In a train yard, there are 6 flat cars, 7 boxcars, and 3 livestock cars. A train is made up of 9 cars. Which would you use to find the number of ways the train could be made up?


A. 16P9

B. 16P7

C. 9P16

D. 9P7

Answer:

One

Step-by-step explanation:

4x + 5 = 10

Subtract 5 from both sides.

4x = 5

Divide both sides by 4.

x = 5/4

There is one solution.

Answer:

(t, t -1, t)

Step-by-step explanation:

You have three unknowns but only 2 equations, so you can't really SOLVE this...you can get a solution with a variable still in it (I forget what this is called.  I think it refers to infinite many solutions).  Here's how it works:

Set up your matrix:

[tex]\left[\begin{array}{ccc}1&-2&1\\2&-1&-1\\\end{array}\right] \left[\begin{array}{ccc}2\\1\\\end{array}\right][/tex]

You want to change the number in position 21 (the 2 in the scond row) to a 0 so you have y and z left.  Do this by multiplying the top row by -2 then adding it to the second row to get that 2 to become a 0.  Multiplying in a -2 to the top row gives you:

[tex]\left[\begin{array}{ccc}-2&4&-2\\2&-1&-1\\\end{array}\right]\left[\begin{array}{ccc}-4\\1\\\end{array}\right][/tex]

Then add, keeping the first row the same and changing the second to reflect the addition:

[tex]\left[\begin{array}{ccc}-2&4&-2\\0&3&-3\\\end{array}\right] \left[\begin{array}{ccc}-4\\-3\\\end{array}\right][/tex]

The second equation is this now:

3y - 3z = -3.  Solving for y gives you y = z - 1.  Let's let z = t (some random real number that will make the system true.  Any number will work.  I'll show you at the end.  Just bear with me...)

lf z = t, and if y = z - 1, then y = t - 1.  So far we have that y = t - 1 and z = t.  Now we solve for x:

From the first equation in the original system,

x - 2y + z = 2.  Subbing in t - 1 for y and t for z:

x - 2(t - 1) + t = 2.  Simplify to get

x - 2t + 2 + t = 2  and  x - t = 0, and x = t.  So the solution set is (t, t - 1, t).  Picking a random value for t of, let's say 2, sub that in and make sure it works.  If:

x - 2y + z = 2, then t - 2(t - 1) + t = 2 becomes t - 2t + 2 + t = 2, and with t = 2, 2 - 2(2) + 2 + 2 = 2.    Check it:  2 - 4 + 4 = 2 and 2 = 2.  You could pick any value for t and it will work.

Answer:

48.3 cm²

Step-by-step explanation:

The area (A) of the yellow region = area of square - area of quarter circle, that is

A = 15² - ([tex]\frac{1}{4}[/tex] πr² )

  = 225 -( [tex]\frac{1}{4}[/tex] × π × 15² )

  = 225 - 176.71 ≈ 48.3

Answer:

12-5.5=h

12-5.5=6.5

Kyle needs to volunteer 6.5 more hours.

Step-by-step explanation:

Answer:

5.5 + h = 12

Step-by-step explanation:

Here, h represents the number of hours, Kyle still needs to volunteer this week,

Given,

He volunteered 5.5 hours at the library this week.

Since, the total number of hours he needs to volunteer = 5.5 + h

According to the question,

5.5 + h = 12

Which is the required equation.

Answer:

1 m 79 cm

Step-by-step explanation:

Subtract 1.46 m from 3.25 cm:  1.79 cm, or 1 m 79 cm

Answer:

the answer is the letter a) -sin x

Step-by-step explanation:

Simplify the expression.

sine of x to the second power minus one divided by cosine of negative x

(1−sin2(x))/(sin(x)−csc(x))

sin2x+cos2x=11−sin2x=cos2x

cos2(x)/(sin(x)−csc(x))csc(x)=1/sin(x)cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x))sin2(x)− 1=-cos2(x)cos2(x)/(( -cos2(x))/sin(x))

=-sin(x)

Answer:

[tex]-cos \ x[/tex]

Step-by-step explanation:

First of all, we must have to understand what is the described expression in the paragraph

"sine of x to the second power minus one divided by cosine of negative x"

In this sentence, we need to identify what are the elements and operations involved in the expression.

In the sentence appears ""to the second power", "minus" and "divided by" (highlighted)

"sine of x to the second power minus one divided by cosine of negative x"

Therefore, the expression must has three operations:

Now, we can identify what are the elements: "sine of x", "one" and "cosine of negative x"

Therefore, the expression is:

[tex]\frac{(sin\ x)^{2}-1}{cos(-x)}[/tex]

In order to find the simplified expression, we must have to apply these trigonometric identities:

Applying the first and third identities, we have:

[tex]\frac{(sin\ x)^{2}-1}{cos(-x)}=\frac{sin\x^{2}x-1}{cos\ x}[/tex]

From the second trigonometric identity, we have:

[tex]cos\x^{2}x=\ 1-sin\x^{2}x[/tex]

Now, multiplying by -1 in both sides:

[tex](-1)(cos\x^{2}x)=(-1)(1-\ sin\x^{2}x)[/tex]

In the left side, multiplying by -1 the sign of the expression changes:

[tex](-1)(cos\x^{2}x)=-cos\x^{2}x[/tex]

In the right side, multiplying by -1 changes the order of the substraction:

[tex](-1)(1-\ sin\x^{2}x)=\ sin\x^{2}x-1[/tex]

Putting all together:

[tex]-cos\x^{2}x=\ sin\x^{2}x-1[/tex]

Now, replacing values we have:

[tex]\frac{sin\x^{2}x-1}{cos\ x}=\frac{-cos\x^{2}x}{cos\ x}=-\frac{cos\x^{2}x}{cos\ x}[/tex]

Finally, the property of the first trigonometric identity (property of exponentiation) can be apply in this case:

[tex]-\frac{cos\x^{2}x}{cos\ x}=-\frac{(cos\ x)^{2}}{cos\ x}=-cos\ x[/tex]

The answer is:

The man did consume two standard drinks in two hours.

According to the standard drink conversion, we know that each 12 ounce beer we have one (1) standard drink, and each 1.5 ounce shot of liquor, we have another standar drink.

Calculating we have:

[tex]DrinksConsumed=12Oz(Beer)+1.5Oz(Liquor)=1StandardDrink+1StandardDrink\\\\DrinksConsumed=1StandardDrink+1StandardDrink=2StandardDrinks[/tex]

We have that the man did consume two standard drinks in two hours.

Have a nice day!

A man who consumed two 12 ounce beers and a 1.5 ounce shot of liquor has consumed three standard drinks according to the National Institute on Alcohol Abuse and Alcoholism's definition of a standard drink in the United States.

According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), a standard alcoholic drink in the United States is equivalent to 14 grams (0.6 ounces) of pure alcohol. This typically is found in a 12-ounce beer, a 5-ounce glass of wine, or a 1.5 ounce shot of distilled spirits or liquor. The man in the question consumed two 12 ounce beers and one 1.5 ounce shot of liquor. Given that both the beer and the shot each lay within the standard drink size, we can conclude that the man consumed three standard drinks in total. Alcohol consumption and understanding standard drinks is important to monitor one's drinking habits for overall health.

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Answer:

B. f -1(x) = x + 2 / 5

[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]

Step-by-step explanation:

To find the inverse of a function we need to interchange x and y an solve for y.

Since [tex]f(x)=y[/tex], then

[tex]f(x)=5x-2[/tex]

[tex]y=5x-2[/tex]

[tex]x=5y-2[/tex]

Add 2 to both sides

[tex]x+2=5y-2+2[/tex]

[tex]x+2=5y[/tex]

Divide both sides by 5

[tex]\frac{x+2}{5}=\frac{5y}{5}[/tex]

[tex]\frac{x+2}{5}=y[/tex]

[tex]y=\frac{x+2}{5}[/tex]

[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]

We can conclude that the correct answer is B. f -1(x) = x + 2 / 5

Answer:

Step-by-step explanation:

I(x)=P(13x) = 2(13x)²+3(13x) +4

I(x)=P(13x).= 338x²+39x+4

Answer:

The answer would be the large album has 54 more stamps than the small album.

Step-by-step explanation:

... 92 - 38 = 54

Do you need a drawing done though?

Answer:

Step-by-step explanation:

So the table means that there are 20 1's, 120 2's, 40 3's, and 20 4's.

The total number is 20+120+40+20 = 200.

So the probability of each is:

1: 20/200 = 0.10

2: 120/200 = 0.60

3: 40/200 = 0.20

4: 20/200 = 0.10

A bar graph that represents the probability distribution of each card is shown in the image below.

In Mathematics and Statistics, a frequency table can be used for the graphical representation of the frequencies or relative frequencies that are associated with a categorical variable or data set.

Based on the frequency, the total number of deck of cards can be calculated as follows;

Total number of deck of cards = 20 + 120 + 40 + 20

Total number of deck of cards = 200 cards.

Next, we would determine the probability distribution of each card as follows:

P(X = 1) = 20/200 = 0.10.

P(X = 2) = 120/200 = 0.60.

P(X = 3) = 40/200 = 0.20.

P(X = 4) = 20/200 = 0.10.

Answer:

  3, -8, 11

Step-by-step explanation:

The first factor is zero when x=3.

The second factor is zero when x=-8.

The third factor is zero when x=11.

Whenever any factor is zero, the polynomial is zero.

The zeros are 3, -8, 11.

Answer:

[tex]x=10, NL=8, NP=12[/tex]

Step-by-step explanation:

we know that

Applying the Intersecting secant Theorem

[tex]NL*NM=NP*NO[/tex]

substitute the given values and solve for x

[tex](3+5)*3=(2+x)*2[/tex]

[tex](8)*3=(2+x)*2[/tex]

[tex]24=(2+x)*2[/tex]

[tex]12=(2+x)[/tex]

[tex]x=12-2=10[/tex]

Find the value of NP

[tex]NP=(2+x)=2+10=12[/tex]

therefore

[tex]x=10, NL=8, NP=12[/tex]

Answer:

x = 7; NL = 12; NP = 20

Step-by-step explanation:

ur welcome

Answer: 12800m^2

This shape is made up of a rectangle and a triangle.

Rectangle

= 120 x 60

= 7200

Triangle

= (200 - 60) x (120 - 40) x 0.5

= 140 x 80 x 0.5

= 5600

Total Shape

= 7200 + 5600

= 12800m^2

The number of runners run at most 2 miles per day is 13.

2 miles = 6

3 miles = 4

4 miles = 2

5 miles = 1

Now if we add this,

So,

= 6 + 4 + 2 + 1

= 13

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Answer:

13

Step-by-step explanation:

Its easy, but its a trick question into getting you to click 6

Answer:

1

Step-by-step explanation:

y = mx + b

y = 1/2 x - 1

y = 1/2 (4) - 1

y = 2 - 1

y = 1

When x = 4, the function y = (1/2)x - 1 evaluates to y = 1. This linear equation has a slope of 1/2 and a y-intercept of -1.

To find the value of the function y = (1/2)x - 1 when x = 4, you simply need to substitute x = 4 into the equation and solve for y:

y = (1/2)(4) - 1

y = 2 - 1

y = 1

So, when x = 4, the value of the function y is 1.

In a more general sense, this equation represents a linear function with a slope of 1/2 and a y-intercept of -1. The slope (1/2) represents the rate of change, meaning that for every unit increase in x, y increases by 1/2. The y-intercept (-1) is the value of y when x is 0.

When x = 4, as calculated above, y is 1. This means that if you were to plot this function on a coordinate plane, the point (4, 1) would lie on the graph.

For more question on slope visit:

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Answer: 7. y = 2 sin (2x) - 3

              [tex]\bold{8.\quad y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)}[/tex]

Step-by-step explanation:

The general form of a sine equation is: y = A sin (Bx - C) + D    where

7. Given:

--> y = 2 sin (2x) - 3

8. Given:

[tex]\implies y=sin\bigg(8x + \dfrac{8}{\pi}\bigg)[/tex]

A = 0.5 x 10.4 x 16.9

A = 87.88

The area of the triangle is 87.88 ft²

Answer:

The T-shirts cost $10 and the jeans cost $20.

Step-by-step explanation:

I guess you want to find the cost of the T-shirts and jeans at his first buy,

Let the cost be  $t and $j for T-shirts and jeans respectively.

Then we have the system:

2t + j = 40...................(1)

and a month later:

0.5*2t  + 0.5*5j = 60

t + 2.5j = 60................(2)

Multiply by - 2:

-2t - 5j = -120.............(3)

Adding equations (1) and (3):

-4j = -80

j = -80 /  -4

j =  $20.

Substituting j = 20 into equation (2):

t + 2.5(20) = 60

t = 60 - 50

t = $10.

t = $55

Answer: B Scientific Method

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{4\times 4}{16}\\ h=&4 \end{cases}\implies V=\cfrac{1}{3}(16)(4)\implies V=\cfrac{64}{3}\implies V=21.\overline{3}[/tex]

Answer:

21.03^3  this is the answer.

Answer:

Imagination is more important than knowledge. --Clifford big red dog

Step-by-step explanation:

a) To find the average cost per pair of shoes, we need to divide the total cost by the number of pairs produced. Since the manufacturer produced x pairs of shoes, the total cost is 12,000+19x dollars. Therefore, the average cost per pair is given by:

Average cost per pair = (12,000+19x) / x

b) Using the given information that this month, the manufacturer produced 1000 more pairs of shoes than last month, we can represent the number of pairs produced last month as x−1000. Since the average cost per pair dropped by $0.43, the equation representing the situation is:

(12,000+19(x)−43(x)) / x=Average cost per pair

Solving this equation will provide us with the value of x.

c) Yes, there is a mathematical restriction on the domain. Since the number of pairs produced cannot be negative (it doesn't make sense to produce a negative number of shoes), the domain must be restricted to x>0.

d) In the context of the problem, the reasonable domain would be x>0 since the number of pairs of shoes produced cannot be negative. Additionally, since the manufacturer produced 1000 more pairs of shoes this month than last month, it's reasonable to assume that the number of pairs produced last month is also positive, leading to a positive change of 1000 pairs. Therefore, the domain would be x>1000.

a) The expression for the average cost per pair of shoes is given by:

Average cost per pair = (12,000+19x) / x

To represent the situation, we use this expression to equate the average cost per pair before and after the change in production.

b) Substituting x+1000 for x in the expression, we get:

(12,000+19(x+1000)) / (x+1000) = Average cost per pair

We solve this equation to find the value of x.

c) Yes, there's a restriction on the domain. Since the number of pairs of shoes cannot be negative, the domain must be x>0.

d) Considering the context, the reasonable domain is x>1000, as the manufacturer produced 1000 more pairs this month than last month. Also, x must be positive, so x>0. Thus, the domain is x>1000.

Complete Question:

The cost in dollars to manufacture x pairs of shoes is given by 12,000 + 19x. This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.

a) Write an expression for the average cost per pair of shoes. Use this expression to write an equation to represent their situation.

b) Solve your equation

c) Are there any mathematical restrictions on the domain? Explain.

d) Determine reasonable domain in the context of the problem. Use your answers to parts I and II to answer the question.

[tex]

\frac{\frac{9}{10}}{\frac{-3}{5}}=\frac{45}{-30}=-\frac{9}{6}=\boxed{\frac{3}{2}}

[/tex]

Hope this helps.

r3t40

Answer:

  (x +2)(x -4)(x -5)

Step-by-step explanation:

When you divide the cubic by (x +2), the factor that has -2 as a root, you get a quadratic with roots 4 and 5. Thus the factors are ...

  (x +2)(x -4)(x -5)

___

In the attachment, we have done the division using a graphing calculator. You can also do it by polynomial long division or by synthetic division. The resulting quadratic is ...

  x^2 -9x +20 = (x -4)(x -5) . . . . . factor the quadratic

[tex]f(x)=2\sqrt x[/tex] is continuous on [0, 4] and differentiable on (0, 4), so the MVT holds. We have

[tex]f'(x)=\dfrac1{\sqrt x}[/tex]

so that by the MVT, there is some [tex]c\in(0,4)[/tex] such that

[tex]f'(c)=\dfrac{f(4)-f(0)}{4-0}\implies\dfrac1{\sqrt c}=\dfrac{2\sqrt4}4=1[/tex]

[tex]\implies1=\sqrt c\implies \boxed{c=1}[/tex]

Answer:

x= 16/9

Step-by-step explanation:

[tex]f(x) = 2\sqrt{x}[/tex] is differentiable on [0,4] so the Mean Value Theorem For Integrals applies.

Average Value of the Integral:

[tex]\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx = \frac{1}{4-0} \int\limits^4_0 {2\sqrt{x} } \, dx[/tex]

After evaluating you will get  [tex]\frac{8}{3}[/tex]

Now, this is the average value so you still need to find the x-value using the original equation:

[tex]\frac{8}{3} =2\sqrt{x}\\\\\frac{4}{3} = \sqrt{x}\\\\\frac{16}{9} =x[/tex]

The domain are the x values.

The problem is saying the x value is all numbers between 4 and 8

Replace x in the equation with 4 and 8 and solve to find the range for the y values:

y =4(4) -1 = 16-1 = 15

y = 4(8) - 1 = 32-1 = 31

So Y would be between 15 and 31.

The first answer is the correct one.

Answer:  B) -6x³ + 4x²

Step-by-step explanation:

         f(x): -3x⁴ - 2x³ + 3x²

     + g(x): 3x⁴ - 4x³ +   x²

f(x) + g(x):        - 6x³ + 4x²

Answer:

  $388.16

Step-by-step explanation:

Her monthly interest rate is 3.8%/12, so the amount of interest due on the first payment is ...

  $260,000 × 0.038/12 ≈ $823.33

Then the amount applied to the principal is ...

  $1211.49 -823.33 = $388.16

Answer:

$148.21

Step-by-step explanation:

A suitable financial calculator, web site, or spreadsheet can figure this for you. Or you can use the formula given in your reference material (text or web site).

Answer:

Michelle's monthly payment will be $148.21.

Step-by-step explanation:

The EMI formula is =

[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1}[/tex]

Here,

p = $10125

r = [tex]12.5/12/100=0.010417[/tex]

n = [tex]10\times12=120[/tex]

Putting all these values in the formula we get,

[tex]\frac{10125\times0.010417\times(1+0.010417)^{120} }{(1+0.010417)^{120}-1}[/tex]

=>[tex]\frac{10125\times0.010417\times(1.010417)^{120} }{(1.010417)^{120}-1}[/tex]

=$148.21

So, Michelle's monthly payment will be $148.21.

Answer:

There is no clear relationship between the number of times students arrive late and the distances they live from school.

Step-by-step explanation:

By looking at the graph, there is no clear direction or association that the graph has. Therefore, there is no clear relationship between the variables being compared.

Answer:

looking at the graph, there is no clear direction or association

Step-by-step explanation: