The volume of a rectangular box can be found using the formula lwh where l represents the length, w represents the width, and h represents the height of the box. What is the volume of a box with the following dimensions?
I = 4 centimeters
W= 5 centimeters
H=6 centimeters

Check the picture below.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^5\div y^2\times x^3\times y^5\implies \cfrac{x^5}{y^2}\cdot x^3\cdot y^5\implies x^5\cdot y^{-2}\cdot x^3\cdot y^5 \\\\\\ x^{5+3}y^{-2+5}\implies x^8y^3[/tex]

Answer:

x⁸y³

Step-by-step explanation:

x⁵ ÷ y² × x³ × y⁵

It will be easier to solve this problem if you first rearrange the expression to associate like terms.

(x⁵ × x³) × (y⁵ ÷ y²)

Now, you can use the rules of exponents: When multiplying, you add exponents; when dividing, you subtract exponents.

x⁵ × x³ = x⁵⁺³ = x⁸  

y⁵ ÷ y² = y⁵⁻² = y³

Thus,

(x⁵ × x³) × (y⁵ ÷ y²) = x⁸y³

Answer: his shoe size was 11

Step-by-step explanation:

Answer:

I hope this helps

Step-by-step explanation:

Answer:

It's B.

Step-by-step explanation:

The range is 344 - 111

= 233.

Arranging the data in ascending order:

111 133 134 183 284 339 344

The lower quartile = 133 and the upper quartile = 339.

So the interquartile range =  339 - 133

= 206.

We first need to list the following Data Set:

111, 133, 134, 183, 284, 334, 339

Range = highest value - lowest value =

Range = 339 - 111 = 228

Interquartile range = upper quartile - lower quartile =

(or IQR = interquartile range, another term)

Interquartile range = 334 - 133 = 201

ANSWER

The y-intercept is (0,-11)

The x-intercepts are:

(-1,0) and (11,0)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} - 10x - 11[/tex]

To find the y-intercept, we put x=0 into the function.

[tex]f(0) = {0}^{2} - 10(0) - 11[/tex]

[tex]f(0) = - 11[/tex]

The y-intercept is (0,-11)

To find the x-intercepts, we put f(x)=0.

[tex]{x}^{2} - 10x - 11 = 0[/tex]

[tex](x + 1)(x - 11) = 0[/tex]

This implies that,

[tex]x = - 1 \: or \: x = 11[/tex]

The x-intercepts are:

(-1,0) and (11,0)

For Future Reference____

-1 & 11 are the X Intercepts

Answer:

16 dresses

Step-by-step explanation:

you can make 16 because when you divide the length of cloth (40 ft) by 2.5 (2 ft 6in) you get 16

Answer:

16

Step-by-step explanation:

We know 6 inches is .5 of a foot

1 ft = 12 inches

6 inches /12 inches = 1/2 ft

We have 40 ft of cloth and each dress is 2.5 ft long

Take 40 ft and divide by 2.5

40 ÷ 2.5 =16

We can make 16 dresses

Answer: A?

Step-by-step explanation:

Answer:

-5x

Step-by-step explanation:

you multiply them together

(-5)(x)= -5x

Answer:

-5x

Step-by-step explanation:

-5 * X =

Answer:

199 a 426 students

Step-by-step explanation:

first to see what amount we are talking about in each case, let's see how many students each percentage represents

22% of students:  (22 * ​​1420 students) /100  = 312.4 students

8% of students: (8*1420 students)/100 = 114.6 students

that is, that the average number of students who work part time is 312.4 students. And that number can vary up to 114.6 students above and up to 114.6 students below

that can be expressed as

22% + 8% = 312.4 + 113.6 = 426 students

and

22% -8% = 312.4-113.6 = 198.8≅ 199 students

Answer:

-8

Step-by-step explanation:

-4a + 8z

= -4(8)+8(3)

= -32+24

= -8

use the substitution method

-4a+8z

-4(8)+8(3)

-32+24 Negative number times (*) and positive number=negative number

=-8

Answer is -8

Answer:

[tex]f(x)=6.50x+48.00[/tex]

Step-by-step explanation:

Let

x ----> the number of adult tickets

f(x) ----> amount of money collected

To find the amount collected multiply the number of adult tickets by the cost and multiply the number of student tickets  by the cost, and then sum the two quantities

The linear equation that represent this problem is

[tex]f(x)=6.50x+4.00(12)[/tex]

[tex]f(x)=6.50x+48.00[/tex]

Answer:

Step-by-step explanation:

F(x)=6.50x+48.00

This statement is true.

When you buy a share in a company, you are investing your money, and you may earn more money if the share’s value rises, or you may lose money if the share’s value falls.

Investing in a company by buying shares makes you a shareholder, with potential income from dividends and stock appreciation. However, it carries risk as there is no guarantee for profits. Diversification is a key strategy when investing in stocks to mitigate risks.

Buying shares in a company is a common method of investment, wherein you become a shareholder and own a part of the company's equity. As a shareholder, you have a claim to the company's assets and profits proportional to the amount of stock you own. There are two primary ways that shareholders can earn money from their investments. One way is through dividends, which are payments distributed from the company's profit to shareholders. The other way is through appreciation in the stock's value, as the company grows and becomes more profitable; this increases the stock's market price, and you can sell your shares for a profit. It's important to understand that purchasing stock does involve risk, as there is no guarantee of dividends or stock appreciation. However, for many, owning stock is preferred over other investments like bonds because of the potential for higher returns. Lastly, when buying stock, especially that of your employer, it's advisable to follow general rules of portfolio investing, such as diversification, not to expose yourself to undue risk.

Answer:

- 160 I think

Step-by-step explanation

I think i'm right but there are

200 blocks and there are 40 left out so then i did 40 - 200 = -160

If the original price is X, then(1-29%)X=284, so X=284/(1-0.29)=400

The original price of the suit is $400.

To find the original price, we must multiply the discounted value with the reciprocal of the percentage that it represents.

The discounted price is $284.

The percentage of discount is 29%.

Therefore, the percentage which represents the price is 100 - 29 which is 71%.

Therefore, we can find the original cost by multiplying the discounted price by the reciprocal of 71/100. This can be done as shown below:

The original price = 284 * 100/71

= $400.

We have found the original price. The original price is found to be $400.

Therefore, we have found that the original price of the suit is $400.

Learn more about percentages here: https://brainly.com/question/24304697

#SPJ2

Answer:

4/21

Step-by-step explanation:

⇒This question is on probability

⇒Number of boys=3

⇒Number of girls=4

⇒P(S)= 4+3=7

Probability for a girl to win is= 4/7

We have 3 awards a free movie ticket, a collectible poster, or a free popcorn

P(S)= 3

Probability of being awarded a free popcorn = 1/3

The probability that a girl will win free popcorn =

[tex]\frac{4}{7} * \frac{1}{3} = \frac{4}{21}[/tex]

Answer:

4/21

Step-by-step explanation:

Answer:

475

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

Answer:

28.8

Step-by-step explanation:

Range = Highest number - Lowest number

Highest number: 42

Lowest number: 13.2

42 - 13.2 = 28.8

I hope this helps! :D

28.8 because the range is the biggest minus the smallest so 42 - 13.2

Answer

so it is answer B

Step-by-step explanation:

since the sample space is 10, the chance of selecting theyellow ball is 1/10

which is unliekly

B) unlikely

it’s a 10% chance to get a yellow ball and a 90% chance to get a red ball

Answer: [tex]g(x)=(3)^{-x}[/tex]

Step-by-step explanation:

We know that if a figure is reflected across y axis then its y coordinate remains same but the x coordinate changes its polarity.

i.e. the function [tex]f(x)[/tex] will become [tex]f(-x)[/tex] .

Now, the given function :[tex]f(x)=(3)^x[/tex]

Then , after reflection across y axis the new function will become:

[tex]g(x)=f(-x)=(3)^{-x}[/tex]

Answer:

280

Step-by-step explanation:

<1=100 <4=150 <3=30

mADB=100+150+30=280

Answer with explanation:

Given

m∠1=100°

[tex]m \widehat{BC}=30 ^{\circ}[/tex]

To Find:---m∠A D B

Solution

In Δ A OD

Represent the center of circle by O.

→ m∠1=100°

→OD=O A----------Radii of Circle

→∠ADO=∠D A O--------If opposite sides are equal angle opposite to them are equal.

In ΔA OD, Using Angle Sum property of Triangle

→∠ADO+∠D A O+∠A OD=180°

→2 ∠ADO+100° =180°-------------------[∠ADO=∠D A O]

→2∠ADO=180° -100°

→2∠ADO=80°

Dividing both sides by , 2 we get

⇒∠ADO=40°

⇒⇒⇒∠A DB=40°

≡⇒If you are asking about

[tex]m \widehat{ADB}=180 ^{\circ}[/tex]

Because Angle in a semicircle is Right Angle.Diameter B D divides the circle into two equal arc measure of each arc being 180 degree.

⇒⇒If you are asking about Angle made by Major arc ADB, then

[tex]m \widehat{ADB}=\angle AOD + \widehat{BOD}\\\\=100 ^{\circ}+180 ^{\circ}=280 ^{\circ}[/tex]

Option B

The correct answer is 6

Answer:

Option B is the correct answer

Step-by-step explanation:

Both collections follow arithmetic progression.

Back then, they had the same number of rare coins, which means their first term of AP is same. Let it be a.

Miguel's AP have a common difference 5 and Grace's AP have a common difference 3.

Let the number of weeks completed be n.

We have

           a + ( n-1 )x 5 = 38  -------- eqn 1

           a + ( n-1 )x 3 = 24  -------- eqn 2

eqn 1 - eqn 2

          a + ( n-1 )x 5 - (a + ( n-1 )x 3) = 38 - 24

          ( n-1 )x 2 = 14

          n-1 = 7

          n = 8

Substituting in eqn 1

           a + ( 8-1 )x 5 = 38

                     a = 38 - 35 =3

So at starting they both have 3 rare coins.

Total rare coins = 3 + 3 = 6

Option B is the correct answer

Answer:

120

Step-by-step explanation:

A triangles angles always add to 180 degrees.

180=20+40+x

180-20=160

160-40=120

120=x

Answer:

120

Step-by-step explanation:

20+40=60

180-60

120

Answer:

A.22

Step-by-step explanation:

Answer:

d. 19

Step-by-step explanation:

A matrix is an array of rectangular shape which consists of numbers, symbols, or expressions, arranged in rows and columns.

[tex]\begin{bmatrix}28&21&19\\17&24&15\\22&29&17\end{bmatrix}[/tex]

[tex]w_{1,3}[/tex] means element in first row third column. First row means Frank and third column means August.

So, the number of lawns mowed by Frank in August is

[tex]w_{1,3}=19[/tex]

Answer:

x=28 (Yup you're correct)

Step-by-step explanation:

As this problem is involving the Opposite angle and the Hypotenuse, we can use the sin function in order to solve this. The setup is as follows

[tex]sin(30)=\frac{14}{x}[/tex]

Now we can solve for x

[tex]sin(30)=\frac{14}{x}\\\\x=\frac{14}{sin(30)}[/tex]

Now we can plug it into a calculator to get

[tex]x=28[/tex]

Answer:

Step-by-step explanation:

(Look at the picture)

We have the triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.

We have a = 14. Therefore x = 2a ⇒ x = 2(14) = 28

[tex]\bf \begin{array}{llll} x+y=1&\times(-1)\implies &\begin{matrix} -x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-y&=-1\\ x-y=-6&&\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~~~ -y&=-6\\ \cline{3-4}\\ &&~\hfill -2y&=-7 \end{array} \\\\\\ y=\cfrac{-7}{-2}\implies \blacktriangleright y=\cfrac{7}{2} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{substituting on the 1st equation}}{x+\left( \cfrac{7}{2} \right)=1\implies x=1-\cfrac{7}{2}}\implies \blacktriangleright x=-\cfrac{5}{2} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(-\frac{5}{2}~~,~~\frac{7}{2} \right)~\hfill[/tex]

The elimination method shows that the system of equations x + y = 1 and x - y = -6 has a single solution, which is the ordered pair (-5/2, 7/2).

To solve the system of equations x + y = 1 and x - y = -6 using the elimination method, we can add the two equations together to eliminate y. The resulting equation would be:

2x = -5

Dividing both sides by 2 gives us x = -5/2. We can then substitute the value of x back into either of the original equations to find y. Using the first equation x + y = 1:

-5/2 + y = 1

Adding 5/2 to both sides gives us y = 1 + 5/2, which simplifies to y = 7/2.

The solution set is therefore (-5/2, 7/2).

This system of equations has a single solution, so the correct answer is A, and the solution set is written as an ordered pair.

Answer:

The solution is the point (3,5)

The graph in the attached figure

Step-by-step explanation:

step 1

Line A ----> (2,6),(6,2)

Find the equation of the line A

Find the slope

m=(2-6)/(6-2)

m=-1

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=-1

point (2,6)

substitute

y-6=-1(x-2)

y=-x+2+6

y=-x+8 ------> equation of the line A

step 2

Line B ----> (0,3),(4.5,6)

Find the equation of the line B

Find the slope

m=(6-3)/(4.5-0)

m=(2/3)

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=(2/3)

point (0,3)

substitute

y-3=(2/3)(x-0)

y=(2/3)x+3 ------> equation of the line B

step 3

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both lines

The solution is the point (3,5)

see the attached figure

Its DE and ik its too late but the points is good. oof

Answer:

Step-by-step explanation:

[tex]\dfrac{1}{2}x+3<2x-6\qquad\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup^1\cdot\dfrac{1}{2\!\!\!\!\diagup_1}x+2\cdot3<2\cdot2x-2\cdot6\\\\x+6<4x-12\qquad\text{subtract 6 from both sides}\\\\x<4x-18\qquad\text{subtract 4x from both sides}\\\\-3x<-18\qquad\text{change the signs}\\\\3x>18\qquad\text{divide both sides by 3}\\\\x>6[/tex]

321

Look for a pattern: The term is 11 more than the number before. this means 11 is added each time.

Since you start with 2 and the number goes up by 11 per term, the equation you would use to find the nth term would be 11n+2

To find the 29th term, simply plug in 29

11n+2

11(29)+2

321 

The 29th term is 321.

First you have to find the rate of change. It would be 11 because 35 - 24 = 11, 24 - 13 = 11 and 13 - 2 = 11.

These are the first 4 terms so just keep adding on 11 until you get 29 terms.

2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167, 178, 189

1    2   3    4    5    6    7    8    9    10    11    12  13    14     15    16   17      18

200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310

   19   20   21     22    23    24    25    26    27    28    29

Your final answer would be 310.

Answer:

7

Step-by-step explanation:

Using the trigonometric identity

• 1 + cot²x = cosec²x, then

2(cosec²Θ + cosec²Θ - 1 )

= 2(2cosec²Θ - 1)

= 4cosec²Θ - 2

= 4 × ([tex]\frac{3}{2}[/tex] )² - 2

= 4 × [tex]\frac{9}{4}[/tex] - 2

= 9 - 2

= 7

3 kids and $24 will give each 24/3=$8 each

$8 for 4days is 8/4=$2 a day they spent