A troupe of 12 dancers is going to line up on stage. Of these dancers, 6 are wearing green and 6 are wearing blue. A dancer wearing green must be in the first position and they must alternate between colors. In how many ways can the dancers line up?

The option B is correct, The second expression gives the correct value -24.

According to the statement

we have given that the some expression and a = -2 and b = 3 and we have to which expression gives a output of answer -24 after put the values in the expressions.

So, For this purpose

First expression:

[tex]a\sqrt{16} + b - 10[/tex]

Put a = -2 and b = 3

then

[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]

Second expression:

[tex]a(\sqrt{16} + b) -10[/tex]

Put a = -2 and b = 3

then

[tex]a(\sqrt{16} + b) -10\\-2(4 +3) -10\\-14-10\\-24[/tex]

Now,

Third expression:

[tex]a\sqrt{16} + (b - 10)[/tex]

Put a = -2 and b = 3

then

[tex]a\sqrt{16} + (b - 10)-2*4 + (-7)\\-8-7\\-15[/tex]

Now,

Fourth expression and first expression are same,

So,

Fourth expression:

[tex]a\sqrt{16} + b - 10[/tex]

Put a = -2 and b = 3

then

[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]

The second expression gives the correct value -24.

So, The option B is correct, The second expression gives the correct value -24.

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The amount she should invest today in the annuity is $455,450.40.

The first step is to determine the future value of the monthly annuity.

Future value = monthly payment x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Future value : 3250 x [(1.003^180) - 1] / 0.003 = 774,171.92

The second step is to determine the present value of this future annuity:

774, 171.92 / (1.036^15) = $455,450.40

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By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.

According to the image, we have a composite figure formed by two right prisms. The surface area of this figure is the sum of the areas of its faces, represented by squares and rectangles:

A = 2 · (4 cm) · (5 cm) + 2 · (2 cm) · (4 cm) + (2 cm) · (5 cm) + (3 cm) · (5 cm) + (5 cm)² + 4 · (3 cm) · (5 cm)

A = 166 cm²

By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.

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The value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7

The eight-digit number is given as:

7448X24Y

Also, from the question

The number is divisible by 8 and 9

When a number is divisible by 8, then the last three digits of that number would be divisible by 8.

When a number is divisible by 9, the sum of the digits of the number would be divisible by 9.

So, we have:

24Y is divisible by 8

The possible value of Y from the above statement is 0

This is so because 240 is divisible by 8

The sum of the digits of the number would be divisible by 9.

This means that:

7 + 4 + 4 + 8 + X + 2 + 4 + Y = 29 + X + Y

Substitute 0 for Y

29 + X + Y = 29 + X + 0

Evaluate the sum

29 + X + Y = 29 + X

36 is divided by 9

So, we have

29 + X = 36

Subtract 29 from both sides of the equation

X = 7

So, we have

X = 7 and Y = 0

X - Y is calculated as:

X - Y = 7 - 0

Evaluate the difference in the above equation

X - Y = 7

Hence, the value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7

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Answer: 0

Step-by-step explanation: I am going by the words , there WERE 3 ponies. So Sarah couldn’t take any rides.

Answer:

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a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

We have,

(a) To write the number 0.00000896 moles per liter in scientific notation, we move the decimal point to the right until there is one

non-zero digit to the left of the decimal point.

The number of decimal places we moved to the decimal point will be the exponent of 10 in the scientific notation.

So,

= 0.00000896

= 896/100000000

= 896 x 100/100 x [tex]10^{-8}[/tex]

= 896/100 x [tex]10^{-8 + 2}[/tex]

= 8.96 × [tex]10^{-6}[/tex]

(b)

To write the number 1.1105 pounds in standard notation, we simply write the number as it is, without any scientific notation or exponent.

1.1105 pounds is written in standard notation as 1.1105 pounds.

Thus,

a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

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Step-by-step explanation:

(7m - 3)² = 49m² - 42m + 9

play it through and do the actual multiplication behind the square :

(7m - 3)² = (7m - 3)(7m - 3) =

= 7m×7m + 7m×(-3) + (-3)×7m + (-3)(-3) =

= 49m² - 2×21m + 9 = 49m² - 42m + 9

For the given set A, A is a set of x, where x depends on n. x= 11, where the values of n in ascending order are 1,2,3,4.

Simply put, a set in mathematics is a grouping of different items.

An element of the set is any component of the set. When writing a set, curly brackets are utilized.

The components of a set can be represented using a variety of notations. Typically, sets are represented using a set builder form or a roster form.

According to the question,

A = {11,22,33,44}

The elements of set A are all multiples of 11. These can be expressed as 11*n, here, n has the values of 1,2,3 and 4.

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Answer:

Step-by-step explanation:

8weeeks bc 22.50*8=180

Answer:

Option 3

Step-by-step explanation:

[tex]\frac{5}{3}=\frac{AD}{7-AD} \\ \\ 35-5AD=3AD \\ \\ 35=8AD \\ \\ AD=4 \frac{3}{8}[/tex]

The value of the evaluation of logarithm e^in4 is 4

Given the expression as;

e^in4

To put in logarithmic form, equate to the power of the "Lin,ln value"

Now, let's equate it to the value of the exponential

e^in4 = 4

We have that'

[tex]loge x = loge 4[/tex]; this is the logarithmic form of the expression but we need to find the value of 'x'

To find the value, let's cancel out the like variables, we have

[tex]x = 4[/tex]

Then we have the value to be

x = 4

Thus, the value of the evaluation of logarithm e^in4 is 4

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Answer:

mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Answer:

The number of points of intersection between the rectangle and hexagon is = 4

The point of intersection between two or more lines is where the lines met at a particular plane. The point of intersection an equally be referred to as the vertex.

A rectangle is a quadrilateral because it's made up of four sides of which the two sides which are opposite, are equal and parallel.

A triangle is a polygon that is made up of three lines that meet to form edges and angles.

A hexagon is a polygon that is made up of six sides and six angles.

From the attached image, the rectangle which has four sides, made an intersection with the hexagon at four points which are marked with an asterisk.

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Answer:

2

Step-by-step explanation:

Answer:

33 units²

Refer to the attached page

I've shown the complete calculation over there.

Answer: 33

Step-by-step explanation:

one easy way to do it is by finding the area of the 4 triangles.

because the top two and the bottom two are the same that helps a lot. The first triangle is 9 times three and then cut your answer in half. Do the same thing for the other 9 times three triangle you will end up with 27. for the top two you would multiply 3 times two to get 6 cut 6 in half to get 3. do the same or the other triangle and now you just have to add.

3 plus 3 plus 13.5 plus 13.5

to get 33

The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

Given that the function is f(x)=IxI+5.

We are required to find the range of the function.

Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.

Function is f(x)= IxI+5

We know that IxI=x for x>=0 and -x<0.

We have to just put the value of IxI in f(x) to get the range of function.

f(x)=x+5 for x>=0 and -x+5 for x<0.

Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.

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Step-by-step explanation:

4W-8=3W+6

4W-3W=6+8

W=14°

lets find the value of W in this straight line

4W-8°=180°(angle on a straight line)

collect like terms

4W=180°+8°

4W=188°

divide both sides by the coefficient of W which is 4

W=47°

if i am correct pls rate it

Answer:

6x<48

Step-by-step explanation:

ik its this one because theres 48 players and 6 teams both are even numbers so if you did 48÷6x you would get 8 but theres fewer than 48 kids

The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

The given parameters are:

Rate, r = doubles every two days

Initial number of strain, a = 1

This means that the function is an exponential function.

An exponential function is represented as:

A(d) = a * r^d

Since the strain doubles every two days, we have:

A(d) = a * r^(d/2)

Substitute the known values in the above equation

A(d) = 1 * 2^(d/2)

Evaluate the product

A(d) = 2^(d/2)

When there are 256 bacterial cells, the equation becomes

2^(d/2) = 256

Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

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Answer:

4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

Step-by-step explanation:

28[tex]v^{7}[/tex]x³[tex]y^{6}[/tex] - 12[tex]v^{9}[/tex][tex]x^{9}[/tex] ← factor out 4[tex]v^{7}[/tex]x³ from each term

= 4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])

Answer:

y = 1/2 x  + 3

Step-by-step explanation:

Find slope, m = (y1-y2)/(x1-x2) =  (7-0) / (8- - 6)  = 7/14 = 1/2

   ( does not matter which one you assign as point 1 or point 2)

Point (-6,0)  slope form ( you can use either point)

(y-0) = 1/2 (x- -6)

y = 1/2 x +3

Answer:

a. 400

b. 4$

Step-by-step explanation:

2$ equals 0 Quantity

3$ equals 100 Quantity

4$ equals 200 Quantity

We can see that starting from 2$, a dollar will increase the Quantity by 100

The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

Given the function;

f(x) = −4| x-3 | + 12

First, we find the x-intercepts by simply substituting 0 for y and solve for x.

f(x) = −4| x-3 | + 12

y = −4| x-3 | + 12

0 = −4| x-3 | + 12

−4| x-3 | + 12 = 0

−4| x-3 | = -12

Divide both sides by -4

| x-3 | = 3

We remove the absolute value sign

x - 3 = ±3

x = 3±3

x = 3-3, 3+3

x = 0, 3

Hence, x-intercepts are: ( 0, 0 ), ( 6, 0 )

Next, we find the y-intercept by substituting 0 for x and solve for y.

f(x) = −4| x-3 | + 12

y = −4| 0-3 | + 12

y = −4| -3 | + 12

We remove the absolute value sign

y = −4(3) + 12

y = −12 + 12

y = 0

Hence, y-intercept is: ( 0, 0 ).

The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.

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Using the z-distribution, the 95% confidence interval for the proportion is given as follows:

(0.4576, 0.5824).

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The other parameters for the interval are given as follows:

[tex]n = 246, \pi = 0.52[/tex].

The lower and upper bound of the interval, respectively, are given by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]

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Answer:

Step-by-step explanation:

Begin by filling in x as -2 and y as √12 in the given expression:

[tex]2(3(-2)^3+2(\sqrt{12})^2)[/tex].  Work inside the parenthesis first and deal with those exponents:

(-2)³ is the same as (-2)(-2)(-2) which is -8;

(√12)² is the same as (√12)(√12) which is √144 which is 12.

Filling those simplifications in:

[tex]2(3(-8)+2(12))=2(-24+24)=2(0)=0[/tex]

Answer: (x-2)

Step-by-step explanation:

This problem is a middle-term factorization, or factoring by splitting the middle term.

We have the equation

x^2 - 18x + 32

This equation represents the area, and area = length x width for all rectangles. We also know the width, x-16, which makes it easier for us. The length must also be in the same format.

x^2 - 18x + 32

= x^2 - 16x - 2x + 32

= x(x-16) - 2(x - 16)

= (x-16) (x-2) -------> we get this through taking (x-16) common

We could also pretend that the length is x - y, where y is the number we need to finish the equation.

x^2 - 18x + 32

= (x-16) (x-y)

= x^2 -16x - xy + 16y

-16 minus 2 is -18, which is our middle term.

Therefore, y = 2. This is also verified because is 16y = 32, the constant term, then through transposing we get y = 2.

Our answer is that the length is (x-2).

Answer:

A cone has one -third times the volume of a cylinder with the same base and altitude. True

The answer is A. True.

Assuming the cylinder and cone have same base and altitude, the formulas are :

Based on this, we can understand that :

A cone has one-third times the volume of a cylinder with the same base and altitude.

The value of the probability P(A) is 0.40

The given parameters about the probability are

P(A or B) = 0.6

P(B) = 0.3

P(A and B) = 0.1

To calculate the probability P(A), we use the following formula

P(A and B) = P(A) + P(B) - P(A or B)

Substitute the known values in the above equation

0.1 = 0.3 + P(A) - 0.6

Collect the like terms

P(A)= 0.1 - 0.3 + 0.6

Evaluate the expression

P(A)= 0.4

Hence, the value of the probability P(A) is 0.40

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The length of the vine wounded to the tree is 21 feet.

Circumference is the perimeter of a circular object. Therefore,

circumference = 2πr

where

The circumference of the tree is 3 feet. A vine was wound around 7 times .

The length of the vine can be calculated as follows:

Therefore,

circumference = 3 ft

length of the vine = 7 × 3

length of the vine = 21 feet

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Answer:

85 C

Step-by-step explanation:

Temperature range means the difference between the maximum and minimum in temperature for an area. 40C-(-45C)=85 C