If d is the standard deviation of x, y, z, what is the standard deviation for x+5, y+5, z+5.1. d2. 3d3. 15d4. d+55. d+15

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

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:  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

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:

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.

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:

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: 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

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:

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:

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