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Help asap To measure the thickness of a dime, you would use meters centimeters kilometers millimeters

Help asap To measure the thickness of a dime, you would use meters centimeters kilometers millimeters

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1. 7.2 aliens =1 monster. 1 monster= 15.5 oranges. Using the conversion above, about how many oranges are equal to 1 alien? 2. In a scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represents 1 square meters? 3. While driving with his father, Amit holds his breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds that he holds his breath, on average for about 8 seconds. If his father drives the car at 60 mph through the tunnel, according to the average time, Amit holds his breath, about how long is the tunnel. 4. Lea’s car travels on average of 30 miles per gallon of gas. If she spent \$20.70 on gas for a 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?

127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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Fined the volume of the solid in cubic millimeters

Solution:

The Given Rectangle having dimensions

Length = 80 cm

Let the Six squares which has been cut from this rectangle have side of length a cm.

Area of each square = (Side)²= a²

Area of 6 Identical Squares = 6 × a²= 6 a²

If four squares are cut from four corners and two along Length,

then , Length of Box = (80 – 3 a)cm, Breadth of Box = (50 – 2 a)cm, Height = a cm

Volume of Box =V = Length × Breadth × Height

V = (80 – 3 a)× (50 – 2 a)× a

V   = 4000 a – 310 a² + 6 a³

For Maximum Volume

V’= 0 , where V’ = Derivative of V with respect to a.

V’= 4000 – 620 a + 18 a²

V’ =0

18 a² – 620 a + 4000= 0

9 a² – 310 a + 2000=0

using determinant method

cm

V”=1 8 a – 310 = -ve

which shows , when a = 8.6 cm , volume is maximum.

So, V = 4000×8.6 – 310×(8.6)²+6×(8.6)³=15288.736 cm³

OR

If four squares are cut from four corners and two along Breadth,

then , Length of Box = (80 – 2 a)cm, Breadth of Box = (50 –  3 a)cm, Height = a cm

Volume of Box =V = Length × Breadth × Height

V = (80 – 2 a)× (50 – 3 a)× a

V   = 4000 a – 340 a² + 6 a³

For Maximum Volume

V’= 0 , where V’ = Derivative of V with respect to a.

V’= 4000 – 680 a + 18 a²

V’ =0

18 a² – 680 a + 4000= 0

9 a² – 340 a + 2000=0

Using Determinant method

cm

V”=18 a -340= -ve value when a = 7.6 cm, shows volume is maximum when a = 7.6 cm

V= 4000×7.6 -340 × (7.6)² +6× (7.6)³=13395.456 cubic cm

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The hypotenuse of a right triangle is 26 millimeters. One leg of the right triangle is 10 millimeters. What is the length of the other leg? 18 millimeters 20 millimeters 24 millimeters 28 millimeters

The given statement is False.

Step-by-step explanation:

Let us suppose a triangle ABC.

The law of cosine is given by

And the Pythagorean theorem is given by

Now, in order to the law of cosine to be in the form of Pythagorean theorem, we must have 2abcos C =0.

a and b can’t be zero since it represent the sides of the triangle. Hence, we have

cos C= 0

thus, the value of C is 90 degrees. Hence, the triangle must be a right angle triangle.

Thus, the triangle shouldn’t be acute triangle.

Therefore, the given statement is false/

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Susan dropped a nail into a graduated cylinder filled with water. She then recorded the number of millimeters the water rose in the cylinder. Which property of the nail can be determined by the change in height of the water?

19.2 g of B2H6 will produce 1.39 moles of water

Further Explanation

Moles, Atomic mass and Molecular mass

• 1 mole of a pure substance contains a mass that is equal to the relative atomic mass or molecular mass of the substance.
• Therefore; molar mass is given as grams per mole of a substance
• Hence;

Molar mass = mass of a substance/ Number of moles

g/mol = g /mole

M = m/n; where M is the molar mass, m is the mass and n is the number of moles

• From this relationship we can therefore, calculate mass by multiplying the number of moles by molar mass of a substance.
• That is; Mass = moles x molar mass
• To calculate number of moles;

We have; n = m/M

Number of moles = Mass of the substance/ Molar mass

In this question;

The equation for the reaction is;

B₂H₆ + 3O₂ → 2HBO₂ + 2H₂O

Step 1; Moles of B₂H₆

Molar mass of B₂H₆ is 27.66964 g/mol

Therefore;

Number of moles = Mass/molar mass

= 19.2 g/27.66964 g/mol

= 0.6939 moles B₂H₆

Step 2: Moles of H₂O

Mole ratio; 1 mole B₂H₆ produces 2 moles of H₂O

Therefore;

Moles of H₂O = 0.6939 moles x 2

= 1.3878 moles

= 1.39 moles of H₂O

Keywords: Moles, Molar mass, mole ratio

Level: High school

Subject: Chemistry

Topic: Moles

Sub-topic: Moles, Molar mass

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An​ assembly-line machine turns out washers with the following thicknesses​ (in millimeters). Find the mean and standard deviation of the thicknesses. 1.42, 1.83, 1.43, 1.87, 1.22, 1.44, 1.72, 1.91, 1.42, 1.87, 1.42, 1.99, 1.27, 1.94, 1.67, 1.22

When the profit is 0; then P(t)=0
You have this equation:
t⁴-5t²+4=0

Then, you have to do the following change:
t²=z

you have this other equation:
z²-5t+4=0

Now, you can solve this square equation:
z=[5⁺₋√(25-16)]/2=(5⁺₋√9)/2=
you have two solutions for z.
z₁=(5-3)/2=1
z₂=(5+3)/2=4

Now; if z=1; then
t²=z
t²=1
t=⁺₋√1

We have two solutions:
t=-1 this is not a valid solution:
t=1;

Then in 2001  (2000+t=2000+1=2001) the profit was 0.

If z=4, then:
t²=z
t²=1
t=⁺₋√4

We have two solutions:
t=-2 this is not a valid solution:
t=2;

Then in 2002  (2000+t=2000+2=2002) the profit was 0.

Answer: the yeares in which the profict was 0, were 2001 and 2002.