Which of the following expressions are equivalent to 48a^3-75a? Select all that apply.

Answer 1) 3(48a^3-75a).
Answer 2) 3a(16a^2-25)
Answer 3)3a(4a+5)(4a+5)
Answer 4) 3a(4a+5)(4a-5)
Answer 5) -3a(25-16a^2)
Answer 6) -3a(5-4a)(5+4a)

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:

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: 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]

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:  B) -6x³ + 4x²

Step-by-step explanation:

         f(x): -3x⁴ - 2x³ + 3x²

     + g(x): 3x⁴ - 4x³ +   x²

f(x) + g(x):        - 6x³ + 4x²

Answer:

The percentage of the people who live in the forests that are indigenous is [tex]20\%[/tex]

Step-by-step explanation:

we know that

To find the percentage of the people who live in the forests that are indigenous, divide the number of people that are indigenous by the total number of people that live in forests

so

[tex]\frac{60}{300} =0.2[/tex]

Convert to percentage

Multiply by 100

[tex]0.2*100=20\%[/tex]

Answer: INTRODUCTION

"Of all the environmental impacts of the study projections, deforestation probably poses the most serious problems for the world, particularly for the developing world."

Global 2000

"It has been predicted that within the next 25-30 years, most of the humid tropical forest as we know it, will be transformed into unproductive land, and the deterioration of the savannah into desert will continue at ever-increasing speed."

As you read this sentence, 50 to 100 acres of primary tropical forests will be eliminated, disrupted, degraded or impoverished. Yearly, an area of tropical forest the size of Great Britain is "converted" from an area equal to the size of Europe.

If present trends continue, by the year 2000, all tropical forests, with the exception of two areas - the western Brazilian Amazon and Central Africa - will have been destroyed. Since 1950, according to the U.N. Food and Agriculture Organization (FAO), half of the world's forests have disappeared. Latin America has lost 37 percent of its tropical forests; Central America, 66 percent; Southeast Asia, 38 percent; Central Africa, 52 percent. Nearly 20 million acres are destroyed annually.

As areas of tropical forests are destroyed or degraded, tribal groups are forced to change their resource base. In some cases they move into areas occupied by other groups, straining the area's resources. In other cases they are forced to relocate outside of forests, permanently altering their way of life by converting to agriculture or to cash employment. Rarely are the rights of these groups to the lands they occupy recognized. Further, their intimate knowledge of the area's resources and how to manage them are nearly always ignored.

Millions of indigenous people live in tropical moist forests which cover some 3.6 million square miles in 70 countries. More than 80 percent of these forests are found in Bolivia, Brazil, Colombia, Gabon, Indonesia, Malaysia, Peru, Venezuela, and Zaire, while 30 additional countries contain sufficient tracts to have significant ecological and biotic values. If these areas are to be managed effectively into the next century, the indigenous peoples that inhabit them should be consulted.

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:

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

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:

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:

  (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

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:

A.  5 seconds

Step-by-step explanation:

This quadratic (second degree polynomial) models parabolic motion.  The vertex of the function is the projectile's max height.  When the height of the object is 0 is when it hits the water.  Set the function equal to 0 then and factor.  I used the quadratic formula on my calculator, but if you need to, stick it into the quadratic formula and do it long hand.  The values of x (which is actually time here) are -1 and 5.  The two things in math that will never ever be negative are distance measurements and time, so we can disregard the -1 and say that it takes 5 seconds for the rocket to hit the water.

It would take 5 seconds for the rocket to hit the lake.

An equation is used to show the relationship between two or more variables and numbers.

Let g(x) represent the height of the rocket at time x seconds. Given that:

g(x)= -16x² + 64x + 80

The rocket touches the lake, when the height is 0. Hence:

0 = -16x² + 64x + 80

x = 5 seconds.

It would take 5 seconds for the rocket to hit the lake.

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Answer: B Scientific Method

[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]

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

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:

  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.

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.

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:

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

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:

$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:

Step-by-step explanation:

I(x)=P(13x) = 2(13x)²+3(13x) +4

I(x)=P(13x).= 338x²+39x+4

A = 0.5 x 10.4 x 16.9

A = 87.88

The area of the triangle is 87.88 ft²

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:

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]

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:

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