A toy ball can be modeled as a sphere. Jeriel measures its diameter as 21.9 cm. Find
the ball's volume in cubic centimeters. Round your answer to the nearest tenth if
necessary.

Answer:

f^-1(x) = [tex]\sqrt[3]{(x + 4)/3}[/tex]

Step-by-step explanation:

y = 3x^3 - 4  ==> solve for x

y + 4 = 3x^3  ==> isolate x by adding 4 on both sides

(y + 4)/3 = x^3  ==> divide 3 into both sides

x = [tex]\sqrt[3]{(y + 4)/3}[/tex] ==> isolate x by taking the cube root on both sides

y = [tex]\sqrt[3]{(x + 4)/3}[/tex] ==> switch both x and y

f^-1(x) = [tex]\sqrt[3]{(x + 4)/3}[/tex]

Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.

The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. Polynomials are mathematical expressions made up of variables (also known as indeterminates) and coefficients. A mathematical expression known as a polynomial is made up of two or more algebraic terms that are added, subtracted, or multiplied (never divided!). In polynomial expressions, which often also have at least one variable, constants and positive exponents are frequently utilized. The equation x2 4x + 7 denotes a polynomial.

given

a) (a - b)(a - b) = a² - 2ab + b²

b. (a + b)(a - b) = a²-6²

c. (a+b) (a²-ab+6²) = a³ - 6³

d. (a-b) (a² + ab +6²) = a³ - 6³

e. (a + b)(a + b) = a² + 2ab + b²

Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.

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The complete question is :- Match the following polynomial by its factored form .

a. (a - b)(a - b)

b. (a + b)(a - b)

c. (a+b) (a²-ab+6²)

d. (a-b) (a² + ab +6²)

e. (a + b)(a + b)

The intercepts of the graph are

The polynomial is given as

G(x) = -2(3x+4)(x-1)(x-3)^2

Rewrite as

G(x) = -2(3x+4)(x-1)(x-3)²

The x-intercepts of a polynomial are the points at which the polynomial crosses the x-axis.

To find the x-intercepts, we need to set y = 0 and solve for x.

-2(3x+4)(x-1)(x-3)² = 0

Divide through by -1

(3x+4)(x-1)(x-3)² = 0

Now we can solve for each factor equal to zero:

3x+4 = 0, x = -1.33

x-1 = 0, x = 1

x-3 = 0, x = 3

So the x-intercepts are -4/3, 1, 3

The y-intercept of a polynomial is the point at which the polynomial crosses the y-axis.

For this polynomial, we have

G(0) = -2(30+4)(0-1)(0-3)² = -2(4)(-1)(9) = 72

So the y-intercept is (0, 72)

See attachment for the graph

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Answer: b

Step-by-step explanation:

Answer:

[tex]x=8.5[/tex]

Step-by-step explanation:

By the definition of a midpoint, [tex]TU=UV[/tex].

[tex]6=2x-11 \\ \\ 2x=17 \\ \\ x=8.5[/tex]

Answer:

Below

Step-by-step explanation:

Use the distance formula  ( a modification of Pythagorean theorem)

d^2 = ( x1-x2)^2 + (y1-y2)^2

  d^2 = (-7-2)^2 + (-6-4)^2

    d =  sqrt (181) =~ 13.454

Answer:

Step-by-step explanation:

Since 5 miles is approximately 8 kilometers, and Sawyer lives 12.7 kilometers from the soccer field, Sawyer lives farther than Jabar from the soccer field.

So Sawyer lives about 4.7 kilometers farther from the soccer fields.

Answer:

6

Step-by-step explanation:

20 divided by 3 without any remainders, fractions, or decimals is 6.

Hope I helped!

Answer:

the answer is 1

Step-by-step explanation:

b(n) = -4 so b(n) is 2-4 then n is -1

b(n) = -2

n = -1

Answer:

Step-by-step explanation:

b(n) = -4 -2(n -1)

Find the 12th term in the sequence.

Put 12 where n is and evaluate.

The 12th term of the sequence is -2052.

The geometric series of the pattern is -512 for n = 9: -2, -4, 8-16,. is a geometric progression  and .

In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward illustration and converges to a sum of 2. (or 1 if the first term is excluded).

is a geometric progression  and r= 2.

is a geometric progression ai —2 and r= 2.

= —512

The place w Formulas are employed.

In this instance, we have  and n=9. These values are added to the formula above to get the following results:

an

9—1

-2. (256)

= —512

The initial terms in this series are:

8, -16...

The total number of terms in a geometric sequence makes up a geometric series. Using the initial term  and the common ratio r, it is possible to determine the nth partial sum of a geometric series as follows: .

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Answer:

x=2.28

Step-by-step explanation:

7x +y=11 we substitute y by ( -5)

7x +(-5)=11 (+)×(-)= --

7x-5=11

7x=11+5 when we move -5 to the opposite it become +5

7x =16

x=16 ÷7

x=2.28

Answer:

x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2

Step-by-step explanation:

Solve for x:

x^2 - 5 x + 7 = 0

Subtract 7 from both sides:

x^2 - 5 x = -7

Add 25/4 to both sides:

x^2 - 5 x + 25/4 = -3/4

Write the left hand side as a square:

(x - 5/2)^2 = -3/4

Take the square root of both sides:

x - 5/2 = (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2

Add 5/2 to both sides:

x = 5/2 + (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2

Add 5/2 to both sides:

Answer: x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2

Answer:

23.2wx - 13.2w

Step-by-step explanation:

4w (5.8x - 3.3) =

4w * 5.8x - 4w * 3.3 = distribute 4w to 5.8x and 3.3

4 * 5.8 *w * x - 4w * 3.3 =

23.2 * w * x - 13.2w  ==> simplify

23.2wx - 13.2w

Answer:

Below

Step-by-step explanation:

3 (x-12) = 15     divide both sides of the equation b y 3 to get :

x-12 = 5           now add 12 to both sides

x = 17       Done.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Solving for x or simplify this equation}[/tex]

[tex]\mathsf{3(x - 12) = 15}[/tex]

[tex]\huge\textbf{DISTRIBUTE 3 within PARENTHESES}[/tex]

[tex]\mathsf{3(x) + 3(-12) = 15}[/tex]

[tex]\mathsf{3x - 36 = 15}[/tex]

[tex]\huge\textbf{ADD 36 to BOTH SIDES}[/tex]

[tex]\mathsf{3x - 36 + 36 = 15 + 36}[/tex]

[tex]\huge\textbf{SIMPLIFY IT}[/tex]

[tex]\mathsf{3x = 15 + 36}[/tex]

[tex]\mathsf{3x = 51}[/tex]

[tex]\huge\textbf{DIVIDE 3 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{3x}{3} = \dfrac{51}{3}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT}[/tex]

[tex]\mathsf{x = \dfrac{51}{3}}[/tex]

[tex]\mathsf{x = 17}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 17}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

A table which has a constant of proportionality between y and x of 0.9 include the following: B. table B.

In order to have a proportional relationship and equivalent ratios that is constant, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) based on the given parameters in each table:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 17/18

Constant of proportionality (k) = 0.94 (False).

For the variables x and y in table B, the constant of proportionality (k) is given by;

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 3.6/4 = 5.4/6 = 10.8/12

Constant of proportionality (k) = 0.9 (True).

For the variables x and y in table C, the constant of proportionality (k) is given by;

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 3.3/3

Constant of proportionality (k) = 1.1 (False).

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The time when the two submarines will be at the same depth is 25 minutes.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, Submarine A is 1200 feet underwater and has descended at a constant rate of 12 feet per minute. Submarine B is 1100 feet underwater but descends at a constant rate of 16 feet per minute

The equation will be:

1200 - 12m = 1100 - 16m

Collect the like terms

16m - 12m = 1200 - 1100

4m = 100

Divide

m = 100 / 4

= 25 minutes

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The Z-Score associated on moving one standard devations to the right is equals to the 1.0, i.e., Z = 1.00. So, correct answer is option (c).

We have, The number of classes, n = 5

Mean of size of five classes,µ = 44

Standard deviations for five classes,σ = 8

The dynamic equation for conversion to z-scores in real-time is, Z = (Xᵢ - µ )/standard deviations (s)

Z-Score : A Z-Score is a metric that represents that how closely a value relates to mean of set of values. If Z score value is zero that means data point's scores are same as mean score.

Formula for Z- Score is Z = (X - µ)/σ

where, X ---> data values

µ --> mean of values

σ --> standard deviation

For 32, Z = (X - µ)/σ = (32 - 44)/8 = -1.50

For 42 , Z= (X- µ)/σ = (42 - 44)/8 = -0.25

For 48, Z = ( 48 - 44)/8 = 0.5

For 52, Z = ( 52 - 44)/8 = 1.0

For 54, Z = (54 - 44)/8 = 1.25

When we move One standard deviations to right , that means X = 44 + 8 = 52 , So the Z-Score for 52 is Z = 1.0. Hence, required value is 1.0.

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Complete question:

The dot plot below shows the sizes for five classes with a mean of 44 and standard deviation of 8. The dynamic equation shows the mathematical conversion to z-scores in real-time. Drag the vertical line to see the corresponding z-score for each possible class size,

Z =( Xᵢ - X)/s Created by Gary M. McClelland, Professor Emeritus | University of Colorado Boulder Cengage Learning. All Rights Reserved. 1. Make sure the green line is on the mean value of x= 44. Next, move the green line one standard deviation to the right. What Z-score is associated with this value?

a. ) Z-0.75

b) Z= 0.80

c) Z = 1.00

d) Z = 0.5

The value for expression 2/3xy² when x = -1/3 and y = 1/2 is 8.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is 2/3xy².

The value of x is given as x = -1/3.

The value of y is given as y = 1/2.

To find the value of the expression, substitute the value of x and y in the expression -

= 2/3xy²

Expand using the power rule -

= [2/(3 × (-1/3) × (1/2)²)]

Use the arithmetic operation of multiplication -

= [2/(3 × (-1/3) × (1/4)]

= [-2/(-3/12)]

= -2/(-1/4)

The denominator will reciprocate -

= -2 × -4

= 8

Therefore, the final value is obtained as 8.

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The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.

The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

transformation of functions

f(x) - f(x) -2

translate 2 units down

f(x) - f(x - 2)

translate 2 units right

f(x) - f(x) + 2

translate 2 units up

The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.

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Answer: y = 40

Step-by-step explanation:

we know 5x=40 so the 2 bottom angles combined are 80

so you have 2y+20=100

2y=80

y=40

The person must leave the money for  18.6 .

         [tex]A= P (1 +\frac{r}{n} )^{nt}[/tex]

        A =Amount = 2900

        P = Principal = 1000

        r = ratio =  5.75%

        2900 = 1000[tex](1 +\frac{5.75}{12} )^{12x[/tex]

        2900 = 1000 [tex](1 +\frac{575}{120000} )^{12x[/tex]

        2900 = 1000[tex](1 +\frac{23}{4800} )^{12x\\\\[/tex]

        2900 = 1000[tex](1 +\frac{4823}{4800} )^{12x\\\\[/tex]

       2900/1000 = 1000[tex](\frac{4823}{4800} )^{12x\\\\[/tex]

               29/ 10 = [tex](\frac{4823}{4800} )^{12x\\\\[/tex]

         12x = [tex]log _{\frac{4823}{4800} }\frac{29}{10}[/tex]

            [tex]x = \frac{log _{\frac{4823}{4800} }\frac{29}{10}}{12}[/tex]

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Answer:

12

Step-by-step explanation:

2w + 4 = 28

2w = 24

w = 12

w = 12.

[tex]2w+4=28[/tex]

[tex]2w+4-4=28-4\\ \\2w=24[/tex]

[tex]\frac{2w}{2} =\frac{24}{2} \\ \\w=12[/tex]

To verify the answer, write the original expresion and substitute variable "w" by the calculated value (12). If the calculations equal the same number of both sides of the equal sign (=) then the answer is correct.

[tex]2(12)+4=28\\ \\24+4=28\\ \\28=28[/tex]

The same number appears on both sides of the equal sign. Hence, the answer is correct!

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If triangle ABC has the following measurements, than the measure of side c is 25.08

What is triangle ?

A triangle in which it contains three sides and three angles and the sum of three angles be 180 degrees.
Given ,

a = 17

b = 23

C = 76 degrees.

So,

we know that,

c = [tex]\sqrt{a^{2}+b^{2}-2abcosc }[/tex]

c = [tex]\sqrt{17^{2} + 23^{2} - 2*17*23*cos76 }[/tex]

c = [tex]\sqrt{289 + 529 - 884*cos76}[/tex]

c = [tex]\sqrt{818-189}[/tex]

c = [tex]\sqrt{629}[/tex]

c = 25.08

hence , If triangle ABC has the following measurements, than the measure of side c is 25.08

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Answer:

x = - 2

Step-by-step explanation:

the magnitude of a vector < a, b, c > is

[tex]\sqrt{a^2+b^2+c^2}[/tex]

given vector < 1, 2, x > has magnitude of 3 , then

[tex]\sqrt{1^2+2^2+x^2}[/tex] = 3

[tex]\sqrt{1+4+x^2}[/tex] = 3

[tex]\sqrt{5+x^2}[/tex] = 3 ( square both sides to clear the radical )

5 + x² = 3² = 9 ( subtract 5 from both sides )

x² = 4 ( take square root of both sides )

x = ± [tex]\sqrt{4}[/tex] = ± 2

since x is negative then x = - 2

Answer is B

y=16.9x+0.7

To Calculate line of best fit you can simply input the values into the stats function on your calculator and using the "Reg" function to get your values of the standard equation form of your line of best fit which is y=bx+a

b=16.9

a=0.7

If the streetlights are spaced in the same way, there will be 48 streetlights on the 4-mile road.

First, we know that there are 18 streetlights evenly spaced on a 1.5 mile road.

Then the space between consecutive streetlights is:

1.5mi/18 = (3/36) mi = (1/12) mi

Now, the number of streetlights that we will have on a 4-mile road is given by the quotient between the length of the road and the distance between consecutive streetlights, it is:

N = 4mi/(1/12 mi) = 12*4 = 48

There will be 48 streetlights on a 4 mile road.

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The mathematical expression which correctly uses exponents to write "6 factors of 2" include the following: B. 2⁶

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as bⁿ.

In Mathematics, factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors simply refers to numbers which can be multiplied together to get another number.

Next, we would translate the word statement into an algebraic expression as follows;

6 factors of 2 = 2 × 2 × 2 × 2 × 2 × 2

6 factors of 2 = 2⁽¹ ⁺ ¹ ⁺ ¹ ⁺ ¹ ⁺ ¹ ⁺ ¹⁾

6 factors of 2 = 2⁶

In this context, we can reasonably infer and logically deduce that "6 factors of 2" can be correctly written by using an exponent as 2⁶.

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Complete Question:

Which of the following correctly uses exponents to write "6 factors of 2"? A. 6² B.2⁶ C. 6 ∙ 2 D. 12

Answer:

B. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means that there are 10³ cubic decimeters in a cubic meter.

Step-by-step explanation:

When we cube a number, we multiply the number by itself twice.

Therefore a cubic meter is:

To calculate the number of cubic decimeters in a cubic meter, we need to cube the number of decimeters in a meter.

Given there are 10 decimeters in a meter, then there are 10³ cubic decimeters in a cubic meter:

The area of rectangle with length 3x + 2 and width 3x - 4 is 9x² - 6x - 8.

Once the length and width of a rectangle are known, the area is calculated. The area of a rectangle can be calculated by multiplying its length and width.

Here given that,

The rectangle's length is (3x + 2) units.

The width of the rectangle is (3x - 4).

We must determine the area of a rectangle.

Now,

Since the area of a rectangle equals length x width .

As a result, the area of a rectangle equals,

A = (3x + 2)  (3x - 4)

By simplifying the expression we get,

= (3x)(3x) + (3x)(-4) + 2(3x) + 2(-4)

= 9x² - 12x + 6x - 8

= 9x² - 6x - 8

Therefore the area of rectangle will be 9x² - 6x - 8.

The complete question:

"The length of a rectangle is 3x + 2 and the width is 3x – 4. What is the area of the rectangle in terms of x?"

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