When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 977,647 radioactive atoms, so 22,353 atoms decayed during 365 days. a. Find the

Answer:

9x + 4

Step-by-step explanation:

Combine like terms which are 5x and 4x and 6 and -2

The solution to the equation is x = 17/30.

To solve the equation, start by combining like terms on both sides.

On the left side, we have the fraction 2/3 and the term -4x.

On the right side, we have the fraction 7/2 and the term -9x.

To combine the fractions, we need a common denominator.

The least common multiple of 3 and 2 is 6.

So, we can rewrite 2/3 as 4/6 and 7/2 as 21/6.

Now, the equation becomes:

4/6 - 4x = 21/6 - 9x

Next, let's get rid of the fractions by multiplying both sides of the equation by 6:

6 * (4/6 - 4x) = 6 * (21/6 - 9x)

This simplifies to:

4 - 24x = 21 - 54x

Now, we can combine the x terms on one side and the constant terms on the other side.

Adding 24x to both sides gives:

4 + 24x - 24x = 21 - 54x + 24x

This simplifies to:

4 = 21 - 30x

Next, subtract 21 from both sides:

4 - 21 = 21 - 30x - 21

This simplifies to:

-17 = -30x

Finally, divide both sides by -30 to solve for x:

-17 / -30 = -30x / -30

This simplifies to:

x = 17/30

So the solution to the equation is x = 17/30.

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Answer:

2880 tiles

Step-by-step explanation:

A rectangular path has dimensions 60 m and 3 m.

Area of a rectangular path = length × breadth = 60 × 3 = 180 \(m^2\)

Use \(1\,m^2=10000\,cm^2\)

So,

Area of a rectangular path = 180(10000) = 18,00,000 \(cm^2\)

Side of a square tile = 25 cm

Area of a square tile = side × side = 25(25) = 625 \(cm^2\)

Number of square tiles = Area of a rectangular path ÷ Area of a square tile

= \(\frac{1800000}{625} =2880\) tiles

Answer:

Step-by-step explanation:

if you modify the parent function to go up and down

for example parent function is y=|x| to go down 3 you do y=|x|-3

if you modify the parent function to go left  and right

for example parent function is y=|x| to go right 3 you do y=|x-3|

a.goes down 3, and 2 to the right

y=|x-2|-3

b. 3 down and 1 to the left

y=(x+1)²-3

c. 5 up and 2 to the right

d. 1 up and 5 to the right

The blood viscosity and vessel length remain relatively constant, the regulation of vessel radius becomes the primary mechanism for controlling resistance in the body.

Blood viscosity refers to the thickness or stickiness of blood, which is determined by the number and size of red blood cells, as well as the concentration of proteins and other substances in the plasma.

Blood viscosity affects resistance because the thicker the blood, the more difficult it is for it to flow through the blood vessels.

Blood vessel length refers to the distance that blood has to travel through the vessels, which affects resistance because the longer the vessel, the more difficult it is for blood to flow through it.

However, vessel length remains relatively constant in the body because it is determined by the body's anatomy and does not change significantly over time. Therefore, the only time when vessel length can change is during a surgical procedure or injury that alters the anatomy of blood vessels.

Mathematically, the resistance to blood flow (R) can be calculated using the formula R = (8 x viscosity x length) / (π x radius⁴).

This formula shows that blood viscosity and vessel length are directly proportional to resistance, while vessel radius is inversely proportional.

Therefore, any increase in blood viscosity or vessel length will increase resistance, while any decrease in vessel radius will increase resistance.

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Answer:

B, D, H, I, J

Step-by-step explanation:

Median: A line segment that joins the vertex of a triangle to the midpoint of the opposite side.

Answer:

\(g(x) = \frac{x^2}{8}\)

Step-by-step explanation:

The function f(x) is compressed b a factor of 8 to function g(x).

This means that the function f(x) is multiplied by 1/8 (vertical compression) to get g(x)

\(f(x)=x^2\)

\(=> g(x) = 1/8 * x^2\\\\g(x) = \frac{x^2}{8}\)

That is the equation of g(x)

Answer:

rational number is the number that can change to fraction but irrational number can't

The axis of symmetry and vertex of the graph of 2 - 12x + 2 y = 3x  The correct answer is b. Axis: x = 2 Vertex: (2, 2).

To find the axis of symmetry and vertex of a graph, we need to manipulate the given equation into vertex form, which is in the form of (x - h)^2 = 4p(y - k), where (h, k) represents the vertex.

Starting with the given equation 2 - 12x + 2y = 3x, we rearrange it as 3x - 2y = -2. Next, we isolate the x term by subtracting 3x from both sides: -2y = -3x - 2. Then, we divide both sides by -2 to get y isolated: y = (3/2)x + 1.

Comparing this equation to the vertex form, we see that the coefficient of x is 3/2, which is equivalent to 6/4 or 1.5. This tells us that the vertex lies on the line x = 2. Therefore, the correct answer is b. Axis: x = 2 Vertex: (2, 2).

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The ratio of apples to bananas, given 6 bananas and 2 apples, is 1:3. The ratio of apples to bananas can be determined by dividing the number of apples by the number of bananas.

In this case, there are 2 apples and 6 bananas. Dividing 2 by 6 gives us the ratio of 1:3. To represent the ratio in the given answer choices:

Choice (a) states 2:6, which is incorrect as it does not match the given quantities.

Choice (b) states 6:2, which is also incorrect as it swaps the quantities. Choice (c) states 2:8, which is incorrect as it changes the quantity of bananas.

Choice (d) states 8:2, which is incorrect as it swaps the quantities. Therefore, the correct ratio of apples to bananas is 1:3, indicating that for every apple, there are three bananas.

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The standard error of the mean is $128.125.

Sample size, N = 256

Mean Sample Price: $35,420

$2,050 is the standard deviation.

Mean Standard Error,

The confidence interval of the mean is calculated as follows:

Om = o ÷ sqrt(N)

Om is equal to the sample distribution's mean standard deviation, where o is the sampling distribution's standard deviation of a statistic.

n = sample size

So, using the supplied as a substitute for the formula:

Om = $2,050 ÷ sqrt(256)

Om = $2,050 ÷ 16

= $128.125

Consequently, $128.125 is the sample standard deviation of the mean.

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"As x increases, y increases along entire the graph".

A cubic function is a polynomial function of degree 3.

According to the given question.

We have a cubic function

\(f(x) = x^{3} +x^{2}+x+1\)

To find the behavior of graph, we will draw the graph of the cubic function.  

For this we will find the values of f(x), for different values of x.

So,

At x = 0

\(f(0) = (0)^{3} +(0)^{2} +0+1=1\)

At  x = -1

\(f(-1) = (-1)^{3} +(-1)^{2} +(-1)+1\\\)

\(\implies f(-1) = -1+1-1+1=0\)

At x = 1

\(f(1) =(1)^{3} +(1)^{2} +1+1\)

\(\implies f(1) = 1+1+1+1=4\)

At x = -2

\(f(-2) = (-2)^{3} +(-2)^{2} +(-2)+1\)

\(f(-2) = -8+4-2+1= -5\)

If we draw a graph using these points (0, 1), (-1, 0), (1, 4) and (-2, -5).

We see that "as x increases, y increases along entire the graph".

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3.31×\(10^-^5\) g is equivalent to 0.0331 μg which is obtained by using the conversion factor.

To convert from grams to micrograms, we need to consider the conversion factor that relates the two units. The prefix "micro-" represents a factor of \(10^-^6\), which means there are 1,000,000 micrograms in a gram. Therefore, to convert grams to micrograms, we multiply the given value by 1,000.

In this case, we have 3.31×\(10^-^5\) g. To convert this value to micrograms, we can multiply it by 1,000:

= 3.31×\(10^-^5\) g × 1,000

= 3.31×\(10^-^5\) × 1,000

= 3.31×\(10^-^5\) × \(10^{3}\)

= 3.31×\(10^(^-^5^+^3^)\)

= 3.31×\(10^-^2\)

= 0.0331 μg

Therefore, 3.31×\(10^-^5\) g is equivalent to 0.0331 μg.

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Anwser:

180/3=60

60/12=5

3x(12x5)=180

b=5

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

3/4*1/3=1/4..……...

Answer:

Multiplying 1 / 3 by 4 / 4 = 4 / 12

4 quarters of 1 / 3 = 4 / 12

Therefore, 3 /4 of 1 / 3 = 3 / 12 = 1 / 4

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a + b)²

= (a + b)(a + b)

Each term in the second factor is multiplied by each term in the first factor, that is

a(a + b) + b(a + b) ← distribute parenthesis

= a² + ab + ab + b² ← collect like terms

= a² + 2ab + b²

Answer:

(a+b) is squared which means (a+b)(a+b)

Lets prove it

= (a+b)(a+b)

= a(a+b) + b(a+b) (Here a will mutiply by (a+b) and b will mutiply with (a+b)

= a²+ab + ab + b²

= a²+ 2ab + b²

Hence proved (a+b)² = a²+ 2ab + b²

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The required equation will be 200-80h=20 as the statement says, "You want to take a bus to go visit your friend in a different city. The distance between two cities is 200 kilometers and the bus drives 80 kilometers per hour. If the bus is 20 kilometers away from your friend’s city".

In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Equations can be classified into three types based on their degree:

Here,

The distance between two cities=200 KM

The speed of bus=80 KM/hour

Time travelled=h hours

The distance travelled by bus=80h

The difference between distance=20

200-80h=20

As stated in the statement, the required equation is 200-80h=20 "You want to take the bus to see a friend in another city. The distance between the two cities is 200 kilometers, and the bus travels at an average speed of 80 kilometers per hour. If the bus is 20 kilometers away from your friend’s city".

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If Lysosomes break open during the process of digestion, releasing enzymes into the cytoplasm. The statement that may explain why the entire cell may not be digested is: 3. The pH of the cytoplasm causes the enzymes to function less effectively.

Lysosomes can be defined as vesicles that is made up of enzyme. This Lysosomes  enables the process of digestion to take place and the enzyme found in lysosomes also  help to break down biological molecule.

The reason why the whole cell may not be digested  in an situation where enzymes  are released into the cytoplasm  is that the pH of the cytoplasm  led to the enzymes  not to function effectively.   Optimum PH is required for cytoplasm  to function more effectively.

Therefore the correct option is B.

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Could you please provide the units

Hope this helps

Answer:

A)  81 x $2 = $162. So 81  boxes of juice cost $162

B) 78 x $4 = $312. So 78 muffins cost $312

C)  52 x $29 =$1,508. So 52 CDs cost $1,508

D)  I can’t see the picture to the side

Answer: (3,3)

Step-by-step explanation:

Answer:

40 pensil

Step-by-step explanation:

Dari pertanyaan di atas, kita diberitahu bahwa:

Dita memiliki 10 kotak pensil

1 kotak pensil = 36 pensil

10 kotak pensil =

Cross Multiply

10 × 36 = 360 pensil.

Dari pertanyaan tersebut, kami diberitahu bahwa Dita memiliki 9 orang teman dan ia membagikan semua pensilnya secara merata kepada mereka di hari ulang tahunnya.

Jumlah pensil yang diterima setiap teman dihitung sebagai:

360 pensil ÷ 9 teman

= 40 pensil.

Oleh karena itu, setiap teman mendapat 40 buah pensil.

Answer: B

Step-by-step explanation:

9/6 divided by 3/2

you flip 3/2 to 2/3 and multiply

9/6 times 2/3 = 1

Answer:

Step-by-step explanation:

\(area = \frac{1}{2} \times base \times height \\ 16 {cm}^{2} = \frac{1}{2} \times 2x \times x \\ 16 {cm}^{2} = \frac{2 {x}^{2} }{2} \\ \\ 16 {cm}^{2} \times 2 = 2 {x}^{2} \\ 32 {cm}^{2} = 2 {x}^{2} \\ \frac{32 {cm}^{2} }{2} = {x}^{2} \\ 16 {cm}^{2} = {x}^{2} \\ \sqrt{16 {cm}^{2} } = \sqrt{ {x}^{2} } \\ 4cm = x \\ \)

Answer:

Step-by-step explanation:

Answer:

Any better explanation

Answer:

49

Step-by-step explanation:

Given

v² - 14v

To complete the square

add ( half the coefficient of the v- term )² to v² - 14v

v² - 14v + (- 7)²

= v² - 14v + 49

= (v - 7)² ← a perfect square

The length of the diagonal of the room is approximately 21.2 feet when rounded to the nearest tenth.

Given information:

A square room in Denise's house measures 15 feet by 15 feet.

Since the room is square, the diagonal forms the hypotenuse of a right triangle whose legs are the sides of the square.

Each side of the square measures 15 feet, so we have:

d² = 15² + 15²

Simplifying:

d² = 2(15²)

d² = 2(225)

d² = 450

Taking the square root of both sides:

d ≈ 21.2

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Answer:

33

Step-by-step explanation:

do it in reverse

there are 3 numbers

average is 20

that means total is 20 times 3 which is

60

7+20+x=60

27+x=60

x=60-27=

33

Answer:

x = 33

Step-by-step explanation:

we find the "average" of a data set by adding all of the numbers in the data set together, and then dividing by the number of numbers/values present

for example,

the average of 2 and 20

2 + 20 = 22

(there are two numbers, so we divide by 2)

22 / 2 = 11

so, this example has an average of 11

we can apply the same logic to a variable:

we know that

\(\frac{20+7+x}{3}\)  = 20

We can now solve for x:

\(\frac{20+7+x}{3}\) = 20  

 · 3          ·3      {multiply both sides by 3}

20 + 7 + x = 60  {combine like terms}

27 + x = 60  {subtract 27 from both sides to isolate x}

x  = 33

{check answer:
7 + 20 + 33 = 60

60 / 3 = 20      (divided by 3 because we have 3 numbers) }

so, the value of x is 33

(x = 33)

hope this helps!!

Answer:

f(-5) = 4(-5) + 1 = -20 + 1 = -19

f(-1) = 4(-1) + 1 = -4 + 1 = -3

f(2) = 4(2) + 1 = 8 + 1 = 9

f(3) = 4(3) + 1 = 12 + 1 = 13

f(5) = 4(5) + 1 = 20 + 1 = 21

To remove the discontinuity at \(\displaystyle\sf x=1\), we need to find the new value \(\displaystyle\sf f(1)\) should be assigned.

Given the function \(\displaystyle\sf f(x)\):

\(\displaystyle\sf f(x)=\begin{cases}x^{2}+2, & x<1\\2x, & x=1\\3, & x>1\end{cases}\)

To remove the discontinuity at \(\displaystyle\sf x=1\), we need to ensure that the left-hand limit and the right-hand limit of \(\displaystyle\sf f(x)\) at \(\displaystyle\sf x=1\) are equal.

The left-hand limit is obtained by evaluating \(\displaystyle\sf f(x)\) as \(\displaystyle\sf x\) approaches \(\displaystyle\sf 1\) from the left:

\(\displaystyle\sf \lim_{x\to 1^{-}}f(x)=\lim_{x\to 1^{-}}(x^{2}+2)=(1^{2}+2)=3\)

The right-hand limit is obtained by evaluating \(\displaystyle\sf f(x)\) as \(\displaystyle\sf x\) approaches \(\displaystyle\sf 1\) from the right:

\(\displaystyle\sf \lim_{x\to 1^{+}}f(x)=\lim_{x\to 1^{+}}3=3\)

Since the left-hand limit and the right-hand limit are both equal to \(\displaystyle\sf 3\), we can assign \(\displaystyle\sf f(1)\) the value of \(\displaystyle\sf 3\) to remove the discontinuity.

Therefore, the new value for \(\displaystyle\sf f(1)\) should be \(\displaystyle\sf 3\).

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