Lloyd's Cereal company packages cereal in 1 pound boxes (16 ounces). A sample of 16 boxes is selected at random from the production line every hour, and if the average weight is less than 15 ounces, the machine is adjusted to increase the amount of cereal dispensed. If the mean for 1 hour is 1 pound and the standard deviation is 0.1 pound, what is the probability that the amount dispensed per box will have to be increased?

Answer:

Step-by-step explanation:

h(t)=160t-16t^2=-16(t²-10t+25-25)

=-16(t-5)²+400

max. height reached=400 ft

Answer:

The maximum height 400 feet is attained at t = 5 seconds.

Step-by-step explanation:

All powers of [tex]t[/tex] in the equation for [tex]h(t)[/tex] are integers that are greater than or equal to zero. Additionally, the greatest power of [tex]t[/tex] is two. Hence, [tex]h(t)[/tex] is a quadratic equation about [tex]t[/tex].

In this case,

The question is asking for the maximum value of this equation. Start by finding the [tex]t[/tex] (time) that would maximize the value of the polynomial.

The graph of a quadratic equation looks like a parabola. Additionally, since the coefficient of [tex]t^2[/tex] is less than zero, the parabola opens downward. The maximum value of the parabola would be at its vertex. Additionally, at the vertex,

[tex]\displaystyle t = -\frac{b}{2a} = -\frac{160}{2 \times (-16)} = \frac{160}{32} = 5[/tex].

In other words, the rocket is at its maximum height when time is equal to 5 seconds.

To find that height, let [tex]t = 5[/tex] and evaluate [tex]h(t) = 160 \, t - 16\, t^2[/tex]:

[tex]160\, t - 16\, t^2 = 160 \times 5 - 16 \times 5^2 = 400[/tex].

That is: the maximum height of the rocket would be 400 feet.

Answer:

  1000

Step-by-step explanation:

Each value of the first digit can be paired with any value of the second digit, so there are 10×10 = 100 possible pairs of the first two digits. Each of those can be combined with any third digit to give a total of ...

  10×10×10 = 1000

possible combinations.

Final answer:

A combination lock with a 3-digit code where each digit can be 0-9 allows for 1000 different combinations, as calculated by 10 x 10 x 10, which equals 10³ or 1000.

Explanation:

The question asks how many different 3-digit combinations are possible with a combination lock where each digit can range from 0-9. Each digit of the code is independent and can take any of the ten possible values (0-9), leading to a total combination of possibilities calculated by multiplying the number of choices for each digit position. Given that there are three digit positions and each can be any of the ten digits, the calculation is as follows:

10 (choices for first digit) × 10 (choices for second digit) × 10 (choices for third digit) = 10³

Therefore, there are 1000 different possible combinations for the lock, ranging from 000 to 999.

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

90 students represent x percent of the boys at Jones Elementary School.

So, it is expressed as

[tex]90=\dfrac{x}{100}[/tex]

If the boys at Jones Elementary make up 40% of the total school population of x students,

[tex]90=\dfrac{x}{100}\times 0.4x\\\\9000=0.4x^2\\\\\dfrac{9000}{0.4}=x^2\\\\22500=x^2\\\\x=\sqrt{22500}\\\\x=150[/tex]

Hence, the value of x is 150.

Therefore, Option 'B' is correct.

Answer:

Option 1) d

Step-by-step explanation:

We are given the following information in the question:

The standard deviation of x, y, z = d

We have to find the standard deviation for

x+5, y+5, z+5

The standard deviation of x+5, y+5, z+5 = d

Thus, the correct option is

Option 1) d

Answer:

Step-by-step explanation:

We would apply the simple interest formula which is expressed as

as

I = PRT/100

Where

P represents the principal or amount borrowed.

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 15 months. Converting to years, it becomes = 15/12 = 1.25 years

P = $400

R = 5%

Therefore

I = (400 × 5 × 1.25)/100

I = 2500/100

I = 25

The total amount that she would pay her friend back would be

400 + 25 = $425

Answer:280 miles

let x=rate of speed on the way to mountains

x+21=rate of speed on the way home

travel time*rate=distance

8x=5(x+21)

8x=5x+105

3x=105

x=35

8x=280

how far away does Bob live from the mountains? =280 miles

Final answer:

Bob lives 280 miles away from the mountains. We solved for the slower speed and then calculated the distance using the time it took Bob to get to the mountains and his average speed during that trip.

Explanation:

Finding the Distance to the Mountains

To find out how far Bob lives from the mountains, we need to set up an equation based on the information given about time and average speed. Since the average rate was 21 miles per hour faster on the return trip and the times for the trips are known (8 hours to the mountains and 5 hours returning), we can let the slower speed be 's' and the faster speed be s' + 21'.

We can now create two equations based on the definition that Distance = Speed *Time:

Coming back home (faster speed): Distance = (s + 21) *5 hours

Since the distance to the mountains and back home is the same, we can equate these two expressions:

s * 8 = (s + 21)* 5

Calculating the Speed and Distance

Now we solve for 's':

8s = 5s + 105

8s - 5s = 105

3s = 105

s = 35

Thus, the slower speed was 35 miles per hour. We can plug this back into either equation to find the distance:

Distance = 35 miles/hour * 8 hours

Distance = 280 miles

Therefore, Bob lives 280 miles away from the mountains.

Answer:

Step-by-step explanation:

Since the length of time taken on the SAT for a group of students is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = length of time

u = mean time

s = standard deviation

From the information given,

u = 2.5 hours

s = 0.25 hours

We want to find the probability that the sample mean is between two hours and three hours.. It is expressed as

P(2 lesser than or equal to x lesser than or equal to 3)

For x = 2,

z = (2 - 2.5)/0.25 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

For x = 3,

z = (3 - 2.5)/0.25 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.97725

P(2 lesser than or equal to x lesser than or equal to 3)

= 0.97725 - 0.02275 = 0.9545

Final answer:

The probability that the sample mean is between two and three hours is practically 1, or 100%.

Explanation:

To find the probability that the SAT exam completion time sample mean for a group of students is between two and three hours, we need to calculate the z-scores for 2 hours and 3 hours and then use these z-scores to determine the corresponding probabilities.

Given:

- Population mean (= 2.5 hurs

- Standard deviation = 0.25 hours

- Sample size  = 60

We'll use the z-score formula:

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

For X = 2  hours:

[tex]\[ z = \frac{2 - 2.5}{\frac{0.25}{\sqrt{60}}} \][/tex]

[tex]\[ z = \frac{-0.5}{\frac{0.25}{\sqrt{60}}} \][/tex]

[tex]\[ z \approx \frac{-0.5}{\frac{0.25}{7.746}} \][/tex]

[tex]\[ z \approx \frac{-0.5}{0.0323} \][/tex]

[tex]\[ z \approx -15.49 \][/tex]

For X = 3 hours:

[tex]\[ z = \frac{3 - 2.5}{\frac{0.25}{\sqrt{60}}} \][/tex]

[tex]\[ z = \frac{0.5}{\frac{0.25}{\sqrt{60}}} \][/tex]

[tex]\[ z \approx \frac{0.5}{\frac{0.25}{\sqrt{60}}} \][/tex]

[tex]\[ z \approx \frac{0.5}{0.0323} \][/tex]

[tex]\[ z \approx 15.49 \][/tex]

Using the z-scores, we consult a standard normal distribution table or use a calculator to find the corresponding probabilities. Then, we calculate the difference between the two probabilities to get the probability that the sample mean is between two and three hours. Let me calculate the exact probabilities.

Using the z-scores calculated:

For z = -15.49 , the corresponding probability is practically 0 (since it's far in the left tail of the distribution).

For z = 15.49, the corresponding probability is practically 1 (since it's far in the right tail of the distribution).

Therefore, the probability that the sample mean is between two and three hours is practically 1, or 100%.

Answer:

C. 122

Step-by-step explanation:

Given,

Dimension of the cake:

Length = 12 in      Width = 16 in      Height = 4 in

We have to find out the area of the tray that is not covered by the cake.

Indra centered the cake on a circular tray.

Radius of the tray = 10 in.

So area of the tray is equal to π times square of the radius.

Framing in equation form, we get;

Area of tray =[tex]\pi\times r^2=3.14\times{10}^2=3.14\times 100=314\ in^2[/tex]

Since the cake is placed in circular tray.

That means only base area of cake has covered the tray.

Base Area of cake = [tex]length\times width=12\times 16=192\ in^2[/tex]

Area of the tray that is not covered by the cake is calculated by subtracting area of base of cake from area of circular tray.

We can frame it in equation form as;

Area of the tray that is not covered by the cake = Area of tray - Base Area of cake

Area of the tray that is not covered by the cake =[tex]314-192=122\ in^2[/tex]

Hence The area of the tray that is not covered by the cake is 122 sq. in.

The points after Dilation are (0,0), (9,-3), and (9,9).

Step-by-step explanation:

The given points are A(0,0), B(3,-1), and C(3,3).

The scale factor is 3.

[tex]D_{new}[/tex]([tex]p_{x} , p_{y}[/tex]) = scale factor × ([tex]p_{x} , p_{y}[/tex]) .

If the triangle starts form the origin (0,0) retains the same after the dilation.

[tex]D_{Anew}(p_{x} , p_{y})[/tex]= (0,0).

For point B(-1,3),

[tex]D_{Bnew}(p_{x} , p_{y})[/tex] = 3 × (3,-1).

[tex]D_{Bnew}(p_{x} , p_{y})[/tex] = (9,-3).

For Point C(3,3),

[tex]D_{Cnew}(p_{x} , p_{y})[/tex] =  3 × ( 3,3).

[tex]D_{Cnew}(p_{x} , p_{y})[/tex] = ( 9,9).

Refer the graph for dilated triangle.

Answer:

[tex]18x+12y\geq 300[/tex]

Step-by-step explanation:

Let

x ---> the number of an adult tickets

y ---> the number of a child tickets

Remember that the word "at least" means "greater than or equal to"

so

The number of an adult tickets multiplied by its price ($18) plus the number of a child tickets multiplied by its price ($12) must be greater than or equal to $300

The inequality that represent this situation is

[tex]18x+12y\geq 300[/tex]

using a graphing tool

the solution is the shaded area

Remember that the number of tickets cannot be a negative number

see the attached figure

Answer:

The cost of a 12 minute call to France is $ 3.63

Step-by-step explanation:

given:

The cost of 15 minute call to France = $ 4.29

The cost of 10 minute call to France   = $ 3.19

To Find :

The cost of a 12 minute call to France = ?

Solution:

Let the flat fee be X

and the cost per minute be Y

so the  15 minute call to France will be

X + 15(Y) = 4.29---------------------------(1)

the  10 minute call to France will be

X + 10(X) = 3.19----------------------------(2)

Subtracting (2) from (1)

X + 15(Y) = 4.29

X + 10(Y) = 3.19

-      -           -

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

      5Y = 1.10

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

[tex]Y =\frac{1.10}{5}[/tex]

Y = 0.22

So the cost per minute of a call = $0.22

substituting the values in (1)

X + 15(0.22) = 4.29

X + 3.3 = 4.29

X = 4.29 -3.3

X = 0.99

Now the cost of 12 minute call is

=>X + 12(Y)

=> 0.99 + 12(0.22)

=> 0.99 + 2.64

=> 3.63

Number -13 is classified as real and integer

Solution:

Given that The number -13 can be classified as

Let us first understand about real numbers, whole numbers, Integers and irrational numbers

Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."

But -13 is a negative number. Therefore -13 is not a whole number

Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers. They are called "Real Numbers" because they are not Imaginary Numbers.

Therefore -13 is a real number

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043.

Therefore -13 is a integer

An irrational number is real number that cannot be expressed as a ratio of two integers. An irrational number is not able to be written as a simple fraction because the numbers in the decimal of a fraction would go on forever

But -13 can be expressed in fraction as [tex]-13 \div 1[/tex]

Therefore -13 is not a irrational number

Thus we can conclude that number -13 is classified as real and integer

Answer:

Ecological validity

Step-by-step explanation:

Well, to complete the sentence, first we need to be aware of types of validity of experiments such as criterion validity, ecological validity, content validity , factorial validity, etc.

In this particular example, it is stated that the results of an experiment can be applied to real-world conditions. Therefore, the experiment is said to have ecological validity considering the fact that results applied to real-world conditions.

When the results of an experiment can be applied to real-world conditions, that experiment is said to have external validity.

External validity refers to the degree to which the findings of a study can be generalised beyond the study's specific conditions to real-world situations. It's crucial for research to have external validity to ensure its applicability and relevance outside of the laboratory setting.

Answer:

8 chickens

Step-by-step explanation:

Firstly, we need to know the number of eggs produced by a single chicken in 24 hours.

Since 2 chickens produce 6 eggs in 24hours, this means 1 chicken will produce 3 eggs in 24 hours.

Now, we need 24 eggs to be produced. Since the time is the same 24hours, meaning time is constant, the number of chickens required to produce 24 eggs will be 24/3 = 8 chickens

Hence, we can say that 8 chickens will produce 24eggs in 24 hours

8 chickens will be needed to produce 24 eggs in 24 hours.

Given,

2 chickens produces 6 eggs in 24 hours.

So, 1 chicken produces 3 eggs in 24 hours.

We have to calculate the no of chicken needed to produce 24 eggs in 24 hours.

Since 1 chicken produces 3 eggs in 24 hours.

So, 1 egg is produced by  [tex]\dfrac{1}{3}[/tex] chicken in 24 hours .

Now, 24 eggs is produced by [tex](\frac{1}{3} \times24=8)[/tex] chickens.

Hence 8 chickens will be needed to produce 24 eggs in 24 hours.

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Answer:

Domain: set of all real numbers; (-∞, ∞)

Range : {y | y f > 2}

Check the attached figure to visualize the graph.

Step-by-step explanation:

The graph of the given function is attached. Please check the attached figure.

As the function is given as:

                                              [tex]f(x) = (\frac{1}{3})^{x} +2[/tex]

As the table of some of the values of x and y values for [tex]f(x) = (\frac{1}{3})^{x} +2[/tex] is given as follows:

               -2                    11

                -1                    5

                 0                   3

                 1                   2.33

                  2                  2.111

Hence, it is clear that the function is defined for every input value of x. So, domain is the set of all real numbers.

Domain: set of all real numbers; (-∞, ∞)

If we carefully analyze the graph of this function, it is clear that no matter what input value of x we put, range or y-value of this function would always be be greater than 2. Check the attached graph figure to better visualize the range of the function.

Range can also be denoted as: Range : {y | y f > 2}

Keywords: graph, function, domain and range

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Answer: 13

Step-by-step explanation: first we have to know what an integer, which is a single whole number without fractions or decimal numbers e.g. 1,2,3,4,5,6,7,8,9

So now we are to find the least possible positive difference between two digit integers with combination of 2,4,6,9

So first, since it has to be the lowest difference, we have to look between these numbers for the lowest difference between the given integers, 6-4 = 2, 4-2 = 2, now the rest of the combination will give numbers higher that 2, e.g. 9-6 = 3, 6-2 = 4, 9-4 = 5, 9-2 = 7, so we can say our two digit integers can start with either 4 and 2, or 6 and 4, which is the tens in the two digit integers, so to get the least difference in this values, the units number of the bigger two digit integer will be smaller than the units number of the smaller two digit integers

So let's take the number 2, and 4

The bigger two digit integer will obviously start will 4, and since it's supposed to have the smaller units number, the two digit integer will be 46, and the second two digit integer will be 29, the finding the difference

We have 46-29=17

The taking the other combination of integer to give the smallest value, which was 2, (6 and 4) then giving the units number of the bigger integer which will be the smaller units number value (2), that two digit integer will be 62, and the other 49, finding the difference

62-49= 13

So therefore the least possible positive difference = 13

Basically you want to find an equivalent fraction for 3/5 in the answer choices.

12/20 equals 3/5 because 3/5 x 4/4 (or 1) = 12/20

answer: 4

Final answer:

Option 4) 12/20 simplifies to 3/5

Explanation:

To find which numbered choice has a value equivalent to the ratio Archie made in his basketball game, we need to compare each option to the fraction 3/5. We're looking for a fraction that has the same value when simplified.

Thus, the choice with a value equivalent to 3/5 is option 4) 12/20.

Answer: the length is 6 feet. The width is 2 feet

Step-by-step explanation:

The garden pool is rectangular in shape.

Let L represent the length of the rectangular garden.

Let W represent the width of the rectangular garden.

The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that

L× W = 12 - - - - - - - - - - 1

The length of the pool needs to be 2ft more than twice that width. This means that

L = 2W + 2 - - - - - - - - - - - 2

Substituting equation 2 into equation 1, it becomes

W(2W + 2) = 12

2W^2 + 2W = 12

2W^2 + 2W - 12 = 0

W^2 + W - 6 = 0

W^2 + 3W - 2W - 6 = 0

W(W + 3) - 2(W + 3) = 0

W - 2 = 0 or W + 3 = 0

W = 2 or W = - 3

Since the Width cannot be negative, then the width is 2 feet

Substituting W = 2 into equation 2. It becomes

L = 2×2 + 2 = 6 feet

To find the number of tiles required to tile the inside of a rectangular room, calculate the area of the room, and divide it by the area of each tile.

To find the number of 1 ft.² tiles required to tile the inside of the room, we need to calculate the area of the room. Let's assume the length of the room is X feet. Since the room is 12 feet wider than its length, the width of the room would be X + 12 feet. The area of the room is given by length multiplied by width, which is X * (X + 12). To convert this into square feet, we need to multiply by 1, as 1 square foot is 1 ft.². Therefore, the area can be expressed as X * (X + 12) ft².

Next, we need to divide the area of the room by the area of each tile, which is 1 ft.². The formula to calculate the number of tiles required is:

Number of tiles = (Area of the room) / (Area of each tile)

Substituting the values into the formula, we get:

Number of tiles = X * (X + 12) ft² / 1 ft²

Simplifying, we have:

Number of tiles = X * (X + 12) ft²

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Answer:

Chris will make $1905.22 by selling gold.

Step-by-step explanation:

Amount of gold Chris will have = 42 g

Current rate of gold = $1286 per ounce

We need to find the amount Chris will make after selling the gold.

Now we will first find Current rate of gold in grams.

We know that 1 ounce = 28.3495 grams.

So we can say that

28.3495 g = $1286

So 1 g = Rate of gold for 1 gram.

By Using Unitary method we get;

Rate of gold for 1 gram = [tex]\frac{1286}{28.3495} \approx \$45.3624[/tex]

Now we will find the amount for 42 g of gold

if 1 g = $45.3624

so 42 g = Amount of money for 42 g

Again by using Unitary method we get;

Amount of money for 42 g = [tex]42 \times 45.3624 \approx \$1905.22[/tex]

Hence Chris will make $1905.22 by selling gold.

Chris can get $1,736.10 by selling 42 grams of gold.

Chris's uncle from Japan has promised to give him 42 grams of gold. The local jewellery exchange will buy gold for $1286 per ounce. To find out how much money Chris can get for selling the gold, we need to convert grams to ounces and then multiply by the price per ounce. There are approximately 31.1035 grams in an ounce. So, to convert grams to ounces we use the following formula:

Divide the amount of gold in grams by the number of grams per ounce. 42 grams ÷ 31.1035 grams/ounce = 1.35 ounces.

Multiply the amount of gold in ounces by the current price of gold per ounce. 1.35 ounces × $1286/ounce = $1,736.10.

Answer:  The required probability is [tex]\dfrac{3}{16}.[/tex]

Step-by-step explanation:  Given a deck of 52 cards.

We are to find the probability of drawing exactly 1 heart in 2 draws with replacement.

Number of hearts in the deck = 13.

Let S be the sample space of drawing two cards from the deck of 52 cards and E denote the event of drawing exactly 1 heart in 2 draws with replacement.

Then,

[tex]n(S)=^{52}C_1\times^{52}C_1=52\times52,\\\\\\n(E)=^{13}C_1\times^{52-13}C_1=13\times39.[/tex]

Therefore, the probability of event E is

[tex]P(E)=\dfrac{n(E)}{n(S)}=\dfrac{13\times39}{52\times52}=\dfrac{1\times3}{4\times4}=\dfrac{3}{16}.[/tex]

Thus, the required probability is [tex]\dfrac{3}{16}.[/tex]

Answer: The probability you draw exactly 1 heart in 2 draws with replacement is 3/16

Step-by-step explanation:

The probability of picking a heart in a pack of 52 playing card is

13/52=1/4

The probability of drawing exactly one heart in 2 draws with replacement mean;

That the first draw is a heart and the second draw is not a heart

The probability that the second draw is not a heart is= 1-1/4= 3/4

Therefore

The probability you draw exactly 1 heart in 2 draws with replacement is

1/4 * 3/4 = 3/16

Answer:the length is 8.7 inches. The width is 5.7 inches

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The width of a rectangle is 3 inches less than the length. This means that

L = W + 3

The area of a rectangle is expressed as L×W

The area is 50 square inches. This means that

LW = 50 - - - - - - - - - - 1

Substituting L = W + 3 into equation 1, it becomes

(W + 3)W = 50

W^2 + 3W - 50 = 0

We would apply the general formula for quadratic equations,

x = [ - b ± √(b^2 - 4ac)]/2a

a = 1

b = 3

c = - 50

Therefore,

w = [- 3 ± √(3^2 - 4×1×-50)]/2×1

w = [- 3 ± √(9 + 200)]/2

w = (- 3 ± √209)/2

w = (-3+14.4568)/2 or (-3-14.4568)/2

w = 5.7 or w = -8.7

Since the width cannot be negative, the width would be 5.7 inches.

Substituting w = 5.7 into L = W + 3,

L = 5.7 + 3 = 8.7 inches

The length and width of the rectangle are 8.2 inches and 5.2 inches respectively.

The width of a rectangle is 3 inches less than the length. The area is 50 square inches. Find the length and width. Round to the nearest tenth if necessary.

Let x be the length of the rectangle.

Given width = x - 3

Area = Length x Width = x(x - 3) = 50

x^2 - 3x - 50 = 0

Using the Quadratic Formula, x ≈ 8.2 inches, width ≈ 5.2 inches

Present population of the village is 30051

Solution:

Given that village had a population of 25000 three years ago

During the first year second year and the third year the population increase at a rate of 5%, 6% and 8% respectively

To find: present population of the village

The present population is given by formula:

[tex]\text { present population }=p\left(1+\frac{x}{100}\right)\left(1+\frac{y}{100}\right)\left(1+\frac{z}{100}\right)[/tex]

Where,

p = initial population

x = rate of increase at first year

y = rate of increase at second year

z = rate of increase at third year

Here given that,

x = 5 %

y = 6 %

z = 8 %

p = 25000

Substituting the values we get,

[tex]\begin{aligned}&\text { present population }=25000\left(1+\frac{5}{100}\right)\left(1+\frac{6}{100}\right)\left(1+\frac{8}{100}\right)\\\\&\text { present population }=25000(1.05)(1.06)(1.08)\\\\&\text { present population }=25000 \times 1.20204=30051\end{aligned}[/tex]

Thus present population of the village is 30051

Answer:

Theory

Step-by-step explanation:

The term theory is associated to a "set of logical interrelated concepts, statements, propositions, and definitions", who are "derived from philosophical and logical beliefs from scientific data and from which questions and hypotheses can be deduced, characterize, tested and verified".

So then we can conclude that :

A set of logically interrelated concepts, statements, propositions, and definitions supported by data, testing, and verification to account for or characterize some phenomena is called theory.

Final answer:

A theory is a comprehensive explanation for observed phenomena that is supported by evidence and repeated validation. It is a core component of scientific understanding, which relies on the scientific method for development and verification.

Explanation:

A set of logically interrelated concepts, statements, propositions, and definitions supported by data, testing, and verification to account for or characterize some phenomena is called a theory. In science, a theory is a well-developed set of ideas that propose an explanation for observed phenomena. It involves a hypothesis, or group of hypotheses, that has been substantiated through repeated experiments or empirical observations. Theories are used to make predictions about future observations and can be revised as new evidence is discovered.

The validity of a theory is determined by the accuracy of its predictions and the extent to which it can measure what it is designed to measure. A robust theory not only explains the phenomena in question but is also supported by a wide range of scientific evidence and has been verified multiple times by various groups of researchers using the scientific method.

Answer: Two-sample t-test

Step-by-step explanation:

The Two-sample t-test is used to test the difference between two random and distinct population means. It help test whether the difference between the two populations is statistically significant.

In the case above the researcher wants to determine whether there is a difference in mean number of minutes of television viewing between men and women which makes it a Two-sample t-test.

Answer:

  -1/2

Step-by-step explanation:

Slope is calculated as ...

   (change in y)/(change in x) = (y2 -y1)/(x2 -x1)

   = (-4 -1)/(0 -(-10)) = -5/10 = -1/2

The slope of the line is -1/2.

Answer:

The answer to your question is Midpoint  ( [tex]\frac{1}{2} , -2)[/tex]

Step-by-step explanation:

Data

A (3, -7)

B (-2, 3)

Formula

[tex]Xm = \frac{x1 + x2}{2}[/tex]

[tex]Ym = \frac{y1 + y2}{2}[/tex]

Substitution and simplification

[tex]Xm = \frac{3 - 2}{2}[/tex]

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

[tex]Ym = \frac{-7 + 3}{2}[/tex]

[tex]Ym = \frac{-4}{2}[/tex]

[tex]Ym = -2[/tex]

Solution

Midpoint  ( [tex]\frac{1}{2} , -2)[/tex]

Answer:

3

Step-by-step explanation:

Simplify :

(5-4i)-(2-4i)

5-4i-(2-4i)

=3

Answer:

b) π /16 (1-1/e^2)

Step-by-step explanation:

For this case we have the following limits:

[tex]y =e^{-x} , y=0, x=0, x=1[/tex]

And we have semicircles perpendicular cross sections.

The area of interest is the enclosed on the picture attached.

So we are assuming that the diameter for any cross section on the region of interest have a diameter of [tex]D=e^{-x}[/tex]

And then we can find the volume of a semicircular cross section with the following formula:

[tex]V= \frac{1}{2}\pi (\frac{e^{-x}}{2})^2 dx= \frac{1}{8} \pi e^{-2x}[/tex]

And for th volum we can integrate respect to x and the limits for x are from 0 to 1, so then the volume would be given by this:

[tex]V= \pi \int_0^{1} \frac{1}{8} \pi e^{-2x} dx[/tex]

[tex] V= -\frac{\pi}{16} e^{-2x} \Big|_0^1 [/tex]

And evaluating the integral using the fundamental theorem of calculus we got:

[tex]V = -\frac{\pi}{16} (e^{-2} -1)= \frac{\pi}{16}(e^{-2} -1)=\frac{\pi}{16} (1-\frac{1}{e^2})[/tex]

And then the best option would be:

b) π /16 (1-1/e^2)

Answer: it will take 10 minutes to get back to room temperature.

Step-by-step explanation:

Let us assume that the room temperature is 25 degrees. The current temperature of the soup before the decrease would be 25 + 50 = 75 degrees.

The soup drop about 5 degrees every minute. This is a linear rate. The rate at which the temperature is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 75 degrees

d = - 5 degrees (it is decreasing)

n = t

We want to determine how long it will take to get back to 25 degrees, . Therefore,

25 = 75 -5 (t - 1) = 75 - 5t

5t = 75 - 25 = 50

t = 50/5 = 10 minutes