Question 4-6. Earth is 93 million miles from the Sun. Pluto is 4.67 billion miles from the Earth.Calculate the ratio of the distance from Pluto to Earth to the distance from Earth to the Sun. Use scientific notation to calculate the ratio and express your answer in standard notation. (round to the hundredths place)

\(12b^2\sqrt[3]{2a}\)

In word form, this is 12 b squared (RootIndex 3 StartRoot 2 a EndRoot

Or you could say 12b^2 times the cube root of 2a

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Work Shown:

\(3b^2\sqrt[3]{54a}+3\sqrt[3]{2ab^6}\\\\3b^2\sqrt[3]{27*2a}+3\sqrt[3]{b^6*2a}\\\\3b^2\sqrt[3]{(3)^3*2a}+3\sqrt[3]{(b^2)^3*2a}\\\\3b^2\sqrt[3]{(3)^3}*\sqrt[3]{2a}+3\sqrt[3]{(b^2)^3}*\sqrt[3]{2a}\\\\3b^2*3*\sqrt[3]{2a}+3*b^2*\sqrt[3]{2a}\\\\9b^2\sqrt[3]{2a}+3b^2\sqrt[3]{2a}\\\\(9b^2+3b^2)\sqrt[3]{2a}\\\\\boldsymbol{12b^2\sqrt[3]{2a}}\\\\\)

The idea here is that we break the cube roots into smaller pieces, so we pull out perfect cubes when factoring.

The sum of the expression is 12 b squared (Root Index 6 Start Root 2 a End Root) or 12b²∛(2a).

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

We have the expression,

3 b squared (Root Index 3 Start Root 54 a End Root) + 3 (Root Index 3 Start Root 2 a b Superscript 6 Baseline End Root).

In numerical form,

3b²∛(54a) + 3∛(2ab⁶)

To find the sum of the above expression:

we simplify the expression,

3b²∛(54a) + 3∛(2ab⁶)

= 3b²∛3³(2a) + 3∛(2a)(b²)³

= 9b²∛(2a) + 3b²∛(2a)

= 12b²∛(2a)

Therefore, the sum is 12b²∛(2a).

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Answer:

C. 16oz container

Step-by-step explanation:

I can explain my answer in the comments if needed, but C is the correct answer :)

Answer:

486 mm²

Step-by-step explanation:

Formula: 6a²

a² = 9²

= 81

6(81) = 6 × 81

486

a) She can make 400 milliliters of the fizzy drink.

b) The change does not affect the greatest amount of drink.

We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.

If we divide the total amount of apple juice in 7 parts, then each part has:

280ml/7 = 40ml

Then we need 3 parts of 40ml of the lemonade, this is:

3*40ml = 120ml

Then the total amounf of drink fizz that she can make is:

280ml + 120ml = 400ml.

b) Now she has  160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.

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Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

Without using general formula we will solve it in bit lengthy manner

For first half

Time=Distance/Speed

For second half

Time

So

Average speed

Option C

The answer is 412.3 km/h.

The formula to find average velocity is :

\(\boxed {V_{avg} = \frac{d_{1}+d_{2}}{t_{1}+t_{2}}}\)

Let's find t₁ and t₂.

Now, let's substitute in the formula to get the answer.

Using the percentile concept, it is found that the percentile for 100 is 22.4%, given by option C.

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

\(p = \frac{112}{500}\times 100\% = 22.4\%\)

The percentile for 100 is 22.4%, given by option C.

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Using the Pythagoras theorem, we can find the value of x to be = 10ft.

Option B is correct.

The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.

Here in the question,

We have 2 right-angled triangles.

So, base of the large triangle, x

= √ (13² - 12²) + √ (13² - 12²)

= √ 5² + √ 5²

= 5 + 5

= 10ft.

Therefore, the length of the side, x = 10ft.

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Answer:

If I am not mistaken a=3;b=10;c=23;d=39

Step-by-step explanation:

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Answer:

Step-by-step explanation:

The expression r ∨ (~q → r) can be expressed in English as "Mike is rich or if Mike is not a politician, then Mike is rich."

The first part, "Mike is rich," represents the truth value of the proposition r. The second part, "q → r," is a conditional statement that can be read as "if not q (Mike is not a politician), then r (Mike is rich)." The negation symbol () in this conditional statement represents "not."

Note: The underline should be crossing out what it underlines

Therefore, the entire expression can be read as "Mike is rich or if Mike is not a politician, then Mike is rich."

Answer:

.a^3-2a+3a^2+1\right)and\left(3-2a+a 2\ri

Step-by-step explanation:

pls brainliest

Answer:

the answer is 4a^2

Step-by-step explanation:

i just took the test

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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37.3 %

Explanation

Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %

so

therefore, the answer is 37.3 %

I hope this helps you

Answer:

Step-by-step explanation:

Greatest common factor of 6x and 9y is 3.

6x + 9y = 3(2x + 3y)

:::::

Greatest common factor of 3c and 11c is c.

3c + 11c = (3+11)c

We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

9514 1404 393

Answer:

  A, M, N, F

Step-by-step explanation:

I find it easier to look at the graph, rather than mess with the coordinate transformations. Each image point is the same distance from the line of reflection that its pre-image point is. The line joining the two points is perpendicular to the line of reflection.

See attached for the reflected points.

__

The red and turquoise dashed lines are the lines y=x and y=-x, respectively. The same-colored arrows show the reflection of the relevant point.

_____

The transformations of interest are ...

  (x, y) ⇒ (y, x) . . . . reflection over y = x

  (x, y) ⇒ (-x, y) . . . . reflection over y-axis

  (x, y) ⇒ (x, -y) . . . . reflection over x-axis

  (x, y) ⇒ (-y, -x) . . . . reflection over y = -x

Answer:

5/7

Step-by-step explanation:

ratio of boys to girls---> 2:5

ratio sum: 2+5=7

girls ratio =5/7

OR

total of people in 7th grade choir=28

hence, no of girls in 7th grade choir=5/7 × 28

=20

proportion of girls in choir= 20/28 = 5/7

Answer:

ahfjajsjdjadkfjfjakskhsk

Answer:

14 in .

Step-by-step explanation:

The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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Answer:

x = -14, 0

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

(x + 7)² - 49 = 0

Step 2: Solve for x

Step 3: Check

Plug in x values into original equation to verify they are a solution.

x = -14

Here we see that 0 does indeed equal 0.

∴ x = -14 is a solution of the equation

x = 0

Here we see that 0 does indeed equal 0.

∴ x = 0 is also a solution of the equation.

Answer:

Lesser x=-14 Greater x=0

Step-by-step explanation:

x+7)  

2

−49

(x+7)  

2

(x+7)  

2

​  

​  

=0

=49

=  

49

​  

​  

Hint #22 / 3

\begin{aligned} x+7&=\pm7 \\\\ x&=\pm7-7 \\ \phantom{(x + 7)^2 - 49}& \\ x=-14&\text{ or }x=0 \end{aligned}  

x+7

x

(x+7)  

2

−49

x=−14

​  

=±7

=±7−7

or x=0

​  

The correct answer is 12 teeth

Explanation:

The ratio represented by the diagram is 6:1 or 6/1, this means, for each 6 teeth in the larger gears there is only 1 in the smaller gear. Now, to find the number of teeth if the larger gear is 72 the best is to use cross multiplication. The process is shown below:

1. Write the known values, and use x to represent the value missing

\(\frac{6}{1} = \frac{72}{x}\)

2. Use cross multiplication, and then division to find x

\(6x =72\)

\(x =\frac{72}{6}\)

3. Solve the operation

\(x = 12\)

Answer:

12 Teeth

Step-by-step explanation:

I did it on Khan academy and got it right!!

Answer:

The first one

Step-by-step explanation:

She cant buy anything over $15, but she can buy something thats $15 :))

Answer:

A. P = 50,200(1 + 0.09)2

Answer:

P = 50200(1+0.09)²

Step-by-step explanation:

To find the answer to this question we use the equation new value = original value x \(d^{n}\), where d is the multiplier

We are told that our original value is 50200 and to find the multiplier we have to do 1 + 0.09. This is because the population is increasing by 9% which as a decimal is 0.09!

This means that our equation would be P = 50200(1+0.09)²

Hope this helps, have a lovely day! :)

The Solution of each options are given below.

A set is a grouping of unique items or components. Everything can be an object in a set, including letters, numbers, and even other sets. Sets are indicated by separating the elements with commas and enclosing them in curly braces.

Question asking about: Classify whether the following sets are in extension (E) form or Comprehension (C), also if it is: finite (F), infinite (1), null (N), unitary (U) and Convert from set form by extension to comprehension and vice versa.

a) A = {a, b, c}

Form: Extension (E)

Cardinality: 3 (finite)

b) B = {x / x is a factor of 4}

Form: Comprehension (C)

Cardinality: 3 (finite)

c) C = {x / x - 17 = 2}

Form: Comprehension (C)

Cardinality: 1 (unitary)

d) D = {2, 4, 6}

Form: Extension (E)

Cardinality: 3 (finite)

e) E = {x ∈ ℤ / x > 7}

Form: Comprehension (C)

Cardinality: ∞ (infinite)

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The Solution of each options are given below:

a) Cardinality: 3 (finite)

b) Cardinality: 3 (finite)

c) Cardinality: 1 (unitary)

d) Cardinality: 3 (finite)

e) Cardinality: ∞ (infinite)

Define the term Sets in mathematics?

A set is a collection of special objects or parts. Letters, numbers, and even other sets can all be considered objects in a set. Commas are used to separate the items and curly brackets are used to enclose them to signify sets.

Question asking about: Classify whether the following sets are in extension (E) form or Comprehension (C), also if it is: finite (F), infinite (1), null (N), unitary (U) and Convert from set form by extension to comprehension and vice versa.

a) A = {a, b, c}

Form: Extension (E)

Cardinality: 3 (finite)

b) B = {x / x is a factor of 4}

Form: Comprehension (C)

Cardinality: 3 (finite)

c) C = {x / x - 17 = 2}

Form: Comprehension (C)

Cardinality: 1 (unitary)

d) D = {2, 4, 6}

Form: Extension (E)

Cardinality: 3 (finite)

e) E = {x ∈ ℤ / x > 7}

Form: Comprehension (C)

Cardinality: ∞ (infinite)

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Answer:

The percentage rate per annum is 2.8%

Step-by-step explanation:

We need to multiply the principal by the time, then divide the interest by the product of P×T, so:

1,600 × 5 = 8,000

224 ÷ 8,000 = 0.028

Then we convert our final product to a percentage.

0.028 to a percent is 2.8%

Step-by-step explanation:

did u got the answer??.....

It is very likely that a vacuum will last between 5.5 and 7.5 years.

This is because we can use the properties of the normal distribution to calculate that about 68% of the vacuum cleaners will fall within one standard deviation of the mean, which in this case is between 6.5 - 0.5 = 6 and

6.5 + 0.5 = 7

About 95% of the vacuum cleaners will fall within two standard deviations of the mean, which in this case is between 6 - 0.5 = 5.5 and 6.5 + 0.5 = 7

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