is 66 a perfect cube with prime factorization​

Answer: Option (2)

Step-by-step explanation:

[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].

Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].

So, the answer is Option (2).

The solution to the inequality is (-4, ∞)

The second inequality is given as:

8 - y < 12

Subtract 8 from both sides

-y < 4

Rewrite as:

y > -4

In interval form, we have:

y = (-4, ∞)

Hence, the solution to the inequality is (-4, ∞)

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Using the given exponential function, we have that:

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the function is:

[tex]A(t) = 523(0.5)^{\frac{t}{30}}[/tex]

Hence the initial amount is of 523 grams.

The amount after 50 years will be given by:

[tex]A(50) = 523(0.5)^{\frac{50}{30}} = 165[/tex]

The amount after 50 years will be of 165 grams.

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The amount going to her savings accounts is $192

The given parameters are:

Drawings = 24

Rate = $12

The total amount earned from selling the drawings is:

Total = 24 * $12

Evaluate

Total = $288

She buys books with 1/3.

This means that she saved 2/3

So, we have:

Savings = 2/3 * $288

Evaluate

Savings = $192

Hence, the amount going to her savings accounts is $192

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Answer:

C , D , B

Step-by-step explanation:

Trigonometry is given by three formulas :

SOH - CAH - TOA

Hope this helped and have a good day

Marisol did a mistake while grouping the terms in Step 1, with the sign. Thus, Marisol should go back and group the terms in Step 1 as (6x³ - 22x²) - (9x - 33). Hence, the second option is the correct choice.

The polynomial Marisol had was 6x³ - 22x² - 9x + 33.

The steps she did in the grouping of terms and factoring out the GFC out of the groups were:

Step 1: (6x³ - 22x²) - (9x + 33).

Step 2: 2x²(3x - 11) -3(3x + 11).

After this Marisol was unable to get a common factor to proceed further.

The mistake that Marisol did was in Step 1, as while grouping -9x and +33, she took the minus sign out, which will make -9x to become 9x, but 33 to become -33.

This is where she made the mistake and writing - (9x + 33) in place of - (9x - 33).

Thus, her steps should have been:

Step 1: (6x³ - 22x) - (9x - 33),

Step 2: 2x²(3x - 11) -3(3x - 11), which gives her a common factor (3x - 11), to continue with the third step:

Step 3: (2x² - 3)(3x - 11).

Refer to the attachment for the complete question, as the given question is incomplete.

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The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.

It should be noted that a inference simply means the conclusion that can be deduced based on the information given.

In this case, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette.

Hence, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts. Therefore, ordering matters.

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The amount loaned at the interest rate of 11% is $3000.

The amount loaned at the interest rate of 7% is $16,500

0.11a + 0.07b = 1485 equation 2

Where:

a = amount loaned at the interest rate of 11%

b = = amount loaned at the interest rate of 7%

In order to determine how much was loaned at 7%, take the following steps:

Multiply equation 1 by 0.11:

.11a + 0.11b = 2145 equation 3

Subtract equation 2 from equation 3:

0.04b = 660

Divide both sides by 0.04:

b = 16,500

Subtract 16,500 from 19,500 :

19,500 - 16,500 = $3000

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Answer:

160.14  mm^2

Step-by-step explanation:

Area of a circle = pi r^2

subtract the area of the smaller circle from the larger

  note that the smaller radius = 7 mm

pi ( 10^2  - 7^2 ) =

3.14 ( 51) = 160.14 mm^2

The area of the washer is approximately 160.14 square millimeters.

Use the concept of the circle defined as:

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle.

Additionally, every angle possesses rotational symmetry around the center.

Given that,

The outer radius of the washer: 10mm

Diameter of the hole: 14mm

π value to be used: 3.14

To find the area of the washer:

Subtract the area of the hole from the area of the outer circle.

The area of a circle is given by the formula A = πr²,

Where r is the radius.

For the outer circle:

The radius is 10mm, so the area of the outer circle = 10²π.

The area of the outer circle = 100π mm²

For the hole,

The diameter is 14mm,

So the radius of the hole = 7 mm.

The area of the hole = 7²π

The area of the hole = 49π mm²

To find the area of the washer,

Subtract the area of the hole from the area of the outer circle:

Area of washer = Area of the outer circle - Area of hole

Area of washer = (100π - 49π) mm²

Area of washer = 51π mm²

Area of washer ≈ 160.14 mm²

Hence,

The area of the washer is approximately 160.14 square millimeters.

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The attached figure represents the complete flowchart.

The given statement is:

∠1 ≅ ∠2

To prove

∠3 ≅ ∠4

By vertical angle theorem, we have:

∠2 ≅ ∠4

By transitive property of congruence, we have:

∠2 ≅ ∠3

By transitive property of congruence, we have:

∠1 ≅ ∠3

By vertical angle theorem, we have:

∠3 ≅ ∠4

See attachment for the complete flowchart.

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Answer:

constant (unchanged) ratio of two variable quantities

Step-by-step explanation:

y = k x ( or y = k x )

y = 15 when x = 24, find x when y = 25. find the constant of variation.

Answer:

1960cm squared

Step-by-step explanation:

in case you're still confused ask where you're still confused and I'll offer my assistance.good day.

Step-by-step explanation:

so, what do we need to do ?

just solve these equations and find Sam's age (and Harry's) ?

x = 3y

x = 10 + 2y

so, we simply use the first equation in the second :

3y = 10 + 2y

y = 10

x = 3y = 3×10 = 30

Sam is currently 30 years old, Harry is 10.

The regression equation is (d) log(y) = 0.064x + 1.706

The table of values is given as:

x   2   3   4   5   6

y   73  77  85  101  133

Calculate the logarithm of the y values.

So, we have:

x          2   3   4   5   6

log(y)   1.86  1.89  1.93  2  2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

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Answer: D. log(y) = 0.064x + 1.706

Step-by-step explanation: I got it right on my test

Hence, the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

the correct option is "The 1990s basketball player did better than the current basketball player because his z-score is higher."

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The percentage increase China's population from 1970 to 1995 is: 56.25%.

Percentage increase = (Final Value - Original Value)/Original value × 100.

Given the following:

Original value = 0.8 billion

Final Value = 1.25 billion

Final Value - Original Value = 1.25 - 0.8

Final Value - Original Value = 0.45

Percentage increase = 0.45/0.8 × 100 = 56.25%.

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Answer:
I can help, its 45

Answer:

Since there are 20 chickens in one supermarket, and 25 chickens in the other supermarket, there are 45 chickens to choose from.

Answer:

Step-by-step explanation:

First, let's start by removing the parentheses and simplifying the expression.

3.125 + - 3.9 - 2.46

Adding a negative number is the same as subtracting it, so we can remove the + sign.

3.125 - 3.9 - 2.46

From there, we can do simple subtraction and get:

-3.235

Answer:

3 is the mode

Step-by-step explanation:

Answer:

all real numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Comment

You are going from a very small number (like - 100000) to a very large number (like + 100000).

But neither of those could be the answer. They are either not small enough or not large enough. The domain must look like this.

- ∞ < x < ∞

Answer: So the domain is all the real numbers.

The volume of the baseball roundibg off to nearest whole number is 14 cube inches.

If radius of a sphere is r and the volume of that spherical figure is given by V then,

[tex]V=\frac{4}{3}\pi r^3[/tex]

So in the problem the object is a baseball which is a sphere for sure.

Given that the diameter of that baseball is 3 inches.

So the radius of that baseball is given by = 3/2 = 1.5 inches.

Hence the volume of that base ball is

[tex]=\frac{4}{3}\pi\times(1.5)^3 \approx 14.1372 \approx 14[/tex]

Thus the volume of the baseball rounding off to nearest whole number is given by 14 cube inches.

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There are actually 5040 ways of arranging the letter knitting.

Answer:

slope: 14

y intercept: (0,9)

Step-by-step explanation:

in the form y = mx + b, the slope is m: 14

to solve for the y intercept, we set x as 0: 14 * 0 + 9 = y interecept is 9.

Answer:

In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?

Choose the most logical value for the variable to represent.

x= Diana's age now

This question is impossible to fully answer without further context. (Who is Dianna? Why do we need her age?)

However, it can be noted that [tex]x[/tex] is easily the most common variable name whenever you have a missing value in an equation. Generally, it is understood by mathematicians that [tex]x[/tex] and most other letters denote an unknown value, something to either use in solving the equation or something to find on its own.

The relative frequency of the third class is 3/20.

Relative frequency measures how often a value appears relative to the sum of the total values. It is determined by dividing the frequency of a class by the total frequency.

Relative frequency = frequency of the third class / total frequency

6/(3 + 10 + 6 + 15 + 6)

6/ 40 = 3/20

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Using the Fundamental Counting Theorem, it is found that:

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For the 2 letters(26 outcomes each), and 3 numbers(10 outcomes each), we have that the parameters are:

[tex]n_1 = 26, n_2 = 26, n_3 = 10, n_4 = 10, n_5 = 10[/tex]

Hence the number of catalog numbers is:

[tex]N = 26^2 \times 10^3 = 676000[/tex]

The ID number is divisible by 5 if the last digit is either 5 or 0, hence [tex]n_5 = 0[/tex] and the probability is:

[tex]p = \frac{26^2 \times 10^2 \times 2}{26^2 \times 10^3} = 0.2[/tex]

There is a 0.2 = 20% probability that the ID number is divisible by 5.

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Work Shown:

[tex]a^2+b^2 = c^2\\\\5^2+b^2 = 13^2\\\\25+b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12\\\\[/tex]

I used the pythagorean theorem.