in how many ways can five girls and five boys stand in line if boys and girls must alternate?

[tex]a_n=2^n\\\\a_1=2^1=2\\\\a_2=2^2=4\\\\a_3=2^3=8\\\\a_4=2^4=16\\\\Answer:\ C.\ \{2,\ 4,\ 8,\ 16\}[/tex]

The length of the fabric is 4 cm.

To find the length of the piece of fabric, we need to divide the area by the width. The area of the fabric is given as 20 cm squared and the width is given as 5 cm. So, to find the length, we divide 20 cm squared by 5 cm:

Length = Area / Width

Length = 20 cm2 / 5 cm

Length = 4 cm

Therefore, the length of the piece of fabric is 4 cm.

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That's true. If A is a subset of B, it means that every element in A is also an element in B. This means that B has, at least, as many elements as A. Nothing prevents B from having more elements though, which don't belong to A.

Consider this example:

[tex] A = \{1,2,3,4\},\quad B=\{1,2,3,4,5,6\} [/tex]

A is a subset of B, because every element of A (1,2,3,4) is also an element of B (1,2,3,4 are in B as well).

Still, B has two more elements (5,6) which don't belong to A, so a superset can have (and typically does actually) more elements than its subset.

Final answer:

The statement is true; if set A is a subset of set B (A⊂B), it means all elements of A are also in B, but B can have more elements.

Explanation:

The statement If a ⊂ b, b may have more elements than a is true. In set theory, the symbol ⊂ denotes that one set is a subset of another. If we say that set A is a subset of set B (A⊂B), it means that all elements of A are also in B. However, B can have additional elements that are not in A, which would make it larger. To illustrate, if we have A = {1,3} and B = {1,2,3,4}, A is a proper subset of B because all elements of A are in B, but B has more elements (2 and 4) that are not in A. If A and B were identical, then we would say A = B, not A⊂B.

Answer:

y = 5cos(πx/4) +11

Step-by-step explanation:

The radius is 5 ft, so that will be the multiplier of the trig function.

The car starts at the top of the wheel, so the appropriate trig function is cosine, which is 1 (its maximum value) when its argument is zero.

The period is 8 seconds, so the argument of the cosine function will be 2π(x/8) = πx/4. This changes by 2π when x changes by 8.

The centerline of the wheel is the sum of the minimum and the radius, so is 6+5 = 11 ft. This is the offset of the scaled cosine function.

Putting that all together, you get

... y = 5cos(π/4x) + 11

_____

The answer selections don't seem to consistently identify the argument of the trig function properly. We assume that π/4(x) means (πx/4), where this product is the argument of the trig function.

Answer:

Step-by-step explanation:

You have to start by making a small chart of what  is happening at what time.

x    0        4        8

y    16       6       16

Essentially this is a cosine function.

Now you need to fill in some of the details. The key is what is happening at x = 4 seconds? At that time, you must add a minus amount in the cosine function to the amplitude to get 6. The only way to do that is if you have

y = 5* cos( (x/4)*pi) + 11

y = 5*cos( (4/4)*pi) + 11

y = 5 * cos(pi) + 11

y = 5 * (-1) + 11

y = -5 + 11 = 6

==================

x = 0

y = 5* cos( (pi/4)*0 ) + 11

y = 5 * cos(0) + 11

y = 5 (1) + 11

y = 16

===================

x = 8 seconds

y = 5*cos(8/4)*pi) + 11

y = 5*cos(2*pi) + 11

y = 5 * (1) + 11

y = 16

==================

The question is where did the 11 come from?

The Ferris wheel has a diameter of 10 feet and a radius of 5

The high and low points are 16 and 6.

The center of the Ferris wheel is between 16 and 6. Between in this case means average.

(16 + 6)/2 = 22/2 = 11

Answer: D) $19.37

Step-by-step explanation: usatestprep approved

ANSWER

The possible rational roots are:

[tex]\pm\frac{1}{2},\pm2,\pm \frac{5}{2}[/tex]

EXPLANATION

According to the rational root theorem, the possible rational roots of the polynomial,

[tex]4x^3+9x^2-x+10=0[/tex]

are all the possible factors of the constant term divided by all the possible factors of the coefficient of the highest degree of the polynomial.

Therefore we examine the numerator and denominator of the options provided to see if they are factors of 10 and 4 respectively.

For

[tex]\pm\frac{1}{2}[/tex], we can see that 1 is a factor of 10 and 2 is a factor of 4, hence it is a possible rational root.

The same thing applies to [tex]\pm2,\pm \frac{5}{2}[/tex] also.

As for

[tex]\pm \frac{2}{5}[/tex], 2 is a factor of 10 but 5 is not a factor of 2, hence it is not a possible rational root.

The values of the possible rational roots of 4x³ + 9x² - x + 10 = 0 among the options are;

±½, ±2, ±5/2

          The rational root theorem states that if a polynomial has any rational roots, then the rational roots must be of the form;

±(factors of the coefficient of the constant term/factors of coefficient of the term with the highest degree)

4x³ + 9x² - x + 10 = 0

Thus, the rational roots could be;

±(½, 2, 5/2, 5)

        Looking at the options, the only correct possible rational roots are;

±½, ±2, ±5/2

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I'd like to answer your question but there's not enough information.

Answer:

there needs to be a better explantion

Step-by-step explanation:

1. Factor x^3 + 9x^2 + 6x - 16 using Polynomial Division

(x^2 + 10x + 16)(x -1)

2. Factor x^2 + 10x + 16

(x + 2)(x + 8)(x - 1)

Answer: x - 1

Answer:

x - 1

Step-by-step explanation:

width = volume / height * length

= x^3 + 9x^2 + 6x - 16 / (x + 2)(x + 8)

Since the volume ends in -16  and  last term of denominator

= +2 * + 8 = +16  the least term of the width will be - 1.

Also x^3 / x^2 = x

so the answer is (x - 1)

Plug the x-values from the table into the given equation and solve for y.

y = 5 - x²

First column

replace x with -2

y = 5 - (-2)²

  = 5 - (4)

  = 1

(x, y) = (-2, 1)

Second column

replace x with -1

y = 5 - (-1)²

  = 5 - (1)

  = 4

(x, y) = (-1, 4)

Third column

replace x with 0

y = 5 - (0)²

  = 5 - (0)

  = 5

(x, y) = (0, 5)

Fourth column

replace x with 1

y = 5 - (1)²

  = 5 - (1)

  = 4

(x, y) = (1, 4)

Fifth column

replace x with 2

y = 5 - (2)²

  = 5 - (4)

  = 1

(x, y) = (2, 1)

The correct answer is x=-3.

Given equation:

[tex]\frac{4}{3}x-7 = -11[/tex]  ----- (A)

To solve the above equation, follow these steps:

Step-1:

Add 7 on both sides of equation (A):

(A)=> [tex]\frac{4}{3}x -7 + 7 = -11 + 7 \\ \frac{4}{3}x = -4[/tex]

Step-2:

Multiple 3 on both sides, you will get:

[tex]\frac{4}{3}x * 3 = -4 * 3 \\ 4x = -12 \\ x = -3[/tex]

Hence the correct answer is x=-3.

Answer:

The value of x is -3.

Step-by-step explanation:

Given equation:

4/3 x-7=-11

By adding 7 to both sides of equation:

= 4/3x - 7 + 7 = -11 + 7

= 4/3x = -4

By multiplying 3 on both sides

= 4/3x × 3 = -4 × 3

= 4x = -12

By dividing 4 on both sides of equation:

= 4x/4 = -12/4

= x = -3

Hence by solving equation, the value of x out to be -3.

He spent roughly $903

Answer: 903

Step-by-step explanation:

Answer:

k(x) = x^2 and j(x) = -x^2

Step-by-step explanation:

The higher the coefficient, the steeper the graph. So the ones that work have to be less than 2.

It can't be 3x^2 because 3 is greater than 2x^2.

It can't be -3x^2 because -3 is the same as 3 except on the other side of the graph, and 3 is greater than 2.

It can't be -2x^2 because it has equal steepness as 2x^2, except it's on the opposite side of the graph.

It is x^2 because 1 is less than 2 in 2x^2, so it's less steep.

It is -x^2 because -1 is the same as 1 except on the other side of the graph, and 1 is less than 2.

Hope this helps!

A function maps a given input to a single output, increasing the values of

the factors increases the output and steepness of the function.

The functions that have graphs that have graphs that are less steep than f(x) = 2·x² are;  k(x) = x², and j(x) = -x²

Reasons:

The steeper the graph, the larger the ratio of the Rise to Run of the graph.

Therefore, increasing the multiple of the input of the graph increases the

Rise to Run ratio and therefore the steepness of the graph as follows;

Between points x = 1, and x = 2, for m(x) = 3·x², we have;

[tex]Slope = \dfrac{m(2) - m(1)}{2 - 1} = \dfrac{3 \times 2^2 -3 \times 1^2 }{2 - 1} = \dfrac{12 - 3}{2 - 1} = 9[/tex]

For k(x) = x², we have;

[tex]Slope = \dfrac{k(2) - k(1)}{2 - 1} = \dfrac{ 2^2 - 1^2 }{2 - 1} = \dfrac{4 - 1}{2 - 1} = 3[/tex]

Therefore;

The graphs of k(x) = x², and j(x) = -x², are less steep than f(x) = 2·x².

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Answer:

28

Step-by-step explanation:

Answer:

It is the 2 one sweetheart.

Step-by-step explanation:

The total number of people that all the cars can hold is greater than 480 and less than 500 people.

A:  According to the given situation, where both the number of trolley cars and the number of people in each car must have two digits and be less than 30.

Hence, the possible number of trolley cars in the park = 22 and a possible number of people in each car= 22

B: explain how you found your answer.

Lets suppose the number of cars be =c and the number of persons be= p

As the number of cars and number of person are same, so c=p

so, [tex]c\times c[/tex] should lie the given range of 480 to 500.

Now, the nearest perfect square that lies between 480 and 500 is 484.

The square root of 484 is 22. So, the number of cars and people are 22.

C: This is the only hit and trial method for solving this question.

Answer:

2.897

Step-by-step explanation:

Let us find the mean and variance for the sample first.

105 104 110 112

114 106 108 109

Mean = sum/8 = 108.5

Variance = 12

Std dev = sq rt of variance = 3.464

Std error = std dev/ sq rt n

since n =8, we get std error = 1.225

Since sample size is small, df =8-1 =7

For 95% confidence intervals, t critical value for two tailed=2.365

Margin of error = std error x t critical = 1.225(2.365)

=2.897

Final answer:

To estimate the cost of 7.8 pounds of potatoes at a price of $3.25 per pound, multiply the price by the number of pounds, resulting in a total estimated cost of $25.35.

Explanation:

We need to estimate the cost for 7.8 pounds of potatoes given that potatoes cost $3.25 per pound. To do this, we multiply the price per pound by the number of pounds:

Cost = Price per pound × Number of pounds

Cost = $3.25 × 7.8 pounds

After performing the multiplication, we find that:

Cost = $25.35

Therefore, the estimated cost for 7.8 pounds of potatoes at a price of $3.25 per pound is $25.35.

Answer:

Option B.

B. 5/2 cups of sugar, 19/6 cups of flour

Step-by-step explanation:

Given that Imogen is baking a cake.

The cake  requires two and one-half cups of sugar and three and one-sixth cups of flour.

Sugar required = 2 1/2

To make it improper fraction, we make the integer as a fraction with denominator 2

i.e. 2 1/2 = 2+1/2 =4/2 +1/2

Now we can add these

= 5/2

So 5/2 cups of sugar is required.

Similarly flour required=3 1/6

To make it improper we convert 3 into a fraction with denominator 6.

3=18/6

3 1/6 = 3+1/6 =18/6+1/6 = 19/6

Hence 19/6 cups of flour required.

Answer:

[tex]36.1[/tex] square feet of floor was carpeted.

Step-by-step explanation:

Number of Square feet = Length of the room * Width of the room

Now we have to substitute the values to the above equation,

Number of square feet = [tex]20\frac{1}{2} *15\frac{3}{5}[/tex]

                                      =[tex]\frac{41}{2} +\frac{78}{5}[/tex]

                                      =[tex]\frac{205+156}{10}[/tex]

                                      =[tex]\frac{361}{10}[/tex]

                                      =[tex]36.1[/tex] feet

The answer is D because it passes the horizontal line test.  

[tex]x^3+8y^6\\\\=x^3+2^3y^{2\cdot3}\\\\=x^3+2^3(y^2)^3\qquad|\text{used}\ (a^n)^m=a^{nm}\\\\=x^3+(2y^2)^3\qquad|\text{used}\ (ab)^n=a^nb^n\\\\=(x+2y^2)(x^2-x\cdot2y^2+(2y^2)^2)\qquad|\text{used}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(x+2y^2)(x^2-2xy^2+2^2(y^2)^2)\\\\=(x+2y^2)(x^2-2xy^2+4y^4)[/tex]

Answer:

K12 Here 100% verified

Step-by-step explanation:

30/12=in 1 min you drive 2.5lap

120/48=in 1 min you drive 2.5lap

yes they are equivalant

If they are equivalent, you should be able to cross multiply and get a true statement.

12/30 = 48/120

12(120) = 30(48)

1440 = 1440

This is a true statement, therefore they ARE equivalent.

Convert the equations to slope/intercept form:-

4x + 4y = 1

4y = -4x + 1

y = -1x + 1/4     The slope of this line is -1

x + y = -8

y = -1x - 8  This also has a slope of -1

So B is true.  The lines are parallel.

Final answer:

The two lines with equations 4x+4y=1 and x+y=-8 are parallel because they both have the same slope of -1. They do not intersect at the point (0,-8), nor do they share the same x-intercept since their x-intercepts are different when y=0.

Explanation:

To determine the relationship between the two lines with equations 4x+4y=1 and x+y=-8, we should first put them in slope-intercept form, which is y = mx + b, where m represents the slope and b the y-intercept.

For the first equation, dividing every term by 4 yields y = -x + 0.25, which has a slope of -1. For the second equation, we can see directly that rearranging it gives y = -x - 8, which also has a slope of -1.

Since both lines have the same slope, they are parallel. To check if they intersect at the point (0,-8), we can substitute x=0 into both equations. The first equation gives y = 0.25, which is not -8, so they do not intersect at (0,-8). For the x-intercepts, we set y=0 in both equations. The first gives x = 0.25, and the second gives x = -8, so they do not share the same x-intercept either.

Therefore, the correct answer is B. The lines are parallel.

b – 2a – c

9 - 2(-3) - (-6) = ?

9 - 2(-3) - (-6) = 21

I'm confused too and I'm supposed to be an expert.  I'm not entirely sure what frequency density is.  We'll just treat this as a histogram.

Let's assume each five minute interval gives a value equal to or proportional to the number of people that finished in that interval.

From 0 to 50 we have 10 intervals; let's just make this into a table

0-5  0

5-10 40

10-15 40

15-20 30

20-25 30

25-30 25

30-35 25

35-40 25

40-45 25  

45-50 15

From 0 to 40 that adds up to

0+40+40+30+30+25+25+25 = 215

From 0 to 50 that's

215+25+15 = 255

The fraction less than 40 is 215/255 = 43/51 ≈ .843

Answer: 84.3%

Answer:

84.3%

Step-by-step explanation:

Total frequency is the total area:

Add all the areas

To find each area:

Frequency density × class width

Total frequency:

40×10 + 30×10 + 25×20 + 15×5

= 1275

Less than 40:

Bar 1 + Bar 2 + some part of Bar 3

40×10 + 30×10 + 25×15

= 1075

Percentage (<40) = 1075/1275 × 100

= 4300/51

= 84.31372549%

Answer:

In these functions translation is used.

The transformation means that vertex of function m(s) is translated 18 units downwards.

Step-by-step explanation:

We have been given that average gas mileage m in miles per gallon for a compact car is modeled by  m(s) = - 0.015(s - 47)2 +33 and mileage for an SUV is modeled by my(s) = -0.015(s - 47)2 + 15.

We can see that both functions are parabolic and opens downwards. The vertex of function m(s) is (47,33), while vertex of function my(s) is (47,15). We can describe this change by translation.

This transformation means that function m(s) is translated 18 units downwards and average mileage of SUV is 18 miles/hour lesser than compact car at equal speeds.

The change is a vertical shift, meaning that the SUV's gas mileage drops lower than the compact car's at the same speed, but the rate at which the mileage decreases with speed is identical.

The transformation that describes the change from the compact car's gas mileage model to the SUV's model is a vertical shift. This is because the two equations are identical, except for the constant at the end (33 in the compact car's equation and 15 in the SUV's equation). This constant indicates the vertical position of the parabola described by the equation, so by changing the constant, you're vertically shifting the parabola without changing its shape or orientation.

A vertical shift of the parabola in this context means that the SUV's gas mileage drops lower than the compact car's gas mileage at the same speed. The number being subtracted from the parabola to achieve the shift (-0.015(s - 47)2) remains the same for the SUV and the compact car, meaning the rate at which the mileage changes with speed is the same, but the overall mileage of the SUV is lower due to the difference in constants (33 for the compact car and 15 for the SUV).

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