Solve this system by substitution, y = 4x + 12. -3x + 2y = 4​

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:

$5.68

Step-by-step explanation:

142% of the current price of $4 per gallon is found by multiplying these numbers:

 142% × $4.00/gal = $5.68/gal

_____

Of course, you know that 142% = 142/100 = 1.42. The numbers get multiplied and the units ($/gal) get applied to the result.

Multiplication by 4 is easily done mentally by doubling twice:

 4×1.42 = 2×(2×1.42) = 2×2.84 = 5.68

Answer:

is it twelve ?

Step-by-step explanation:

:-|

Answer:

16 times

Step-by-step explanation:

Since he has a 4-gallon aquarium and a 1-quart container, and since there are 4 quarts in every gallon, he'll need to fill the aquarium with the container full 16 times because for every gallon, he'll need to fill the aquarium 4 times. This is the equation:

4*4=16 times

When translated over the x axis, the x values remain the same and the y values become the opposite sign ( a negative becomes a positive and a positive becomes a negative)

A( 1,4) becomes A’(1,-4)

B(3,-2) becomes B’(3,2)

C(4,2) becomes C’(4,-2)

The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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From the calculation, the growth rate is 0.88.

To find the relative growth rate

P1 = Poe^rt

P2 = Poe^rt

Thus;

1920 = Poe^4r ------ (1)

1966080 =Poe^12r -------(2)

P2/P1 gives;

1966080/1920 = Poe^12r/Poe^4r

1024 = e^12r/e^4r

1024 =e^8r

1024 = (e^r)^8

2^10 = (e^r)^8

e^r = 2^1.25

e^r = 2.38

r = ln(2.38)

r = 0.88

The initial size of the culture is;

1920 = Poe^(0.88 * 4)

Po = 1920/e^(0.88 * 4)

Po = 57

The  expression for the exact number of bacteria after t hours is

P(t) = 57e^0.08t

The growth (in bacteria per hour) after 9.5 hours is

P(t) = 57e^(0.88 * 9.5)

P(t) = 243544

For the number to reach 72,000;

72,000 =  57e^0.88t

72,000/57 = e^0.88t

ln 126 = ln[e^0.88t]

4.8 = 0.88t

t = 4.8/0.88

t = 5.5 hours

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The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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The cost of students ticket is $37.5and the cost of general admission is $187.5.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Assume s be the students tickets cost and g be the general admission cost.

From the given information,

⇒  s + g = 225             ..(1)

 5s + 7g = 1500         ..(2)

From equation (1),

s = 225 - g

Plug the value of s in equation (2)

5(225 - g) + 7g = 1500

1125 - 5g + 7g = 1500

                  2g = 1500 - 1125

                  2g = 375

                    g = 187.5

Plug g = 125 in equation (1),

s + 187.5= 225

        s = 225 - 187.5

        s = 37.5

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The average access time for a cache miss is decreased from 61 cycles to 116 cycles by using critical-word first and early restart, which is a considerable improvement.

Critical-word first and early restart are two approaches we can employ to enhance the L2 cache's performance.

The first word in the cache block is accessed first when using the critical-word first strategy to reduce latency. In our scenario, getting the first 8-byte word requires 100 cycles. So, to speed up access when a cache miss occurs, the critical word should be fetched first.

The number of blocks in the cache can be determined using the formula below, assuming a 1 MB L2 cache with 64-byte blocks:

1 MB = 1024 * 1024 bytes

Number of blocks = 1 MB / 64 bytes = 16384

The first 8 bytes from memory must be retrieved in 90 cycles, and each subsequent 8 bytes must be retrieved in 10 cycles. The duration needed to fetch the complete block therefore is:

Time to fetch block = 90 cycles + 7 * 10 cycles = 160 cycles

Now, With the critical-word first and early restart, let's compute the average access time for a cache miss with and without these features.

Without critical-word first and early restart:

The probability of referencing the first word in a block is 30%.

The probability of referencing the remaining words in a block is (1 - 0.3) / 7 = 0.1.

So, When a cache miss occurs without using critical-word first and an early restart, the average access time is:

Average access time = probability of referencing first word * time to fetch critical word + probability of referencing remaining words * time to fetch block

= 0.3 * 90 cycles + 0.1 * 160 cycles

= 45 cycles + 16 cycles

= 61 cycles

With critical-word first and early restart:

The essential word is retrieved first, which requires 100 cycles.

As soon as the required data is made available, we begin accessing it.

In the background, the remaining words in the block are fetched.

With critical-word first and an early restart, the average access time for a cache miss is as follows:

Average access time = time to fetch critical word + probability of referencing remaining words * time to fetch block

= 100 cycles + 0.1 * 160 cycles

= 100 cycles + 16 cycles

= 116 cycles

Therefore, The average access time for a cache miss is decreased from 61 cycles to 116 cycles by using critical-word first and early restart, which is a considerable improvement.

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The graph is A. And we can calculate the functions as follows

Answer:

8000

Step-by-step explanation:

The expected value of X is given as follows:

E(X) = 8.13.

(representing the expected Apgar score of a randomly selected newborn baby.)

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Hence the expected value of X is calculated as follows:

E(X) = 0 x 0.001 + 1 x 0.006 + 2 x 0.007 + 3 x 0.008 + 4 x 0.012 + 5 x 0.02 + 6 x 0.038 + 7 x 0.099 + 8 x 0.319 + 9 x 0.437 + 10 x 0.053 = 8.13.

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Answer:

The answer is -81.

Step-by-step explanation:

Let me know if I got it wrong.

The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

From the question, we have the following parameters that can be used in our computation:

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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The annual rate of interest which is charged by the loan company given the premises declared in the task content is; 22.05%.

According to the task content; the annual interest rate charged by the company in discuss is to.be determined.

Therefore, it follows from proportion that since, $90 was paid for 167 days;

The amount paid for 360 days will be;

x = (360 × 90)/167

x = $194.01

Therefore, the rate of interest charged per annum can be determined as follows;

194.01 = r% of $880

r = (194.01 × 100)/880

r = 22.05.

Ultimately, the annual rate of interest which is charged by the loan company given the premises declared in the task content is; 22.05%.

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Answer: B. 17

Step-by-step explanation:

4x-3 = 65

Add 3 on both sides

4x = 68

Divide by 4 on both sides

x = 17

BOOM!

Answer:

B) 17

Step-by-step explanation:

To determine the time taken for the plane X to travel:

If plane X averages 800 mph and plane Y averages 400 mph

Distance column is found by multiplying the rate

by time.

The time taken for plane Y to travel = 2hr 30 minutes = 2.5hrs head start

Be sure to distribute the 400(t +2.5)for Plane Y,

and Plane X to distribute 800t

As they cover the same distance

Therefore the plane X will travel for 2 1/2 hours

Hence the correct answer is Option B

Answer:

.3

Step-by-step explanation:

Take path A = .5

Then Path D = .6

P(a and D) = .5 *.6 = .3

The new dimension of the rectangular field are 45 ft by 120ft.

If the field has originally dimensions length L and width W, and we apply a scale factor K, then the new dimensions of the rectangle are:

lenght = K*L

width = K*W

In this case the original dimensions are:

L = 30ft

W = 80ft

And the scale factor is K = 1.5, then the new dimensions are:

L' = 1.5*30ft = 45ft

W' = 1.5*80ft = 120ft

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

Parent function:

f(x) = √x

Add a number to the value of the function, such as k:

f(x) = (√x) + k

If k is positive, the function moves up. If k is negative, the function moves down.

hey!

Step-by-step explanation:

bring -4 to the RHS which then becomes +4.

* bring x/6 to the LHS which will then become -x/6.

So,

x/3 -x/6=2+4

x×2/3×2 - x/6 = 6

2x/6 - x/6=6

x/6=6

×=6×6

x=36

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -8 + 4}{2}~~~ ,~~~ \cfrac{ 6 -2}{2} \right)\implies \left( \cfrac{-4}{2}~~,~~\cfrac{4}{2} \right)\implies (-2~~,~~2)\)

Answer:

The correct option is A. Parallel line.

Answer:

f(x) = -5/9x - 11/9

Step-by-step explanation:

Consider f(x) = y

so if x = -4 => y = 1 and x = 5 => y = -4

so (-4,1) and (5,-4) should be on the same linear equation

Slope m = (y2 - y1)/(x2 - x1)

m = (-4 - 1)/(5 -  -4) = (-5)/(9) = -5/9

y = mx + b

given m = -5/9, x = -4, y = 1

1 = -5/9(-4) + b

b = 1 - 20/9

b = 9/9 - 20/9 = -11/9

so y = -5/9x - 11/9

or f(x) = -5/9x - 11/9

The perimeter of triangle ABC = 60 + 20√3  cm

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

In triangle ADB,

sin (30°) = AD/AB

1/2 = ( 10 √3 ) /AB

AB  = 20√3

In triangle ABC,

cos (30°) = AB/BC

√3 /2 =  20√3 / BC

BC = 40

tan (30°) = AC/AB

1/√3 =  AC/ 20√3

AC = 20

Perimeter of triangle ABC =  AB +BC  + AC

                                           = 20√3  +  40  + 20

                                           = 60 + 20√3

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According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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Step-by-step explanation:

\(\huge\mathfrak\pink{Answer}\)

Total number of students= y

(25/100) xy= 200

25 xy = 200 x 100

25y 20000

y = 20000/25

y 800

total number of students = 800

Step-by-step explanation:

\(\mathfrak\pink{Answer}\)

Total number of students= y

(25/100) xy= 200

25 xy = 200 x 100

25y 20000

y = 20000/25

y 800

total number of students = 800