Hello! I think I have this correct but want to make sure.

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

If we start with 180 g of the isotope, after one half-life the quantity will diminish to  180 g/2 = 90 g which exists half the original quantity.

This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]

After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]

After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]

But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.

The original quantity can then be rapidly computed for six half-lives using the formula below:

[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

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Step-by-step explanation:

Solution:

From the graph, the coordinates of the points A, B and C are (- 1, 0) (0, - 2) and (2, 0) respectively.

Let the equation representing the graph be y = a * x ^ 2 + bx + c

(1)

The curve represented by (i) passes through A(- 1, 0) B(0, - 2) and C(0, 2) So,

- 2 = 0 + 0 + c

c = - 2

Also 0 = a - b - 2

and 0 = a * (0.4 + 2b - 2)

⇒a a - b = 2 2a + b = 1 (ii) ..(iii)

Adding (ii) and (iii)

3a = 3

a = 1

Substituting the value of a in (ii), we have

1 - b = 2

b = - 1

The equation of the curve is y = a * x ^ 2 + bx + c i.e. y = x ^ 2 - x - 2

Answer: Area = 126 square inches

Explanation:

The formula for calculating the area of a triangle is expressed as

Area = 1/2 x base x height

From the information in the diagram,

base = 18

height = 14

Thus,

Area = 1/2 x 18 x 14

Area = 1/2 x 252 = 252/2

Area = 126 square inches

Answer:

just multiply 17×4=?

and it will give u an anserew..

Answer:68 people

Step-by-step explanation:

You take the 17 cars multiplied by four people and you get 68

We have the next function

First we need to make h(x)=y

Then we make x=y and y=x

Then we isolate the y

Therefore the inverse function is

The problem can be modeled with the linear equation:

2c - 1.5 = 6

Where c is the old amount of chips.

So the correct option is the last one.

First, let's define the old amount as the variable "c".

1.5 less than twice the old amount is then written as:

2c - 1.5

And the total text says:

"1.5 less than twice the old amount is equal to 6"

So we have an equation, that equates the above expression and the number y, so we can write the linear equation:

2c - 1.5 = 6

This is the last option

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Based on your earnings from each of the part-time jobs, your fortnightly earnings would be $1,520

First, find out how much you earn in the first part-time job per week:
= (Number of days per week x Number of hours per day x Pay per hour)

= (3 x 6 x 20)

The find out how much you earn in the second part-time job:

= (Number of days per week x Number of hours per day x Pay per hour)

= (2 x 8 x 25)

In a fortnight (two weeks), your earnings would be:

= (2 weeks x (3 x 6 x 20)) + (2 weeks x (2 x 8 x 25))

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

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Fortnightly earnings would be $1,520 based on previous earnings.

Two or more expressions with an Equal sign is called as Equation.

Given that there are two part time jobs.

For first part time

3 days per week I work for 6 hours each day and I earn $20.00 per hour

(3 x 6 x 20)

=360

Second part time

2 days per week, I earn $25.00 per hour, working an 8-hour day.

=2×25×8

=400

Now we need to calculate, the total fortnightly earnings.

= (2 weeks x360) + (2 weeks x 400)

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

Hence $1520 is the fortnightly earnings.

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7069 are the minimum number of balls that must be drawn without replacement to complete the requirement that all balls of a single color be drawn.

First of all, we’ll look at the worst possible scenario and determine the minimum number of balls needed. We know that the color we are looking for is not blue, nor white, nor black (as there are less than 1515 of the same color when talking about those). In our worst possible scenario, we’ll first pull out all the blue, white, and black balls. Add them up. That means that we’ll definitely pull out 2523 balls( 1111 white + 1313 blue + 99 black). We are not done yet. From all the given balls, we are left with red, green, and yellow colored balls. In our worst scenario, we’ll pull out 1514 balls of every single color, and then we’ll finish it with one color (it doesn’t matter which). Since, we have 3 different colors left, that’s 3*1515+1 = 4545+1 = 4546 that is 4546 more balls.

To finish, we simply add the first 2523 balls with 4546, yielding 2523+4546 = 7069 balls.

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Answer: $31,200 per year

Step-by-step explanation:

The question tells us that they are working 40 hours a week and making 15 dollars an hour. We can find out how much they make a week and then multiply by 52 (number of weeks in a year) to find the amount they make in a year.

Per week:

15 * 40 = $600

Per Year:

600 * 52 = $31,200

Answer:

$31,285.74 per year

Step-by-step explanation:

What we know:

- $15 per hour

- 40 hour weeks

- 52.1429 weeks per year

What we need to find out:

- How much money per year

Step 1: Multiply for how much made per week

We know that we need $15 dollars for 40 hours so we start with multiplying them together to see how much we make a year.

40 x 15 = $600 per week

Step 2: Now multiply the amount of weeks a year by the amount made per week

So now we know that we make $600 per week now we have to multiply the amount of weeks in a year by the money made per week so.

52.1429 x 600 = $31,285.74 per year. So the house keeper makes $31,285.74 per year.

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Answer:

$6825.

Step-by-step explanation:

Price in the sale

= 7800 - 12.5% of 7800

= 7800 - 1/8 * 7800

= 7800 - 975

= $6825.

55.557 + 121.4474 + 6.3

we have that

55.557=55.5570

121.4474

6.3=6.3000

so

55.5570

121. 4474

6. 3000

------------------

Answer:

a) £960

b) £576

Step-by-step explanation:

Hi!

Ok so since the store has a 20% sale we multiply 0.2 to the original amount it would have costed without the sale:

a) [tex]1200*0.2 = 240[/tex]

Then we subtract the number we got from the price:

1200 - 240 = 960

Now we do the same thing but this time add since we are trying to find the price of the table before the sale:

b) [tex]480*0.2 = 96[/tex]

480 + 96 = 576

Please ask me if you have any more questions!

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Answer:

Step-by-step explanation:

gas mileage = miles covered/gallons used

but:

miles covered = [tex]35\frac{1}{2}[/tex]

                        = 35.5

gallons used     = 1[tex]\frac{1}{2}[/tex]

                           = 1.5

gas mileage = 35.5/1.5

gas mileage = 23.667 miles/gallon (to 3 decimal places)

gas mileage = miles covered/gallons used

but:

miles covered = [tex]27\frac{1}{5}[/tex]

                        = 27.2

gallons used     = [tex]\frac{4}{5}[/tex]

                         = 0.8

gas mileage = 27.2/0.8

gas mileage = 34 miles/gallon

c)

gas mileage of blue: 23.667 miles/gallon implies the blue car will travel 23.667 miles on 1 gallon

gas mileage of silver: 34 miles/gallon implies the silver car will travel 34 miles on 1 gallon

Hence the silver car would travel a greater distance on 1 gallon than the blue car.

If 830 grams = 1 day.

23.24 kilograms = 4 weeks.

23.24 kilograms were used by Sebastian in those 4 weeks.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 3x = 4 is an equation.

We have,

830 grams is used each day.

830 grams = 1 day ___(1)

1 week = 7 days

Multiply 4 on both sides.

4 weeks = 28 days ___(2)

From (1) and (2) we get,

4 weeks = 28 days

4 weeks = 28 x 1 day

4 weeks = 28 x 830 grams

4 weeks = 23240 grams ____(3)

1000 grams = 1 kg

Multiply both sides by 23240/1000.

23240 grams = 23.24 kilograms _____(4)

From (3) and 94) we get,

4 weeks = 23.24 kilograms

Thus,

23.24 kilograms were used by Sebastian in those 4 weeks.

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Answer: c

Step-by-step explanation:

Elliptical graphs fail the vertical line test as they have same x and y values at some places. Thus elliptical graph is not a function

Answer:

d. y= 2x³

Step-by-step explanation:

All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.

Step-by-step explanation:

open the bracket

y - 1 = 3x - 12

add 1 to both sides

y = 3x - 11

I think that should be it

Answer:y=1/380

Step-by-step explanation:

if you are trying to do y divided by 12 it would be 4560x12

The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.

Given,

A random  sample of n = 40  

The mean time μ = 21.4

and, standard deviation is σ =  3.6 min

The z score (z) is given by the equation:

z = (x - μ) / σ / [tex]\sqrt{n}[/tex]

Substituting , the values we get

z = (20 - 21.4) / 3.6 /[tex]\sqrt{40}[/tex]

z = -2.45

Using the z table:

P(x < 20) = P(z < -2.45)= 0.00714

Hence, The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.  

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3/10ths if im not wrong

=========================================================

Explanation:

A hand of two pairs is when we have 2 cards of the same value, and another 2 of the same value, then the fifth card is something else entirely.

An example hand is:

-------------

We use the nCr formula since order doesn't matter.

C(n,r) = (n!)/(r!*(n-r)!)

For any suit, there are n = 13 cards. We make r = 2 selections for each of the two pair.

C(n,r) = (n!)/(r!(n-r)!)

C(13,2) = (13!)/(2!*(13-2)!)

C(13,2) = (13!)/(2!*11!)

C(13,2) = (13*12*11!)/(2!*11!)

C(13,2) = (13*12)/(2!)

C(13,2) = (13*12)/(2*1)

C(13,2) = (156)/(2)

C(13,2) = 78

There are 78 ways to select which two ranks will be chosen to represent each of the two pair.

Let's say one of the ranks of the two pair is a king. There are n = 4 kings and we select r = 2 of them. That gives C(4,2) = 6 ways to select those two kings. We'll also have 6 ways to select the other two cards in the other pair.

Therefore, we have 78*6*6 = 2808 ways to pick the first four cards that consist of the two pair (eg: 2 kings and 2 queens).

-----------------

So far we've considered just the two pairs. We have one card left to select. There are 13-2 = 11 cards of any particular suit that weren't part of the two pair. There are 4 suits to pick from, which means we have 11*4 = 44 cards to pick from for that fifth and final slot.

-----------------

Summary so far:

That gives 2808*44 = 123,552 different two pair hands possible.

This is out of C(52,5) = 2,598,960 hands

Divide those two values to get the final answer

(123,552)/(2,598,960) = 0.04753901560624

This then rounds to 0.04754 as the final answer.

part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:

Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:

In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:

it means:

For example:

The third part of the questions asks us to solve for "x" the following equation:

To do that we take square root on both sides:

Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:

Answer: 195/4

Step-by-step explanation:

Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.

Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).

Here the ΔCED and ΔPOR,

∠CED=∠POR

Side PR=CD

Side ED=PO

by using SAS rule,

ΔCED≅ΔPOR

Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.

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a. The equation for h is h = 100/x²

b. The function for the volume of the box V, in terms of x is:

v(x) = x²×h

Given, the prism has a square base and a total surface area of 100 cm².

A) let x = the side length of the base and

h = the height of the prism.

equation for h = ?

Volume = b × h

100 cm² = x² × h

h = 100/x²

B) a function for the volume of the box, V, in terms of x.

we know that x is the base and h is the height.

So, volume in terms of x :

v = b×h

v = x² × h

Hence we get the required answers.

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Answer:

  20 cm

Step-by-step explanation:

Given a prism with a right triangle base and a volume of 480 cm³, you want the height of the prism. The base has one side 8 cm, and hypotenuse 10 cm.

The missing edge of the right triangle base can be found using the Pythagorean theorem. It tells us the square of the hypotenuse is the sum of the squares of the other two sides:

  b² = c² +a²

  10² = 8² +a² . . . . . . . use given lengths

  a² = 100 -64 = 36 . . . . subtract 8², simplify

  a = 6 . . . . . . . . . . . . . length of side BC

The area of the right triangle base is ...

  A = 1/2bh . . . . . . . . b is the triangle base; h is its height

  A = 1/2(6 cm)(8 cm) = 24 cm²

The volume of the prism is ...

  V = Bh . . . . . . . . . . . . . . . where B is the base area, and h is the height

  480 cm³ = (24 cm²)h . . . use known values

  h = 20 cm . . . . . . . divide by the coefficient of h

The height of the prism is 20 cm.

a) We will draw the situation.

b) Considering the theory, the vertex of a parabola is represented in (h,k) where h is the x-coordinate, in this case, if our parabola has an amplitude of x=320feet then h=320/2=160feet, and k is the highest y-coordinate 80 feet. So the equation is:

We have to know the value for a, so we will use a point to replace it in the equation and with that, we will know the value, so in x=0 the y-value is 0 too so:

So the equation is:

c. To know the answer to this question we will have to replace x=280feet with the y value we will know if at the moment the ball can go over the tree or if it would crash into it.

At that point, the ball would be 35 feet up so if it could pass over the tree 5 feet higher.

ANSWER

EXPLANATION

Nick has 4 quarts of ice and he wants to split it with 9 members of the team.

To solve this, we have to convert quarts to cups. We have that:

1 quart = 2 pints

and

1 pint = 2 cups

This means that:

1 quart = 2 * 2 cups

1 quart = 4 cups

So, 4 quarts will be:

4 quarts = 4 * 4 cups

4 quarts = 16 cups

Therefore, dividing the ice cream among 9 people would mean that we have to divide 16 cups by 9 people.

That is:

The complete statement is:

1 quart equals 2 pints, which equals 4 cups, so 4 quarts equals 16 cups. Dividing the ice cream among 9 people means each gets 1 7/9 cup(s)​