Prove that : root5 is included between 2.2 and 2.3​

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer: no, no, no, yes

Step-by-step explanation:

Hello!

Just take each value of "u" and multiply it by 4. If the answer is smaller than 32, it is a solution. If not, it isn't a solution.

Step-by-step explanation:

Goal

Given

6c²-5d+8

c = 5 and d = 4

Step 1

6(5)²-5(4)+8

6(25)-20+8

Step 2

150-20+8

150-12

138

Hence, the solution is 138.

Answer:

138 is answer please give brainliest

a rectangular area with a length of 13 inches and a width of 7 inches.

Length of rectangle = 13 inches

Width of rectangle = 7 inches

With Distribution:

The perimeter of any polygon is the sum of all the sides of the polygon

In the given rectangle we have 2 lengths and 2 widthSo,

Perimeter = length + width + Length+ width

Substitute the value and solve

Perimeter = 13 + 7 +13 +7

Perimeter = 20 + 20

Perimeter =40inches

Without Distribution

The perimeter of rectangle is express as :

Perimeter = 2(length + Width)

Substitute the value and solve

Perimeter=2(13+7)

Perimeter=2(20)

Perimeter-40 inches

It was easier without distribution because it becomes calculation easy.

Answer: Perimeter = 40 inches

It is easier to not distribute

Because it makes calculation easy and short.

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

12.5

Step-by-step explanation:

took this test

The interval where function f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

We have,

The function f(x) crosses the x-axis at (-3, 0), (-1.1, 0), and (0.9, 0), it means that f(x) is negative for x values less than -3, between -1.1 and 0.9, and greater than 0.

Therefore, we can say that:

f(x) < 0 for x < -3 and -1.1 < x < 0.9

And,

The function f(x) has a minimum value of (0, -3) and a maximum value of (-2.4, 17).

This means that f(x) is positive for x values greater than -2.4. Therefore, we can say that:

f(x) > 0 for x > -2.4

Now,

Combining these inequalities, we can say that f(x) is negative over the intervals (-∞, -3) and (-1.1, 0.9), and positive over the interval (-2.4, ∞).

So,

The interval where f(x) is negative and greater than 0 is:

(-∞, -3) U (-1.1, 0)

Thus,

The interval where f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

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Answer:  78.064 cubic meter

Step-by-step explanation:

volume of a cuboid=length × breadth × height.

                                =5.6*4.1*3.4

                                =78.064 cubic meter

ANSWER:

B.

STEP-BY-STEP EXPLANATION:

We have the following expression:

We simplify and we have:

Answer:

Below

Step-by-step explanation:

Where the graphs cross or touch each other is a solution.....see graph below   ....how many solutions do YOU see ?

Answer:

Step-by-step explanation:

Let the total number of action figures = x

75% of x = 48

\(\dfrac{75}{100}*x=48\\\\Multiply \ by \ 100\\\\75*x =48*100\\\\Divide \ by \ 75\\\\x=\dfrac{48*100}{75}\\\\\\x=16*4\\\\x= 64\)

Remaining action figures need to be collected = total figures - number of action figures I have

= 64 - 48 = 16

Number of weeks = 16 ÷ 2 = 8

It will take 8 weeks to collect 16 action figures.

Answer:

p = 1

Step-by-step explanation:

10p + 5 = 18p - 6/2

(given)

______________

10p + 5 = 18p - 6/2

+6/2 +6/2

(addition property of equality)

_______________________

10p + 8 = 18p

-10p -10p

(subtraction property of equality

_________________________

8 = 8p

÷8 ÷8

(division property of equality)

______________________

1 = p

(symmetric property of equality)

___

p = 1

l=3w

3w(4)=48

12w=48

w=4

l=12

hope it helps

comment if u have any questions

Answer:

Length is 18; width is 6.

Step-by-step explanation:

The formula for the perimeter of a rectangle is:

\(P=2l+2w\)

We are given that the perimeter is 48 feet. We are also told that the length is 3 times the width. In other words:

\(l=3w\)

So, substitute this for l and 48 for P. Thus:

\(48=2(3w)+2w\)

Distribute:

\(48=6w+2w\)

Combine like terms:

\(48=8w\)

Divide both sides by 8:

\(w=6\)

So, the width is 6.

The length as we know is 3 times the width, so the length is 3(6) is 18.

And we are done!

The fabric  has a cost per yard of $6 per yard

From the question, the given parameters are:

Yards of fabric = 2 1/2 yards

Cost of the fabric = $15

The cost per yard of the fabric is then calculated as

Cost per yard = Cost of the fabric/Yards of fabric

Substitute the known values in the above equation

So, we have

Cost per yard = 15/(2 1/2)

Evaluate the quotient

So, we have

Cost per yard = 6

Hence, the cost per yard is $6 per yard

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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The slope of the line that runs through (6,2) and (2,1) is 1/4.

It is a question from the chapter of straight lines.

The slope of a line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.

Coordinates of two points (6,2) and (2,1) is given.

We have to find the slope of the line formed by the two coordinates.

We know that,

Formula of the slope of the line formed by coordinates of two points (a,b) and (c,d)  is (d-b)/(c-a)

Hence,

The slope of the line that runs through (6,2) and (2,1)  is (1-2)/(2-6) = (-1)/(-4) = 1/4.

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Answer:

Answer is b

Step-by-step explanation:

Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.

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Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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Answer

the box that is lebeled 6 is quadrant 1 and the one beside it is quadrant 2 and the one labeled 8 is the third and the last is quadrant 4

Step-by-step explanation:

so like this- go to this link i drew it for you

Answer:

It does not, unless \(x=0\) or \(x=1\)

If you remember how to raise a power to a given power you remember to multiply the exponents (or, if you don't, apply the definition of \((x^3)^3=(x^3)(x^3)(x^3)=x^9\)

At this point you're being asked if \(x^9=x^6\) and the only two numbers for which this is true are 0 and 1 (side note: if the left hand side was an even function also \(-1\) was a possible candidate, but alas 9 is odd).

Answer:

21 memebers must be present

Step-by-step explanation:

First we have to convert the percent to decimal form for an easier calculation. Do this by taking 60 and dividing by 100.

You should get 0.60, now just multiply .60 by 35 and you'll get the answer of 21.

Answer:

RS 17.10

Step-by-step explanation:

If they earn 0.95 a day, you can multiply that income by the number of days, which is 18.

RS 17.10

Answer:17

Step-by-step explanation:

Answer:

\( - 3(x - 1) = - 1(5 - x) \\ \\ 3 - x + 1 = - 5 + x \\ \\ - x - x = - 5 - 3 - 1 \\ \\ - 2x = - 5 - 3 - 1 \\ \\ - 2x = - 9 \\ \\ x = \frac{ - 9}{ - 2} \\ \\ x = 4.5\)

\(3 - (x - 1) = - 1 - (5 - x)\)

\(3 - x + 1 = - 1 - 5 + x\)

\((3 + 1) - x = ( - 1 - 5) + x\)

\(4 - x = - 6 + x\)

\(4 + 6 = x + x\)

\(10 = 2x\)

\( \frac{10}{2} = x\)

\(5 = x\)

Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

The answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

What is an ellipsoid?

An Ellipsoid is a closed surface on which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the center.

(a)

x = k:

Trace: Circle in the x-z plane

Identification: Circle

y = k:

Trace: Circle in the y-z plane

Identification: Circle

z = k:

Trace: Circle in the x-y plane

Identification: Circle

The surface is an ellipsoid, which is a 3-dimensional surface that is the result of stretching or compressing a sphere along different axes.

(b)

If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, but it is rotated so that its axis is the x-axis.

(c)

If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore, and its shape cannot be determined from the equation alone.

This is because the equation contains a linear term (2y) that makes it non-quadratic.

To find the shape of the surface, a more in-depth analysis would be required.

Hence, the answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

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There are 0.125 miles in one furlong.

It is the conversion of one unit to another unit with its standard conversion.

Examples:

1 hour = 60 minutes

1 minute = 60 seconds

1 km = 1000 m

Given,

There are 8 furlongs in 1 mile.

Since a furlong is 660 feet, we can convert the number of feet into 1 mile.

Now,

1 mile = 5280 feet

Multiply 660/5280 on both sides.

660/5280 mile =  660 feet

0.125 mile = 660 feet

Therefore,

There are 0.125 miles in one furlong.

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