In a set of normally distributed test scores that have a mean of 100 and standard deviation of 15, it would be correct to conclude that approximately 68 percent of the scores would fall between _____ and _____.

Answer:

y = (-11/12)x - 3

Step-by-step explanation:

Recall that for a linear equation in the form y = mx + b,

m = slope and b = y-intercept.

hence to satisfy parts (a) and (b) of the questions, we need to extract the y-intercept from the equation in part (a) and the slope from part (b)

For part (a)

given: y+7x+3=0  (rearrange this to get slope-intercept form)

y+7x+3=0 (subtract 3 from both sides)

y + 7x = -3  (subtract 7x from both sides)

y = -7x - 3

we can see that the y-intercept is -3.

For part (b)

given: -11x -12y=-7  (rearrange this to get slope-intercept form)

-11x -12y=-7  (add 11x toboth sides)

-12y = 11x - 7  (divide both sides by -12)

y = (-11/12) - (7/12)

we can see that the slope is (-11/12).

combining the y-intercept from part (a) and the slope from part (b) into the general equation given in the first line above,

y = (-11/12)x - 3 (answer)

Answer:

Convenience  Sampling

Step-by-step explanation:

The given situation indicates the non-probability sampling because the sampling units are not selected at random and every unit in population has unequal chance of being selected. Convenience sampling is a type of non-probability sampling in which the sampling unit close to interviewer are selected. In the situation statistics student interviews the individual that resides in his building, so it is a convenience sampling.

Final answer:

The statistics student used convenience sampling, a non-probability method, by interviewing individuals in his apartment building to determine cell phone ownership. This method is subject to sampling bias and does not provide generalizable results.

Explanation:

The type of sampling used in the scenario where a statistics student interviews everyone in his apartment building to determine who owns a cell phone is called convenience sampling. This non-probability sampling method involves choosing participants because they are convenient to the researcher, not because they are randomly selected or necessarily representative of the larger population. Therefore, while it is easy and cost-effective, the results of convenience sampling cannot be reliably generalized to the wider population due to potential sampling bias.

Based on the provided conditional statements, if Trisha is drinking water, then it's dinnertime. Additionally, if it's dinnertime, then Anna is drinking iced tea. Given that Trisha is drinking water, we can conclude that Anna is drinking iced tea.

The question here is dealing with conditional statements in logic. It's important to understand that if a conditional statement is true, and the first part (the condition) is true, then the second part must be true as well. In this case, Statement A states that if Trisha is drinking water, then it is dinnertime. So, if Trisha is drinking water (which is confirmed by Statement E), then it is dinnertime.

Statement C further adds to our understanding by stating that if it is dinnertime, then Anna is drinking iced tea and nothing else. Since based on Statements A and E, we know it is dinnertime, then following the logic from Statement C, we can conclude that Anna is drinking iced tea.

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Answer:

$1 coin is 23

$2 coin is 14

Step-by-step explanation:

We need to form mathematical equations that we can solve from this Long citation.

Firstly, let the numbers of $1 coins be a and that of $2 be b.

We know that there are 37 coins. Hence

a + b = 37

Now, total is 51 Canadian dollars.

a + 2b = 51

Let’s now solve this simultaneously

From 2 , a + b + b = 51

Let’s say this is 3. Now substitute 1 into 3.

37 + b = 51, b = 51 - 37 = 14

Since a + b = 37

a = 37 - 14 = 23

Answer:

The answer to your question is  0.83 or 83%

Step-by-step explanation:

Data

5 red marbles

10 blue marbles

14 yellow marbles

Process

1.- Calculate the total amount of marbles

    Total amount = 5 red + 10 blue + 14 yellow

     Total amount = 29 marbles

2.- Calculate the amount of marbles that are not red

     No red marbles = 10 + 14

                                = 24 marbles

3.- Calculate the probability

Probability of not pulling a red marble = [tex]\frac{no red marble}{total amount of marbles}[/tex]

Probability of not pulling a red marble = [tex]\frac{24}{29} = 0.83 or 83%[/tex]

As n goes onto infinity, the expression [tex]\frac{3n^5}{4n^5+1}[/tex] will approach [tex]\frac{3}{4}[/tex]. Note the 3 and 4 come from the leading coefficients of the numerator and denominator respectively. This only works because the degrees for the numerator and denominator are both the same (both are 5).

Since [tex]\frac{3n^5}{4n^5+1}[/tex] is not approaching 0 when n gets really large, adding on successive terms of these values will have the infinite sum diverge. After some very large n, we are effectively adding on 3/4 each time and that just makes the overall sum keep growing forever.

Final answer:

The limit of an infinite series depends on whether it converges or diverges. If it converges, the limit is the value the series approaches as the number of terms approaches infinity. If it diverges, it does not have a finite limit.

Explanation:

The limit of the infinite series depends on the specific series being referred to. To find the limit of an infinite series, you need to determine if it converges or diverges. If the series converges, then the limit is the value that the series approaches as the number of terms goes to infinity. If the series diverges, then it does not have a finite limit.

For example, consider the series 1/2 + 1/4 + 1/8 + ... This is a geometric series with a common ratio of 1/2. It converges to the value of 1, so the limit of this series is 1.

Some various tests and properties can be used to determine if a series converges or diverges. Some common ones include the ratio test, the root test, and the comparison test.

Answer:they would meet at 1 pm

Step-by-step explanation:

The distance between Quebec City and New York City is 520 miles.

At the point where Kate and Will meet, they would have travelled 520 miles.

Let t represent the time it takes Kate to travel a certain distance before they met.

Distance = speed × time

If Kate drives at 55mph, the distance covered would be

55 × t = 55t.will drives at 75 mph

Since Will left same that that Kate left, distance travelled by Will in t hours would be

75 × t = 75t

Since the total distance covered is 520 miles, it means that

55t +75t = 520

130t = 520

t = 520/130 = 4

9 am + 4 hours = 1 pm

Answer:

  1 pm

Step-by-step explanation:

Their combined speed is 55 + 75 = 130 miles per hour. That is the rate at which the distance between them is decreasing. The time it takes for the distance between them to become zero is found from the relation ...

  time = distance/speed

  time = (520 mi)/(130 mi/h) = 4 h

4 hours after 9 am, Kate and Will will meet. That time is 1 pm.

Answer:

i think it is 18 or something

Step-by-step explanation:

Answer:

Side length B is 17.

Step-by-step explanation:

Use the Pythagorean Theorem a^2 + b^2 = c^2. if one of the legs is 8, and another is 15, the hypotenuse will be 17.

Answer:

  D:  2/4

Step-by-step explanation:

Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:

  BC : CD = 2 : 2 = 1 : 1

Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.

__

None of the segments is 3 units long, so neither of answer choices A or B makes any sense.

While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.

There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.

Answer:

B

Step-by-step explanation:

x>4

Answer:

None of the options are right. The correct answer is x < 4

Step-by-step explanation:

2(x + 1) > 3x - 2

2x + 2 > 3x - 2

2 > x - 2

4 > x

x < 4

Answer: avoid passing through the vein.

Step-by-step explanation:

Answer:

Rational Numbers

−17.6 (-176/10)

81

13/14

Rational Numbers

15π

square root −29

Step-by-step explanation:

Rational Numbers are those numbers which can be written as Ratio of two numbers.

Irrationational Numbers are those which cannot be written as ratio of two numbers. such as recurring numbers.

e.g 0.26262626.........

Answer:

There were 15 students in van and 51 students in the bus.

Step-by-step explanation:

Let the number of students in each van be 'x'.

Let the number of students in each bus be 'y'.

Given:

For High School A

number of vans = 11

Number of buses =9

Number of students = 624

now we can say that;

Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.

framing in equation form we get;

[tex]11x+9y = 624 \ \ \ \ equation\ 1[/tex]

For High School B

number of vans = 5

Number of buses = 1

Number of students = 126

now we can say that;

Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.

framing in equation form we get;

[tex]5x+y = 126 \ \ \ \ equation\ 2[/tex]

On solving both equation we will get the number of students in vans and buses.

First we will multiply equation 2 by 9 we get;

[tex]9(5x+y)=126\times 9\\\\45x+9y = 1134 \ \ \ \ equation\ 3[/tex]

Now Subtracting equation 2 from equation 1 we get;

[tex]45x+9y-(11x+9y)=1134-624\\\\45x+9y-11x-9y = 510\\\\34x=510[/tex]

Now dividing both side by 34 we get;

[tex]\frac{34x}{34}=\frac{510}{34}\\\\x= 15[/tex]

Now we will substitute the value of 'x' in equation 2 we get;

[tex]5x+y=126\\\\5\times15+y=126\\\\75+y =126\\\\y=126-75 = 51[/tex]

Hence There were 15 students in van and 51 students in the bus.

Answer:

The answer to your question is 32.64°

Step-by-step explanation:

Data

hypotenuse = 19

adjacent side = 16

x = ?

Process

1.- To solve this problem use trigonometric functions.

The function that relates the adjacent side and the hypotenuse is cosine.

      cos x = [tex]\frac{adjacent side}{hypotenuse}[/tex]

2.- Substitution

      cos x = [tex]\frac{16}{19}[/tex]

3.- cos x = 0.842

4.- cos ⁻¹x = x = 32.64°

Answer:

Option (b) 10 to 20

Step-by-step explanation:

Let the number obtained between the interval be 'x'

Therefore,

according to the question:

multiplying the number with 4 and then adding 8 to it to get 60

thus,

mathematically, we get

4x + 8 = 60

or

4x = 60 - 8

or

4x = 52

or

x = 13

Hence,

The 13 lies between the interval 10 to 20

Option (b) 10 to 20

Answer:

Recursive formula for geometric sequence

[tex]a_{n}=a_{n-1}\times r[/tex]

is [tex]a_{n}=a_{n-1}\times 6[/tex]

and explicit formula for geometric sequence [tex]a_{n}=a_{1}^{r-1}[/tex] is

[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]

Step-by-step explanation:

Given sequence is [tex]\frac{1}{2},3,18,108,648,...[/tex]

To find the recursive and explicit formula for this sequence:

Let [tex]a_{1}=\frac{1}{2},a_{2}=3,a_{3}=18,a_{4}=108,a_{5}=648,...[/tex]

To find the common ratio r:

[tex]r=\frac{a_{2}}{a_{1}}[/tex]

[tex]=\frac{3}{\frac{1}{2}}[/tex]

[tex]=3\times 2[/tex]

[tex]=6[/tex]

Therefore r=6

[tex]r=\frac{a_{3}}{a_{2}}[/tex]

[tex]=\frac{18}{3}[/tex]

[tex]=6[/tex]

Therefore r=6

Therefore the common ration r=6

Therefore the given sequence is geometric sequence

Recursive formula for geometric sequence is [tex]a_{n}=a_{n-1}\times r[/tex]

[tex]a_{n}=a_{n-1}\times 6[/tex]

and explicit formula is [tex]a_{n}=a_{1}^{r-1}[/tex]

[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]

[tex]=(\frac{1}{2})^{5}[/tex]

[tex]=\frac{1}{32}[/tex]

Therefore [tex]a_{n}=\frac{1}{32}[/tex]

Answer:

Recursive: a(n) = 6a(n-1)

Explicit: a(n) = (6^n)/12

Step-by-step explanation:

3 = 6 × ½

18 = 6 × 3

.

.

.

Recursive formula:

a(n) = 6a(n-1)

Explicit:

a(n) = a × r^(n-1)

a(n) = ½ × 6^(n-1)

a(n) = (6^n)/12

Answer:

The amount  we need to invest is 500 muggle money.

Step-by-step explanation:

Amount needle to study at Hogwarts = A = 800 muggle money

Principle amount that we need to invest = P

Duration of investment = T = 5 years

Rate if simple interest = R = 12%

Simple interest =  S.I

A = S.I + P

[tex]800=\frac{P\times 12\times 5}{100}+P[/tex]

[tex]800=0.6P+P[/tex]

[tex]800=1.6P[/tex]

P = [tex]\frac{800}{1.6}=500[/tex]

The amount  we need to invest is 500 muggle money.

Answer:

b. {-9, 3}.

Step-by-step explanation:

x^2 + 6x - 27 = 0

We need 2 numbers whose product is -27 and whose sum is + 6.

These are + 9 and - 3. So the factors are:

(x - 3)(x + 9) = 0

(x - 3) = 0 or (x + 9) = 0

x = 3 or -9.

Answer: option b is the correct answer.

Step-by-step explanation:

The given quadratic equation is expressed as

x^2+6x-27=0

In order to solve the equation by factorization, the first step is to find two numbers such that their sum or difference is 6x and their product is

- 27x^2. The two numbers are 9x and - 3x. Therefore,

x^2 + 9x - 3x - 27 = 0

x(x + 9) - 3(x + 9) = 0

x - 3 = 0 or x + 9 = 0

x = 3 or x = - 9

Answer:

D

Step-by-step explanation:

[-2(x-6)] / [(x+4)(x-4)]

To simplify the given expression, we can break it down into fractions and multiply them together step by step.

The given expression is quite complex, but we can simplify it step by step. Let's break it down:

By following these steps, we have simplified the given expression.

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Answer:

{(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)

Step-by-step explanation:

Sample space is the set of all possible outcomes of an experiment.

Here a person should choose one meal and a hot drink. Hence, each element in the set includes one meal and one beverage, which eliminates 2,because it indicates person choses oatmeal and pancakes which has no beverage. Sets should have elements in pairs so ,We should eliminate 3 ,4,5.

As a result person can choose

oatmeal as  meal and coffee as drink

oatmeal as meal and tea for drink

eggs for meal tea for drink

eggs for meal coffee for drink

pancakes for meal tea for drink finally

pancakes for meal and coffee for drink

The sample space of a distribution is the list of possible options.

The sample space for the meal and the beverage is (a) {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)

From the question, the meals are:

Meals: Oatmeal, Eggs, Pancakes

And the beverages are:

Beverages: Coffee, Tea

This means that, the available selections are:

Hence, the sample space is (a)

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Answer:

A

Step-by-step explanation:

The normal probability has two parameters mean and standard deviation. Every normal probability distribution can become a standard normal probability distribution when mean is zero and standard deviation is 1. This means that standard normal probability distribution centers at 0 and the spread about the mean is 1.

Profit function= 81q +18300+0.00029q2+0.0716q-557

Step-by-step explanation:A profit function shows the relationship between a company's total profit and output.

The profit function is equal to the company's total rebenue(TR) minus total cost of the company(TC).

Mahemathically,Profit = TR-TC.

Let D(q)= TC=-0.00039q2-0.0716q+557C(q)

Let TR= 81q +18300.

Profit=TR-TC

Profit =81q+18300-(-0.00029q2-0.0716q+557)

Profit=81q+18300+0.00029q2+0.0716q-557.

Answer:

10in²

Step-by-step explanation:

5π/4 is 62.5% of a circle if you look at the unit circle.

So just find the area of a circle and take 62.5% of it.

A = πr²

A = π(4)²

A = 16π

16π(.625) = 10

Answer:the speed of the barge in still water is 11 mph

the speed of the current is 3 mph

Step-by-step explanation:

Let x represent the speed of the barge in still water.

Let y represent the speed of the current.

Traveling upstream on the Mississippi River, the barge travels 56 mi in 7 h. This is against the water current. It means that the total speed of the barge would be

x - y mph

Distance = speed × time

Therefore,

56 = 7(x - y)

8 = x - y - - - - - - - - - - - -1

Downstream, it travels the same distance in 4 h. This is in the same direction with the water current. It means that the total speed of the barge would be

x + y mph

Therefore,

56 = 4(x + y)

14 = x + y - - - - - - - - - - - -2

Adding equation 1 and equation 2, it becomes

22 = 2x

x = 22/2 = 11

Substituting x = 11 into equation 2, it becomes

14 = 11 + y

y = 14 - 11 = 3

Answer:

Cookie monster needs to steal at least 6 cookies more.

Step-by-step explanation:

Given:

Number of cookies already stole = 4

Total number of cookies he wants to steal [tex]\geq 10[/tex]

We need to find how many cookie he needs to steal more.

Solution:

Let number of cookies he needs to steal more be 'x'.

Now we can say that;

Number of cookies already stole plus number of cookies he needs to steal more should be greater than or equal to Total number of cookies he wants to steal

framing in equation form we get;

[tex]4+x\geq 10[/tex]

Now using Subtraction property of Inequality we will subtract both side by 4 we get;

[tex]4+x-4\geq 10-4\\\\x\geq 6[/tex]

Hence Cookie monster needs to steal at least 6 cookies more.

The Cookie Monster needs to steal at least 6 more cookies after getting caught.

The Cookie Monster stole 4 cookies initially before getting caught. If he steals no less than 10 cookies each time, we need to determine how many more cookies he needs to steal. Let's represent the number of cookies he needs to steal as x. The equation to represent this situation is: x >= 10 - 4.

Simplifying the equation, we have x >= 6. Therefore, the Cookie Monster needs to steal at least 6 more cookies after getting caught.

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Answer:

C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.

Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.

Step-by-step explanation:

The sample mean obtained was :

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}= 144.3[/tex]

A. The given value is a parameter parameter for the year year because the data collected represent a population population.

False. The data colected represent a sample of the population of interest, so for this case is not a parameter because we don't have the information about all the population of interest.

B. The given value is a parameter parameter for the year year because the data collected represent a sample sample.

False. First the sample average is not a parameter, and second the population mean is not equal to the sample mean most of the times.

C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.

Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.

D. The given value is a statistic statistic for the year year because the data collected represent a population.

False. If is an statistic can't represent the population, since the parameter represent the population not the statistic.

In this exercise we have to use the knowledge of statistics to be able to identify the correct statement, so I can say that it is:

The letter  C

So knowing the statistics topics we can recognize the true alternative:

A. False. The information in visible form colected show a sample of the inhabitants of a place of interest, so for this case exist not a limit cause we forbiddance bear the facts about all the inhabitants of a place of interest.

B. False. First the sample average exist not a limit, and second the inhabitants of a place mean happen inadequate the average value most of the opportunity.

C. Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.

D. False. If exist an detail of action can't represent the inhabitants of a place, because the limit represent the inhabitants of a place not the detail of action.

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Answer:

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5

Step-by-step explanation:

We calculate the following derivatives. Since these are complex derivatives, we also calculate the formula for complex derivatives. We use  Y for the derivative of y . Therefore, we calculate and we get

(a) d dt y7=7Y^6

(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}

(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5

Answer:

B. Negative 80 x + 28 y minus 56

This is equivalent to -80x + 28y - 56

C. 4 (negative 20 x + 7 y minus 14)

This is equivalent to -80x + 28y - 56

Step-by-step explanation:

Let's find out the options that are equivalent to:

8 (negative 10 x + 3.5 y minus 7)

8 ( - 10x + 3.5y - 7) =

-80x + 28y - 56

Options:

A. Negative 80 x + 24.5 y minus 56

This is not equivalent.

B. Negative 80 x + 28 y minus 56

This is equivalent to -80x + 28y - 56

C. 4 (negative 20 x + 7 y minus 14)

-80x + 28y - 56

This is equivalent to -80x + 28y - 56

D. Negative 4 (negative 20 x + 7 y minus 14)

80x - 28y + 56

This is not equivalent.

Answer:

B. Negative 80 x + 28 y minus 56

This is equivalent to -80x + 28y - 56

C. 4 (negative 20 x + 7 y minus 14)

Step-by-step explanation:

For this case we have the following equation:

[tex]T = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

We must solve the equation for the variable "h":

We subtract [tex]2 \pi * r ^ 2[/tex] from both sides of the equation:

[tex]T-2 \pi * r ^ 2 = 2 \pi * r * h[/tex]

We divide by [tex]2 \pi * r[/tex] on both sides of the equation:

[tex]\frac {T-2 \pi * r ^ 2} {2 \pi * r} = h\\h = \frac {T} {2 \pi * r} - \frac {2 \pi * r ^ 2} {2 \pi * r}\\h = \frac {T} {2 \pi * r} -r[/tex]

Answer:

[tex]h = \frac {T} {2 \pi * r} -r[/tex]

Answer: 1. True

Step-by-step explanation:

Given : D = {x|x is a whole number}  = { 0, 1 , 2, 3, 4, 5, ..................}

E = {x|x is a perfect square between 1 and 9} = {4 }

F = {x|x is an even number greater than or equal to 2 and less than 9} ={4 , 6 , 8}

Since intersection of sets contains all the values they have common.

Then, E ∩ F= {4}

Now , D∩ (E ∩ F) =  { 0, 1 , 2, 3, 4, 5, ..................} ∩ {4} = {4}

Hence , The number 4 is D ∩ (E ∩ F).

Thus , the given statement is 1 . true.