Why do you think it might be useful to rearrange formulas before solving for one of the variables? (Relate your answer to the Celsius and Fahrenheit formulas and examples.)

Answer:

yea i think yea yes yes yes yes

Final answer:

Yes, repeating decimals can be expressed as fractions using a simple algebraic equation.

Explanation:

Yes, repeating decimals can be expressed as fractions. To represent a repeating decimal as a fraction, you can use a simple algebraic equation. Let's take an example:

Consider the repeating decimal 0.3333... Now, let x be the number we want to express as a fraction. We can multiply both sides of the equation by 10 in order to move the decimal point to the right and eliminate the repeating part:

x = 0.3333...

10x = 3.3333...

Now, we subtract the two equations to eliminate the repeating part:

10x - x = 3.3333... - 0.3333...

Combining like terms:

9x = 3

Finally, dividing by 9 gives us the fraction representation of the repeating decimal:

x = 3/9 = 1/3

Answer:

B

Step-by-step explanation:

Compare triangle ABC with triangle A'B'C. Let's try to prove that they're similar.

BC = 6 + 3 = 9 units

B'C = 6 units

BC/B'C' = 9/6 = 3/2 = 1.5

AC = 2 + 4 = 6 units

A'C = 4 units

AC/A'C = 6/4 = 3/2 = 1.5

These two pairs of corresponding sides have the same ratio, so that's promising.

Also notice that angle BCA = angle B'CA'. So, by SAS Similarity Theorem, we know that triangles ABC and A'B'C are similar.

By definition, similar triangles have the same corresponding angles.

Angle ABC corresponds to angle A'B'C, so they're equal. Since angle ABC = 40 degrees, then angle A'B'C = 40 degrees, as well.

Hope this helps!

Without proper context or a diagram, it's impossible to definitively state the measure of angle A'B'C. However, as an example, if angle A'B'C is in an equilateral triangle, it would be 60 degrees.

The question appears to be asking about the measure of an angle, designated as A'B'C. However, without proper context or a diagram to reference, it's impossible to definitively state what the measure of angle A'B'C is. It can be any value depending on the context. But, if A'B'C is a part of a triangle or a particular geometric shape with known properties, we can solve it based on the information given related to that specific shape.

For example, in an equilateral triangle, each angle measures 60°. So, if A'B'C is an angle in an equilateral triangle, it would most likely be 60°. Yet, without sufficient context, this is simply a hypothetical situation.

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Answer:

The largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb

Step-by-step explanation:

Given

μ = Mean = 10.4 lb

σ = Standard deviation = 3 lb

Using a confidence level of 90%,

We'll need to first determine the z value that correspond with bottom 5% of consumption of banana

α = 5%

α = 0.05

So,

zα = z(0.05)

z(0.05) = -1.645 ----- From z table

Let x represent the largest annual per capita consumption of bananas

The relationship between x and z is

x = μ + zσ

By substitution;

x = 10.4 + (-1.645) * 3

x = 10.4 - 4.935

x = 5.465

Hence, the largest annual per capita consumption of bananas in the bottom 5% of consumption is 5.465 lb

Answer:

86

Step-by-step explanation:

Answer:

.17

Step-by-step explanation:divide 17 by 100 hope this helps god bless

Answer:

0.17

Step-by-step explanation:

Taking into account the definition of maximum, minimum and vertex of a quadratic function, it takes 12.5 seconds for the projectile to reach maximum height.

A quadratic function is defined in the form:

y= f (x) = ax² + bx + c

Every quadratic function has a maximum or a minimum, which is the vertex of the parabola. If the parabola has an upward concavity, the vertex corresponds to a minimum of the function; whereas if the parabola has concavity downwards, the vertex will be a maximum.

That is, if the coefficient a is positive the parabola is concave and the vertex will be a minimum of the function, while if a is negative the parabola will be convex and the vertex is a maximum.

The maximum or minimum is reached in [tex]xv=\frac{-b}{2a}[/tex]  

The maximum or minimum value of y is obtained by evaluating the function at xv, this is, f (xv).

In this case, the function is:

h(t)= -16t² + 400t

where t is the time in seconds

Being a = -16 and b = 400, the value of a is negative, so the vertex will be the maximum.

You want to know the time it takes for the projectile to reach the maximum height, that is, the maximum in t. That is, you must calculate t using the expression: [tex]t=\frac{-b}{2a}[/tex]

So: [tex]t=\frac{-400}{2x(-16)}[/tex]

Solving:

[tex]t=\frac{-400}{-32}[/tex]

t= 12.5 seconds

It takes 12.5 seconds for the projectile to reach maximum height.

Learn more about cuadratic function with this examples:

There are 4 out of the 7 cards that are odd numbers.

As a fraction: 4/7

As a percent: 57.14%

As a decimal: 0.57

Answer:

A. 57.6

Step-by-step explanation:

6 times 5.2 is 31.2. 4 times 5 is 20. 6 times 5 is 30. 6 times 5 is 30. (31.2/2)+(20/2)+30= 55.6 Then you round nearest tenth. 57.6.

Answer:

Aa 57.6

Step-by-step explanation:

It is correct

correct on E D G E N U I T Y

[tex]2x + 4 = - 8 + 5x \\ 12 = 3x \\ x = 4[/tex]

Answer: the minimum score required for the scholarship is 29.24

Step-by-step explanation:

Since the scores are normally distributed, it follows the central limit theorem. The formula for determining the z score is

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

Since the university plans to award scholarships to students whose scores are in the top 9%, the scores that would be qualified are scores which are at least 91%(100 - 9 = 91).

Looking at the normal distribution table, the z score corresponding to the probability value of 0.91(91/100) is 1.35

From the information given,

µ = 21

σ = 6.1

Therefore,

1.35 = (x - 21)/6.1

6.1 × 1.35 = x - 21

8.235 = x - 21

x = 8.235 + 21 = 29.24

The minimum ACT Reading score required to be in the top 9% for a university scholarship is approximately 29.2, determined by using a z-score of 1.34, the mean score of 21, and the standard deviation of 6.1.

To determine the minimum ACT Reading score required to be in the top 9% of students, and hence eligible for a scholarship at a university, we utilize the concept of z-scores in a normal distribution. A z-score indicates how many standard deviations an element is from the mean.

First, we need to find the z-score that corresponds to the top 9% of the distribution. Standard z-score tables or calculators will show that the z-score for the top 9% is approximately 1.34. This z-score means the score is 1.34 standard deviations above the mean. Next, we apply the z-score formula:

Z = (X - μ) / σ

Where:
Z is the z-score (1.34 in this case),
X is the ACT score we want to find,
μ is the mean (21 for ACT Reading),
σ is the standard deviation (6.1 for ACT Reading).

We can rearrange the formula to solve for X (the ACT score):
X = Z * σ + μ

Substituting the values we have:

X = 1.34 * 6.1 + 21

X ≈ 29.214

The minimum ACT Reading score required for the scholarship is therefore approximately 29.2 when rounded to the nearest tenth.

Answer:

18

Step-by-step explanation:

6*3=18

Answer: 18

Step-by-step explanation: It's easy, you have to divide in order to get 18.

Answer:

B

Step-by-step explanation:

A rational number is one that can be written in the form p/q, where p and q are whole numbers. However, [tex]4\sqrt{20} =8\sqrt{5}[/tex] cannot be simplified further. It is impossible to write it in the form of p/q, so it's not A.

An irrational number is just the opposite of a rational one: it can't be written in the form p/q. Since [tex]4\sqrt{20} =8\sqrt{5}[/tex] isn't rational, it's irrational, so B is correct.

An integer is a number without any decimal values. [tex]4\sqrt{20} =8\sqrt{5}[/tex] is approximately 17.889. Clearly, this is a decimal, so it's not C.

D is wrong because we know [tex]4\sqrt{20} =8\sqrt{5}[/tex] is irrational.

Hope this helps!

Answer:

B. An irrational number

Step-by-step explanation:

4√20 can not be written in the fraction form, hence not rational

√20 is not an integer, hence 4√20 is also not at integer

The functions h(x) = (x - 1)² and g(x) = -(x + 1)(x -1) key aspects shown in the picture.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

h(x) = (x - 1)²

The range of the function:

y ≥ 0

The function increases over the interval (1, ∞)

The function decreases over the interval (-∞, 1)

g(x) = -(x + 1)(x -1)

The range of the function:

y ≤ 1

The function increases over the interval (-∞, 0)

The function decreases over the interval (0, ∞)

Thus, the functions h(x) = (x - 1)² and g(x) = -(x + 1)(x -1) key aspects shown in the picture.

Learn more about the function here:

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Answer: last option

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

[tex]3\sqrt{124} = 3\sqrt{4} \sqrt{31} \\\sqrt{4} = 2\\ 3*2\sqrt{31}=6\sqrt{31}[/tex]

Answer:

The answer to your question is 2046 in²

Step-by-step explanation:

Data

length = 30 in

base = 24 in

hypotenuse = 25 in

Process

1.- Calculate the height of the triangle using the Pythagorean theorem

          c² = a² + b²

-Solve for b

          b² = c² - a²

-Substitution

           b² = 25² - 24²

-Simplification

           b² = 625 - 576

-Result

            b² = 49

            b = 7 in

2.- Calculate the area of the base

Area = base x height

Area = 24 x 7 x 2

        = 336 in²

3.- Calculate the lateral area

Area = 30 x 25 x2

        = 1500 in²

4.- Calculate the last area

Area = 30 x 7

        = 210

5.- Final area

Total area = 210 + 1500 + 336

                 = 2046 in²

Answer:

Step-by-step explanation:No if you use soh cah toa

Answer:

5,000 Joules of work.

Step-by-step explanation:

A 1000-watt microwave does 5000 joules of work in 5 minutes.

Work is defined as the energy transferred to or from an object by applying force along a displacement.

Given that, the power of the microwave is P = 1000 watts and the time is t = 5 s.

The work done by the microwave is given by:

W = P×t

W = 1000 × 5

W = 5000 joules

Hence, a 1000-watt microwave does 5000 joules of work in 5 minutes.

Learn more about the work here:

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The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, P(x) = -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000.

The profit function, P(x), can be obtained by finding the difference between the revenue function, R(x), and the cost function, C(x). In this case, we have:

R(x) = 550[tex]x^3[/tex] - 12,000[tex]x^2[/tex] + 83,000x + 7000

C(x) = 880[tex]x^3[/tex] - 21,000[tex]x^2[/tex] + 150,000x - 160,000

To find P(x), we subtract C(x) from R(x):

P(x) = R(x) - C(x)

Substituting the given functions, we get:

P(x) = (550[tex]x^3[/tex] - 12,000[tex]x^2[/tex] + 83,000x + 7000) - (880x3 - 21,000[tex]x^2[/tex] + 150,000x - 160,000)

Simplifying, we combine like terms:

P(x) = -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000

Therefore, the profit function, P(x), can be expressed as a polynomial in standard form as -330[tex]x^3[/tex] + 9,000[tex]x^2[/tex] - 67,000x + 167,000.

The profit function, P(x), is found by subtracting the cost function, C(x), from the revenue function, R(x). After performing the subtraction and simplifying, the profit function in standard form is P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000.[/tex]

To find the profit function, P(x), we must subtract the cost function, C(x), from the revenue function, R(x). Given the functions:

R(x) = [tex]550x^3 - 12,000x^2 + 83,000x + 7,000[/tex]

C(x) =[tex]880x^3 - 21,000x^2 + 150,000x - 160,000[/tex]

We perform the subtraction:

P(x) = [tex](550x^3 - 12,000x^2 + 83,000x + 7,000) - (880x^3 - 21,000x^2 + 150,000x - 160,000)[/tex]

Expand and group terms:

P(x) =[tex]550x^3 - 12,000x^2 + 83,000x + 7,000 - 880x^3 + 21,000x^2 - 150,000x + 160,000[/tex]

P(x) = [tex](550x^3 - 880x^3) + (-12,000x^2 + 21,000x^2) + (83,000x - 150,000x) + (7,000 + 160,000)[/tex]

Simplify the terms:

P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000[/tex]

The profit function, P(x), in standard form is:

P(x) = [tex]-330x^3 + 9,000x^2 - 67,000x + 167,000[/tex]

Answer: Option "B" is correct.

Step-by-step explanation:

Since we have given that

α= 0.10

Let the population variances are equal and samples are random and independent.

Let [tex]\bar{x}[/tex] be the mean amount spent by a customer at Burger Stop.

Let [tex]\mu[/tex] be the mean amount spent by customer at Fry World.

So, it has given that

the mean amount is spent by a customer at Burger stop is greater than the mean amount spent by a customer at Fry World.

So, Hypothesis would be :

[tex]H_0:\bar{x}=\mu\\\\H_1:\bar{x}>\mu[/tex]

Hence, Option "B" is correct.

Answer:

y = 6/19 = 0.316

Step-by-step explanation:

Saw this on a website

Answer:

For on it depends on how many cards you have and how many 4's there are

Step-by-step explanation:

So say you had 16 cards and 3 of them were 4 the probability of you picking a 4 is 3 of 16.

Final answer:

The probability of drawing a 4 and then another 4 in sequence without replacement from a 52-card deck is 1/221, calculated by multiplying the probabilities of drawing a four on the first and second draws, 1/13 and 1/17, respective

Explanation:

The question involves calculating the probability of drawing two specific cards in sequence without replacement from a standard deck of 52 cards. The condition provided is drawing a 4 first and then drawing another 4 without putting the first card back. To solve this, consider the probability of each event happening.

For the first draw, there are 4 fours in a deck of 52 cards, so the probability of drawing a four (P(A)) is 4/52 or 1/13.

After drawing one four and not returning it, there are now 51 cards left and only 3 fours left. Therefore, the probability of drawing a four as the second card (P(B) given A) is 3/51 or 1/17.

To find the total probability of both events happening in sequence, multiply the probabilities of the individual events: 1/13 * 1/17.

Thus, the probability of drawing a 4 and then another 4 in sequence without replacement is 1/221.

Answer:   888+88+8+8+8 = 1,000

Step-by-step explanation: First of all line all your eights' up and then split them

To add eight 8's and get the number 1000 using only addition, you can express 1000 as the sum of two numbers: 800 and 200.

To add eight 8's and get the number 1000 using only addition, you can express 1000 as the sum of two numbers: 800 and 200. Here's how:

Now, you have 24 and 32, which add up to 56. Finally, add 800 and 200, which equals 1000.

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Answer:

15/23

Step-by-step explanation:

please kindly see the attached for more explanation

Answer:

336.

Step-by-step explanation:

8 x 7 x 6 = 336.

Feel free to let me know if you need more help! :)

Answer:

$49.20

Step-by-step explanation:

Answer:

Step-by-step explanation:

on the box chart it shows that shelter A has the lightest dog

hope i helped :D

Answer:

shelter A. shelter B. Both shelters have a dog with the lowest weight of 8 pounds.

Step-by-step explanation:

Hope this helps :)

Answer:

you would have 80 units of space

Step-by-step explanation:

to find out how much volume there is you have to multiply the base x the width x the height so that would be 8x5x2 and 8x5 is 40 and 40x2 is 80

The box has a volume of 80 cubic inches, determined by multiplying its dimensions: length (8 inches), width (5 inches), and height (2 inches).

To determine the space available for candy in the given box, we need to calculate the volume of the box. The volume of a rectangular box can be found by multiplying its length, width, and height. Here, the box measures 8 inches in length, 5 inches in width, and 2 inches in height.

To find the volume, use the formula:

Volume = Length × Width × Height

In this case, the volume is:

Volume = 8 inches × 5 inches × 2 inches = 80 cubic inches

Therefore, the box has 80 cubic inches of space available for candy.

Answer:

huma's share= Rs.864

Seema's share= Rs.432

Hubna's share= Rs.720

Step-by-step explanation:

Considering 'x' as the share of huma

Therefore , Seema's share will be x/2

And Hubna's share will be 5/3 * x/2 => 5x/6

Total money given in the problem is Rs.2016

In order to find the share of individual, we first have to determine 'x' variable by taking the sum of all shares.

x+x/2+5x/6=Rs.2016

(6x+3x+5x)/6=2016

14x/6=2016

x=2016 * 6/14

x=864.

Therefore,huma's share 'x' will be Rs.864

Seema's share will be = x/2 = Rs.432

And Hubna's share will be = 5x/6= Rs.720

Answer:

10 metal and 20 plastic

Step-by-step explanation:

10 x 25 is 250, 20 x 10 is 200 and 250 + 200 is 450