only need to mention that real-number addition is commutative. Since f is not a number until you evaluate, you couldn't do it before you did.

On a different note, you cannot say that

f+g=f(t)+g(t)

but you can say that (f+g)(t)=f(t)+g(t)

So  V is a vector space with the operations of addition and scalar multiplication.

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Answer:

3 * 8 = 42, divide that by 38, then put it inside the cool looking v sign, and that will give you 89 weed leaves left as trim. Take the 21 add that with the divisor of the previous problem, then you get 25 PLUS the breadsticks, and you get 96. Last step is 96 - 29 = how much bud is left to smoke!

Hope this helped!  

Answer:

12 feet

Step-by-step explanation:

This example can be solved using a proportion. The ratio between the height of the girl and her shadow is equal to the ratio of the height of the tree and its shadow.

Ratio of girl height to shadow length: [tex]\frac{3}{7}[/tex]

Ratio of the tree height and its shadow: [tex]\frac{x}{28}[/tex]

The proportion can be written: [tex]\frac{3}{7}=\frac{x}{28}[/tex]

The relationship between the denominators happens to be obvious, so this can be solved easily. 7 times 4 is 28, and since the ratios are equal, 3 times 4 must be X.

[tex]3\times4=12\\x=12[/tex]

The tree is 12 feet tall!

The equation of the line in slope0intercept form is y = (4/3)x - 5 and the blue line satisfies it.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, Are four lines and we have to determine which line represents the equation - 3y = 15 - 4x.

In slope-intercept form, it is,

y = (4/3)x - 5.

Now, when x is 3, y = - 1 we have t observe the lines here and the blue line satisfies it.

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Answer:

26 is the distance

Step-by-step explanation:

-16 to 10 has a distance of 26

The quotient after the long division of the expression is 2x² +8x -3.

Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too.

The long division method will be done as below,

x - 3 ) 2x³ + 2x² -27x + 2( 2x² +8x -3

        -2x³ +6x²

      ________________

                8x² - 27x + 2

               -8x² +24x

     _________________

                       -3x + 2

                       3x - 9

______________________

                             -7

Hence, the quotient after the long division of the expression is 2x² +8x -3 and the remainder is -7.

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The volume of the cone is 36π * 2√(34).

The formula for the lateral surface area of a right circular cone is:

A = π * r * l

where A is the lateral surface area, π is the constant pi, r is the radius of the base, and l is the slant height of the cone.

Given that the lateral surface area of the cone is 12√(34) * π, we can write:

[tex]12\sqrt{(34)} * \Pi = \Pi * r * l[/tex]

Dividing both sides by π and r, we can find the slant height:

l = 12√(34) / r

= 12√(34) / 6

= 2√(34) units

The volume of a right circular cone can be found using the formula:

V = (1/3) * π * r^2 * h

where V is the volume,

π is the constant pi,

r is the radius of the base, and

h is the height of the cone.

Since the cone is a right circular cone, the slant height is also the height of the cone,

So we can substitute l for h:

V = (1/3) * π * r^2 * l

= (1/3) * π * 6^2 * 2√(34)

= 36π * 2√(34)

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