How can you use surveys, experiments and observational studies to make inferences about a population?

Complete question :

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:

a. More than 20 minutes? b. For 20 minutes or less

Answer: 0.0764 ; 0.9236

Step-by-step explanation:

Mean (m) = 15 minutes

Standard deviation (sd) = 3.5

Z - score :

Z = (x - m) / sd

A) more than 20 minutes

P(X > 20) ; x = 20

Z > (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z > 1.429) = 0.5 - P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 - 0.4236 = 0.0764

2) 20 minutes or less :

P(X <= 20) ; x = 20

Z < (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z < 1.429) = 0.5 + P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 + 0.4236 = 0.9236

Answer:

338 minutes

Step-by-step explanation:

Because it takes one hour to travel 55 miles, it should take approximately 5.6 hours to travel 310 miles. Since one hour is equal to 60 minutes, you would multiply 5.6 by 60 to get 338 minutes.

This tells us our interest rate needs to be 4% in order to grow $500 to $1600 in 12 years compounded quarterly.

We will use the compound interest formula to solve for our unknown interest rate. Recall the compound interest formula:

\(A(r) =A(1+\frac{r}{n} )^n^t\) where A(r) is the ending dollar amount, A is the starting amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

We know that:

A(r) = 1,600

A = 500

n = 4

t = 12

and our r is unknown.

Using our formula gives us:

\(1600 = 500(1+\frac{r}{4} )^4^.^1^2\)

\(1600 = 500(1+\frac{r}{4} )^4^8\)

Next, we will divide by 500:

\(3.5=(1+\frac{r}{4} )^4^8\)

ln of both sides

In 3.5 = In \((1+\frac{r}{4} )^4^8\)

0.54406804435 = 48  In \((1+\frac{r}{4} )\)

0.0113 = ln (1+r/4)

raise to e power

1.0114 = r/4

4.0456 = r

r = 404.56%

This tells us our interest rate needs to be 4% in order to grow $500 to $1600 in 12 years compounded quarterly.

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Answer:

7+1.25m=t

Step-by-step explanation:

The equation that represents the weight of the baby will be W = 1.25 t + 7.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A child was brought into the world with a load of 7 pounds and afterward started to acquire 1.25 pounds each month.

Let 'W' be the weight of the baby and 't' be the number of months. Then the equation is given as,

W = 1.25 t + 7

The equation that represents the weight of the baby will be W = 1.25 t + 7.

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The positive value of tan(1/2)y, with cos y = 8/9, can be expressed as √(1 + cos y) / √(1 - cos y), which simplifies to √(17 + 8√7) / √(17 - 8√7).

We are given that cos y = 8/9. The half-angle identity for tangent states that tan(1/2)y = ±√((1 - cos y) / (1 + cos y)). Since we are looking for the positive value, we can ignore the negative sign. Plugging in the given value of cos y, we have tan(1/2)y = √((1 - 8/9) / (1 + 8/9)).

To simplify the expression, we rationalize the denominators by multiplying both the numerator and denominator by the conjugate of each. Multiplying the numerator and denominator by √(1 + cos y) results in √((1 - cos y) * (1 + cos y)) / √((1 + cos y) * (1 - cos y)). Simplifying further, we get √((1 - \((8/9)^2\)) / (1 - \((8/9)^2\))).

Now, substituting the given value of cos y = 8/9, we have √((1 - \((8/9)^2\)) / (1 - \((8/9)^2\))) = √((1 - 64/81) / (1 - 64/81)) = √((17/81) / (17/81)). Simplifying the expression gives us the final answer as √(17 + 8√7) / √(17 - 8√7), which is the positive value of tan(1/2)y with a rational denominator.

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Answer:

Step-by-step explanation:

it is 2x

Its a triangle

\(\\ \sf\longmapsto Perimeter=31+18+25\)

\(\\ \sf\longmapsto Perimeter=48+25\)

\(\\ \sf\longmapsto Perimeter=73cm\)

Its rectangle

\(\\ \sf\longmapsto Perimeter=2(L+B)\)

\(\\ \sf\longmapsto Perimeter=2(15+10)\)

\(\\ \sf\longmapsto Perimeter=2(25)\)

\(\\ \sf\longmapsto Perimeter=50ft\)

Answer:

a and c

Step-by-step explanation:

The perimeter is the sum of the 3 sides, that is

perimeter = 25 + 18 + 31 = 74 cm → a

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

The opposite sides of a rectangle are equal, so

perimeter = (2 × 10) + (2× 15) = 20 + 30 = 50 ft → c

The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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There is 4 condition will the design have for this study.

Given,

A biologist was interested in studying the snapper turtles' bite holding periods. He timed how long it took snapping turtles to release a piece of wood after they had bit it by dragging it behind them on a rope. The turtles ranged in age from one hour to one day, week to month.

We have to find the number of conditions will the design have for this study;

There is 4 condition will the design have for this study.

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Answer:

16 is the mean

Step-by-step explanation:

I gave you the answer, no problem..

Density of fresh egg = 1.2 g/cm³.

Density of spoiled egg = Density of fresh egg   - 0.3 g/cm³.

Density of spoiled egg =( 1.2 - 0.3 ) g/cm³ = 0.9 g/cm³.

Now, it is given that any object with density less than 1 g/cm³ will float on water.

To tell whether an egg is spoiled or not using water. We should drop egg in water if it float then it is spoiled else it is fresh.

Hence, this is the required solution.

Answer:

y= -4x                                                                                                                                                                                      

Step-by-step explanation:

hope this helps and lmk if you need anything!

Answer: X= (130+46+102) = 82

Step-by-step explanation:

If the surface area of the larger pyramid is 56 cm², the  of the smaller pyramid is approximately 42.7 cm².

To solve this problem, we can use the fact that the surface area of a pyramid is proportional to the square of its scale factor (ratio of corresponding side lengths) and the base area is proportional to the square of its scale factor.

Let the scale factor between the larger and smaller pyramid be x. Then, we have:

x² = 16/12.2
x = sqrt(16/12.2) = 1.143

This means that the corresponding side lengths of the smaller pyramid are 1.143 times smaller than those of the larger pyramid.

The surface area of the smaller pyramid can be found using:

(surface area of larger pyramid) / (base area of larger pyramid) = (surface area of smaller pyramid) / (base area of smaller pyramid)

56/16 = (surface area of smaller pyramid) / 12.2
(surface area of smaller pyramid) = 56/16 * 12.2 = 42.7

Therefore, the surface area of the smaller pyramid is approximately 42.7 cm².

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Their boss should promote and facilitate open communication and understanding between Yan and Tracy to foster a more inclusive and collaborative work environment.

In a diverse workplace, it is crucial for the boss to encourage inclusivity and bridge the gap between individuals with different world views. By promoting open communication and understanding, the boss can create opportunities for Yan and Tracy to learn from each other and gain a broader perspective.

This can be achieved through team-building exercises, diversity training, or creating a supportive space for discussions on cultural differences. The goal is to foster a work environment where individuals feel comfortable expressing their views, learning from others, and working together towards common goals. By addressing the perceived distance between Yan and Tracy, the boss can help create a more inclusive and harmonious work atmosphere.

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There are 5 elements in 32 proper subsets.

What are subsets?

If every element of set A is also an element of set B, then set B is a superset of set A, and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Here, we have

Given:  32 proper subsets.

We have to find how many elements are in 32 proper subsets.

Subsets of a set having n elements = 2^n

2ⁿ = 32

n = 5

Hence, there are 5 elements in 32 proper subsets.

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The triangle with given vertices is not an isosceles triangle.

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].

Let a triangle with vertices be A(-1 ,7), B(5, 5) and C(-2 ,1).

Using the coordinates A(-1, 7) and B(5, 5), we get

AB =√(5-7)²+(5+1)²

AB=√40

AB=2√10 units

Using the coordinates B(5, 5) and C(-2 ,1) we get

BC=√(-2-5)²+(1-5)²

BC=√65 units

Using the coordinates C(-2 ,1) and A(-1 ,7) we get

BC=√(-1+1)²+(7-1)²

BC= 6 units

Therefore, the triangle with given vertices is not an isosceles triangle.

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Answer:

q

Step-by-step explanation:

Answer:

please upload a picture of your question

The stem-and-leaf display of the data is

Stem | Leaves

1 | 2

2 | 2

3 | 3

4 | 5, 8

To start, let's assume we have a set of data values, such as 12, 22, 33, 45, 48, 53, 61, 62, 72, 83, 91, 96, 99.

The stem-and-leaf display consists of two parts: the "stem" and the "leaf." The stem represents the leading digit(s) of the data values, and the leaf represents the trailing digit(s). For example, the number 12 has a stem of 1 and a leaf of 2.

Now, let's organize the data values into their corresponding stems:

Stem 1: 12

Stem 2: 22

Stem 3: 33

Stem 4: 45, 48

Next, we list the leaves corresponding to each stem. The leaves are listed in ascending order next to their respective stems:

Stem 1: 2

Stem 2: 2

Stem 3: 3

Stem 4: 5, 8

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Answer:  34/105

Step-by-step explanation: The idea here is that the fractional parts of the circle graph will all add up to 1 exactly, but the blue segment represents an unknown fraction.

So, this is an exercise in adding fractions with different denominators to get the total known area and then finding the difference between 1 and that known area.

We cannot directly add fractions with different denominators.

To add 1/7 and 1/5 and 1/3, we need to find the least common denominator (LCD) and then express all three numbers in terms of that denominator. In other words, we want a whole number that is evenly divisible by 7, by 3, and by 5 and we want the smallest number for which that is true.

If we multiply all three numbers together, we get 7*5*3 = 105.

That is the LCD. It divides by all 3 numbers (7, 5, 3) and no smaller number will do.

Tan Segment - To take the denominator of 7 and get 105, we multiply by 5*3 = 15, so we do that to both the numerator and denominator of the fraction. We have 1 * 5*3 = 15 on top and 7 * 5*3 = 105 on the bottom, to get the fraction ---> 15/105

Orange Segment - To take the denominator of 5 and get 105, we multiply by 7*3 = 21, so we do that to both the numerator and denominator of the fraction. We have 1 * 7*3 = 21 on top and 5 * 7*3 = 105 on the bottom, to get the fraction ---> 21/105

Purple Segment - To take the denominator of 3 and get 105, we multiply by 7*5 = 35, so we do that to both the numerator and denominator of the fraction. We have 1 * 7*5 = 35 on top and 3 * 7*5* = 105 on the bottom, to get the fraction ---> 35/105

We add the known areas:  15/105 + 21/105 + 35/105 = 71/105

Now we need the Blue Segment:

1 - 71/105 = 105/105 - 71/105 = (105- 71)/105 = 34/105

Since 34 does not divide by any of the three factors of the denominator (3, 5, and 7) the answer cannot be reduced further.

The blue segment area is 34/105

I hope this helps.

The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

The mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. To find the MAD, you need to follow these steps:

1. Calculate the mean of the dataset by adding up all the numbers and dividing the sum by the total number of data points. In this case, the dataset consists of the following numbers: 3, 6, 3.8, 3.2, and 3.4. Adding them up gives us a sum of 19.4. Dividing this sum by 5 (since there are 5 data points) gives us a mean of 3.88.

2. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value. For example, for the first data point, 3, the absolute deviation would be |3 - 3.88| = 0.88. Repeat this step for all the data points.

3. Calculate the mean of the absolute deviations by adding up all the absolute deviations and dividing the sum by the total number of data points. In this case, the absolute deviations are: 0.88, 2.12, 0.72, 0.68, and 0.58. Adding them up gives us a sum of 4.98. Dividing this sum by 5 gives us a mean of 0.996.

So, the mean absolute deviation for the given dataset is approximately 0.996.


The mean absolute deviation helps us understand how much each data point varies from the mean of the dataset. By calculating the absolute deviation for each data point and finding the average, we can determine the typical amount of variation in the dataset.


The mean absolute deviation for the given dataset of 3, 6, 3.8, 3.2, and 3.4 is approximately 0.996. This means that, on average, each data point in the dataset deviates from the mean by approximately 0.996.

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Answer

62

5.3

65

5.8

2.5

Step-by-step explanation:

FOr the first one we have the opposite and adjacent side, so we'll use TOA

let x= angle

tan(x)=4.7/2.5

x=61.99 or 62

2.) for this one we can just use pathagoryeous thereom

2.5²+4.7²=c²

28.34=c²

c=5.323

3.) For this one we know that the angles in a traingle must add to 180

let x= missing angle

25+90+x=180

x=65

4.) For this one we have the adjacent side but need the hypotonouse

we will therefore use CAH

cos(25)=5.3/x

5.3/(cos(25))=x

x=5.8

5.) For this one we will just use the pathagoryeous to solve for the missing side

a²+5.3²=5.8²

a²=6.107

a=2.5

Answer:

50:1

Step-by-step explanation:

Tbh i guessed just try it

Answer:

5 : 6

Step-by-step explanation:

The quantities must have the same units

4 minutes = 4 × 60 = 240 seconds , then

200 s : 4 m

= 200 s : 240 s ( divide both parts by 40 )

= 5 : 6 ← in simplest form

Answer:

Here it is!

Step-by-step explanation:

I graphed it. The second one is just to show the points.

The points are (0,-6) and (-1/2,0)

Brainly pls!

Answer:

476637/1000 or 476.637

Step-by-step explanation:

See attachment below

Answer:

9/8 is greater

Step-by-step explanation:

9/8 is 1.125

11/12 is 0.916