What is the following simplified product? Assume x greater-than-or-equal-to 0 2 StartRoot 8 x cubed EndRoot (3 StartRoot 10 x Superscript 4 Baseline EndRoot minus x StartRoot 5 x squared EndRoot)
24 x cubed StartRoot 5 x EndRoot minus 4 x squared StartRoot 10 x EndRoot
24 x cubed StartRoot 5 x EndRoot minus 4 x cubed StartRoot 10 x EndRoot
24 x cubed StartRoot 5 EndRoot minus 4 x cubed StartRoot 10 x EndRoot
24 x cubed StartRoot 5 x EndRoot + 4 x cubed StartRoot 10 x EndRoot

Step-by-step explanation:

I assume the measuring cylinder measures the cm³ of its normally liquid content.

because for anything else we would need more information about the dimensions of the cylinder.

and so, originally the cylinder shows 40 cm³.

after dropping the stone in, how many cm³ of water is the cylinder then showing ?

let's first mention some facts we are going to use :

water weighs 1 kg (1000 g) per liter.

and 1 liter fits exactly into a cube of

10 cm × 10 cm × 10 cm = 1000 cm³

so, 1 cm³ water weighs exactly 1 g and has therefore a density of 1 g / cm³.

the stone has a density of 8.6 g / cm³, is therefore heavier than water and sinks (and replaces water correspondingly).

how many cm³ does the stone have (and replaces water) ?

well, it has 129 g, and 8.6 g of the stone fill a cm³.

so, it has

129 / 8.6 = 15 cm³

therefore, as these 15 cm³ of stone replace 15 cm³ of water, this is the same as putting 40 + 15 = 55 cm³ of water into the measuring cylinder.

and the cylinder reads now 55 cm³.

FYI : but there is still only 40 cm³ of water in there.

this is actually used to calculate the density of objects (by first weighing and then dropping them into the water to see how much water they replace).

Answer: 55 cm³.

Step-by-step explanation:

[tex]\displaystyle\\m_{stone}=129\ g\ \ \ \ \ \rho_{stone}=8,6\ \frac{g}{cm^3} \ \ \ \ \ V_{water}=40\ cm^3\ \ \ \ \ V=?.\\ \boxed {\rho=\frac{m}{V} }\\V=\frac{m}{\rho} \\V=V_{water}+V_{stone}\\V_{stone}=\frac{m_{stone}}{\rho_{stone}} \\V_{stone}=\frac{129}{8,6}\\V_{stone }=15\ cm^3.\\V=40+15\\V=55\ cm^3.[/tex]

the radius of the new circle =5cm

5cm is your answer love

▪ [tex]\bold{\dfrac{2x-5}{x^{2} -2}}[/tex]

▪ [tex]\bold{\dfrac{dy}{dx}}[/tex]

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

» [tex] \tt{For \: \: y,}[/tex]

[tex]\longrightarrow\sf{y=v \dfrac{2x - 5}{ {x}^{2} - 2} }[/tex]

[tex]\longrightarrow\sf{\dfrac{dy}{dx} = \cfrac{ ( {x}^{2} - 2)(2) - (2x - 5)(2x)}{( {x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow\sf{\cfrac{2 {x}^{2} - 4 - {4x}^{2} + 10x}{ ({x}^{2} - {2}^{2} )}}[/tex]

[tex]\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^{2} - 4 + 10x}{ ({x}^{2} - {2}^{2} )}}}}[/tex]

» [tex] \tt{At \: \: x = 2,}[/tex]

[tex]\longrightarrow\sf{ \dfrac{ - 2(2) {}^{2} + 10(2) - 4 }{( {2}^{2} - 2 {)}^{2} } }[/tex]

[tex]\longrightarrow\sf{\dfrac{ - 8 + 20 - 4}{4} }[/tex]

[tex]\longrightarrow\sf{ \dfrac{8}{4} }[/tex]

[tex]\longrightarrow{\sf = \boxed{\sf {2}}}[/tex] ✓

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

◆ The value of the given differential function at [tex]\sf{x=2}[/tex] is [tex]\sf{2.}[/tex]

The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the length and y represent the width. Hence:

x + 2y = 50

x = 50 - 2y

Also:

xy = 288

(50 - 2y)y = 288

y = 9; and y = 16

x = 32; and x = 18

The dimensions of the rectangular plot of land that sits on a riverbank is 32 m by 9 m or 18 m by 16 m.

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3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.

What is diameter?

we know that

The diameter of the circle is equal to BD

Applying the Pythagoras Theorem

BD² = BE² + DE²

substitute the given values

BD² = (3)² + (2.5)²

BD² = 9 + 6.25

BD² = 15.25

BD = √15.25

BD = 3.9 cm

Therefore , 3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.

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Answer: A. 33

Step-by-step explanation:

Answer:

15740000 million dollars in profit in year 4

Step-by-step explanation:

Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.

Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars

Answer:

5B; 7B; 1,024; see answer

Step-by-step explanation:

5.

We can see from the table that

a1 = 5

a2= 5·2 = 10

a3= 5·2·2 = 5·2² = 20

a4 = 5·2·2·2 = 5·2³ = 40

...

[tex]a_{n} = 5*2^{n-1}[/tex]

7.

Is given that the filter removes 90% of contaminated air

after run 1 :

100% air

90% contamination removed for 100% air

100% is 10%+10%+10%+10%+10%+10%+10%+10%+10%+10%

10% is still contaminated air

after run 2:

10% air

90% contamination removed for 10% air

10% is 1%+1%+1%+1%+1%+1%+1%+1%+1%+1%

1% is still contaminated air

after run 3:

1% air

90% contamination removed for 1% air

1% is .1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%+.1%

.1% is still contaminated air

11.

Figure 1 = 1 piece

Figure 2 = 4 pieces

Figure 3 = 4² = 16

...

[tex]Figure 6 = 4^{(6-1)} = 4^{5} = 1024[/tex]

12.

[tex](c+d)^{6} \\[/tex]

-we know that the coefficients should be 1, 6, 15, 20, 15, 6, 1

-we start with c to the lowest power 0 and d to the highest power 6  and end with  d to the lowest power 0 and c to the highest power 6

[tex](c+d)^{6} = 1*c^{0} d^{6} +6*c^{1} d^{5} +15*c^{2} d^{4} +20*c^{3} d^{3} +15*c^{4} d^{2} +6*c^{5} d^{1} +1*c^{6} d^{0}[/tex]

-we simplify to have the final answer:

[tex](c+d)^{6 } = d^{6} +6cd^{5} +15c^{2} d^{4} +20c^{3} d^{3} +15c^{4} d^{2} +6c^{5} d+c^{6}[/tex]

The value of u in the special triangle is 2√3

The complete question is added as an attachment

From the attached figure, the value of u can be calculated using the following sine trigonometry ratio

sin(x) = Opposite/Hypotenuse

Where

x = 30

Opposite = u

Hypotenuse = 4√3

Substitute the known values in the above equation

sin(30) = u/4√3

Multiply both sides of the equation by 4√3

u = 4√3 * sin(30)

Evaluate the trigonometry expression sin(30)

u = 4√3 * 1/2

Evaluate the product

u = 2√3

Hence, the value of u in the special triangle is 2√3

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Answer:

See below

Step-by-step explanation:

Out of 25 games, they won 14

Fraction won = won / total = 14 / 25

Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %

To find the number of games lost

25-14 = 11

Fraction won = won / total = 11 / 25

Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %

To check your work, the percent total should be 100

56+44 = 100

Answer:

99cm

Step-by-step explanation:

A meter is equal to 100cm

The rope is a metre (m) long but a centimetre (cm) less.

100cm - 1cm = 99cm

Answer:

60m3

Step-by-step explanation:

my son got the right anser

Answer:

60m^3

Step-by-step explanation:

The formula for volume of a rectangular prism is height*width*depth

We can see two distinct shapes here

First, we find the volume for the bigger shape

We can see the measurements that pertain to it...

Width is 6m, depth is 3m, and height is also 3m

Multiply those three, you get 54m^3

Now the smaller shape...

1m in width, 2m in height, and 3m in depth

Multiply those, get 6m^3

Add the two shapes together, 54+6=60m^3

Step-by-step explanation:

The result is 12 cm³ because to get the volume of a figure you have to multiply all the characters

Answer:

2

Step-by-step explanation:

slope : ( The amount y increases , when x is increased by 1 )

slope : { y2 - y1 / x2 - x1 }

slope : y2 = 2

           y1 = -4

           x2 = 5

           x1 = 2

You must minus the values in the formula to find the slope line that passes through the points:

slope : { y2 - y1 / x2 - x1 }

slope : (2) - (-4) / (5) - (2)

=> 2 + 3 / 3

=> 6/3

=> 2

Text explanation:

Difference between both y-coordinates. = 6

Difference between both x-coordinates. = 3

Divide the difference between y and x. =

y/x =2

Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.

Hope this helps! Sorry it took so long! ⸜(｡˃ ᵕ ˂ )⸝ xx

The slope of the line that passes through the points (2, -4) and (5, 2) is 2.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,

Slope = (y₂-y₁)/(x₂-x₁) =  [2 - (-4)] / (5 - 2)= 6/3 = 2

Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.

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The equation which shows the commutative property of addition is (A) 4+3=3+4.

So,

The commutative property for addition states that, a + b = b + a .

Where a, b is any number.

The above condition is satisfied by the equation

Therefore, the equation which shows the commutative property of addition is (A) 4+3=3+4.

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The correct question is given below:

Which equation shows the commutative property of addition?

A. 4+3=3+4

B. 1(3)=3

C. (2+7)+12=2+(7+12)

D. 4+0=4

Answer: No solution

Distribute the parenthesis

3x-15=2x-10+x

Combine like terms

3x-15=3x-10

This answer has no solution for x.

Expected value of playing the game  = $0.8

What is cost ?

Cost of playing = $2

Expected return

10% chance to win $1 = $1  10% = $0.1

25% chance to win back $2 = $2  25% = $0.5

50% chance to win $5 = $5  50% = $2.5

15% chance to lose $2 (being cost) = $2  15% = ($0.3)

= $0.1 + $0.5 + $2.5 - $0.3 = $2.8

Now for this we have to pay fixed cost $2

Thus, expected value of playing game = $2.8 - $2 = $0.8

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[tex] \: \: \: \: \: \: \: y = \frac{ - 7x}{8} + 4 \\ \: \: \: \: \: \: multiply \: all \: by \: 8 \\ \: \: \: \: \: \: \: \: 8y = - 7x + 32 \\ \: \: \: \: \: \: \: \: \: 7x + 8y = 32[/tex]

Answer:

Step-by-step explanation:

Answer:

step 3

Step-by-step explanation:

he should have subtracted 9 to the outside.

whatever you do to the inside you must do to the opposite to the outside

so your final form must be -7(x-3)^2 + 8

Answer:

Ten thousands place

Step-by-step explanation:

84 530 216

Frm here u can see that the 3 is in the ten thousands place

Answer:

A

Step-by-step explanation:

f(-3) = 2^-3

to get rid of a negative in an exponent, move the whole thing to the denominator.

1/(2^3)

2^3 = 2×2×2

1/(2×2×2)

1/8

Answer:

23. 216
24. 56

25. 52

for 26, 27 i'll try to calculate the answer, sorry

Answer:

130 degrees

Step-by-step explanation:

We know (x-10)+(2x+10) is 180 degrees.

So first we need to find x. (x-10)+(2x+10)=3x

3x=180

x=60

Angle TRV is 2x+10.

If we input 60 in the place of x, it is 2(60)+10=120+10=130.

The answer is 130 degrees.

The numbers are 14.42 and 3.6055.

It is the whole which is to be divided into different equal parts. For example, if 10 divided by 2 is 5, then 10 is the dividend here, which is divided into two equal parts whereas 2 is the divisor, the quotient is 5 and the remainder is 0.

We can write the system of equations

x*y=52   .......(1)

[tex]\frac{x}{y}[/tex]=4         ........(2)

We can use substitution to solve

From equation (2) we get,

x = 4y     .......(3)

now substitute in equation (1)

4y*y = 52

[tex]4y^{2} = 52[/tex]

[tex]y^{2} = \frac{52}{4}[/tex]

[tex]y = \sqrt{13}[/tex]

y = 3.605

We can solve for x = ?

from equation (3)

x = 4y

x = 4*3.605

x =   14.42  

Hence, The numbers are 14.42 and 3.6055.

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Answer:

Below in bold.

Step-by-step explanation:

Standard form:

-12x⁴ - 6x² + 3.

Leading Coefficient:

-12.

The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

An equation is an expression that shows the relationship between two numbers and variables.

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let f(t) represents the number of subscribers and t represents the time in months. Hence:

[tex]f(t) = 250(1.4)^t[/tex]

a = 250, b = 1.4

The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.

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Answer: 250,      1 month,      and    1.4

The number of ways people can get off the elevator is 604800 ways.

In this question,

Number of people, n = 7

Number of floors, r = 10

The first person can leave elevator in one of 10 ways. Then second person has to choose from one of remaining 9 floors. Then third person in 8, fourth in 7 ways and so on.

Number of ways people can get off the elevator can be calculated as

⇒ [tex]nP_r=\frac{n!}{(n-r)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(10-7)!}[/tex]

⇒ [tex]10P_{7}=\frac{10!}{(3)!}[/tex]

⇒ [tex]10P_{7}=\frac{(10)(9)(8)(7)(6)(5)(4)3!}{(3)!}[/tex]

⇒ [tex]10P_{7}=(10)(9)(8)(7)(6)(5)(4)[/tex]

⇒ 604800 ways.

Hence we can conclude that the number of ways people can get off the elevator is 604800 ways.

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