The number of atoms in standard form is 4 × 10²⁵ atoms
What is standard form?Standard form is number written in the form a × 10ⁿ where 1 ≤ a < 10 and n is an integer
How to find how many atoms are there in the human body altogether in standard form?Since there are about 40 trillion cells in the human body. and each cell consists of about 100 trillion atoms, we have that
40 trillion cells = 40 trillion × 1 cell
Also, 1 cell = 100 trillion atoms.
So, 40 trillion × 1 cell = 40 trillion × 100 trillion atoms.
Now, we know that 1 trillion = 1000 billion
So, Number of atoms = 40 trillion × 100 trillion atoms
= 40 × trillion × 100 × 1 trillion atoms.
= 40 × 1000 billion × 100 × 1000 billion atoms.
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
We know that 1 billion = 1000000000
So,
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
= 40 × 1000 × 100 × 1000 × 1000000000 × 1000000000 atoms
= 40000000000000000000000000
= 4 × 10000000000000000000000000
= 4 × 10²⁵ atoms
So, the number of atoms in standard form is 4 × 10²⁵ atoms
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Find the measure of the exterior angle.
Answer:
since the degree of the adjacent angles is 180°, we find the answer from that
Answer:
128°
Step-by-step explanation:
it is a right triangle, the bottom right one is, from the drawing, 90 °, the sum of the internal angles of all the triangles is 180 °, so making 180 - 90 - 38 we have the missing internal angle of 52 °.
Then we find the outer angle, the inner-outer sum is 180 °, 180 - 52 = 128 ° (your answer)
Alfred begins collecting model cars. He buys 3 new model cars every week. Is the number of cars he owns proportional to the number of weeks that have passed since he started his collection?
The relationship between the number of weeks and cars are proportional since they are dependent on each other.
ProportionRatio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
In this question, Alfred, buy three car each week. As the number of weeks increase, so is the number of his car increasing at definite proportions.
This implies that we can set an equation to represent the number of cars Alfred will have after certain number of weeks.
Let;
x = number of weeksy = number of carsy = 3x
At week 10, Alfred will have
y = 3(10) = 30 cars
After 10 weeks, Alfred will have 30 cars
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show algebraically the sum of two consecutive numbers is always odd
the sum of two odd integers will always be resulted in an odd digit.
What are odd numbers?Odd numbers are entire numbers that can't be isolated precisely into matches. Odd numbers, when separated by 2, leave a rest of 1. , 3, 5, , 9, 11, , 15 are consecutive odd numbers.
These are added together to get n + n+1, or 2n+1. Since +1 make it odd, 2n is even. Any two successive integer sums are hence odd. According to the solution is "2n + (2n + 1) = 4n +1."
Even numbers result from the addition of two fractions, but still only digits result from the addition of one odd number with one even number. In order to only receive an odd number, add one odd as well as one even.
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Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64
A farmer sold 50 cows. If this was 20% of his herd, how many cows were in his herd?
Compare and Explain: Are they equivalent?
3 hours worked for $12; 9 hours worked for $36
Answer:
Yes they are equivalent.
Step-by-step explanation:
$12 divided by 3 is $4
$36 divided by 9 is also $4
Therefore they are equivalent.
Your welcome
Answer:
Yes!
Step-by-step explanation:
You divide 3 by 12 because that's how much they work for an hour. That means they make $36 for 9 hours.
12 ÷ 3 = 4
36 ÷ 9 = 4
They have the same answer which makes them equivalent.
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
X
15
20
25
30
35
y
175
210
245
280
315
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-6x+35=-6x-35−6x+35=−6x−35minus, 6, x, plus, 35, equals, minus, 6, x, minus, 35
(Choice B)
B
-6x+35=-6x+35−6x+35=−6x+35minus, 6, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice C)
C
6x+35=-6x+356x+35=−6x+356, x, plus, 35, equals, minus, 6, x, plus, 35
(Choice D)
D
6x+35=-6x-356x+35=−6x−356, x, plus, 35, equals, minus, 6, x, minus, 35
The equation which has infinitely many solutions include the following: B. -6x + 35 = -6x + 35
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal.
This ultimately implies that, an equation would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and intercept for the two lines are the same.
In this scenario, we can reasonably and logically deduce that the following equations satisfy the condition for an equation which has infinitely many solutions:
-6x + 35 = -6x - 35 (False).
-6x + 35 = -6x + 35 (True).
6x + 35 = -6x + 35 (False).
6x + 35 = -6x - 35 (False).
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Complete Question:
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A. -6x + 35 = -6x - 35
B. -6x + 35 = -6x + 35
C. 6x + 35 = -6x + 35
D. 6x + 35 = -6x - 35
The l of a rectangular field is 5 metres longer than its width. if the perimeter is 150 metres , find the width
Answer:
width = 35 m
Step-by-step explanation:
w is the width, then l = w + 5
Perimeter P = 2(l + w)
=> 150 =2(w + 5 + w)
75 = 2w + 5
2w = 70
w = 35
5. A rectangular 52 inch flat screen TV has a length of 42 inches. The salesman explains that all TV's are sold by the length of the diagonal. So, a 52 inch flat screen TV actually has a diagonal measure of 52 inches. To the nearest whole inch, what is the height of the TV?
The height of the TV is 31 inches . This can be calculated using Pythagoras theorem.
What is Pythagoras theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Main Body:
according to the question --
hypotenuse = 52 in
base = 42 in
height =?
Pythagoras theorem = [tex]{P^{2} +B^{2} }[/tex] = [tex]H^{2}[/tex]
inserting the values --
52² = 42² +H²
H² = 2704- 1764
H² = 940
H≈31 inches
Hence the height of TV is 31 inches
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Peter puts $300.00 into an account to use for school expenses. The account earns 8%
interest, compounded annually. How much will be in the account after 10 years?
Pls solve all the question as per the questions given below
1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD
1b) The additional information required using ASA Congruency postulate is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence rule used is SAS Congruency postulate.
How to use congruency postulates?1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate means Side - Angle - Side. Thus, the additional information is;
∠AOB ≅ ∠BOD
1b) We want to prove that triangle ABC is congruent to triangle PQR by ASA Congruency. We have that;
∠Q = ∠B and ∠R = ∠C. Thus;
The additional information is BC ≅ QR
2a) The symbolic form of the congruent triangles is written as;
ΔABC ≅ ΔADC
2b) The congruence rule used here is SAS Congruency postulate.
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please I need help asap
Use slope-intercept form to write the equation of a line that has a slope of −3 and passes through the point (1, −5).
Use the drop-down menus to select the proper value for each variable that is substituted into the slope-intercept equation.
y =
✔ –5
x =
m =
The equation of line passes through the point (1, -5) will be;
⇒ y = - 3x - 14
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (1, -5).
And, The slope of the line is,
⇒ m = - 3
Now,
Since, The equation of line passes through the point (1, -5).
And, Slope of the line is,
⇒ m = - 3
Thus, The equation of line with slope - 3 is,
⇒ y - 1 = - 3 (x - (-5))
⇒ y - 1 = - 3 (x + 5)
⇒ y - 1 = - 3x - 15
⇒ y = - 3x + 1 - 15
⇒ y = - 3x - 14
Therefore, The equation of line passes through the point (1, - 5) will be;
⇒ y = - 3x - 14
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a marine biologist wants to estimate the mean size of the barnacle semibalanus balnoides on a stretch of rocky shoreline. to do so, he randomly selected twenty 10 by 10 square inch plots and measured the size of every barnacle in each selected plot. this is an example of
Option B is the correct choice
A marine biologist measured the size of each barnacle in twenty 10 by 10 square inch areas that were chosen at random. Cluster sampling is illustrated by this.
For a study that is a population into clusters, such as districts or schools, researchers will divide the population into multiple groups (clusters) and will then randomly select some of these clusters as your sample. Ideally, each cluster should be a miniature reflection of the population as a whole.
In order to determine the average size of the barnacles Semibalanus balconies along a section of rocky shoreline, a marine biologist is conducting this study. To do this, he measured the size of every barnacle in each of the twenty 10 by 10 square inch plots that were randomly chosen. Cluster sampling is illustrated by this. (Option B)
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COMPLETE QUESTION:
A marine biologist wants to estimate the mean size of the barnacle Semibalanus balconies on a stretch of rocky shoreline. To do so, he randomly selected twenty 10 by 10 square inch plots and measured the size of every barnacle in each selected plot. This is an example of
a. convenience sampling.
b. cluster sampling.
c. stratified random sampling.
d. simple random sampling.
e. voluntary sampling.
PLEASE HELP!
4) The "random walk theory of stock prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year, and that the probability that our portfolio rises in price in any one year is 0.65.
a) What is the probability that the portfolio goes up for 3 consecutive years?
b) What is the probability that the portfolio's value moves in the same direction (either up or down) for 3 consecutive years?
c) What is the probability that the portfolio's value goes up for at least 1 of 3 years?
Part (a)
Each year is independent of any other. This allows us to simply multiply the probability values for each increase. Recall that P(A and B) = P(A)*P(B) if and only if events A & B are independent.
(0.65)*(0.65)*(0.65) = (0.65)^3 = 0.274625
Answer: 0.274625=========================================
Part (b)
We calculated the probability of an increase for each of the 3 years back in part (a). Let's calculate we have a decrease 3 times in a row.
0.65 is the probability of increase for any given year, which makes 1-0.65 = 0.35 the probability of decrease for any given year.
Therefore (0.35)^3 = 0.042875 represents the probability of 3 decreases in a row.
Add this result to what we got in part (a)
0.274625+0.042875 = 0.3175
This is done because we could have 3 increases OR 3 decreases (pick one). Think of it like this P(A or B) = P(A) + P(B) where A & B are mutually exclusive events.
Answer: 0.3175=========================================
Part (c)
In the previous part we calculated 0.042875 as the probability of 3 decreases in a row.
1-0.042875 = 0.957125 is the probability of at least one increase. Note how the events "no increases" and "at least one increase" are complementary events. They are opposite. One or the other must happen, which allows us to subtract from 1.
You can think of it like this
P(no increases) + P(at least one increase) = 1
P(at least one increase) = 1 - P(no increases)
Answer: 0.957125Side note: none of the final answers have been rounded.
The volume of the triangular prism is 12.5 m³. The length is 2.5 m and the base is 2 m. What is the width?
Answer: 4.5m
Step-by-step explanation:
because 12.5 can - by 2.5
then 9.0=9 -5.5=4.5
How do you do this
8×+3x+4+5y+2
Step-by-step explanation:
8x + 3x + 4 + 5y + 2
combine x terms:
11x + 4 + 5y + 2
combine numbers:
11x + 5y + 6
[Please comment if you want the answer specifically for x or y.]
Answer:
8x+3x+4+5y+2
11x+9y+2
20xy+2
=22xy
can yall please help
1. The pairs of polygons are similar.
2. The pairs of polygons are not similar.
3. The missing measure is of x = 5.2.
4. The missing measure is of x = 16.
5. The value is AB = 6.
6. The perimeter of the yellow tile is of 240 cm.
7. The value is DF = 0.75.
What are similar polygons?Similar polygons are polygons that share these two following features:
Congruent angles.Proportional side lengths.Hence, for itens 1 and 2, we have that:
1. The pairs of polygons are similar, as the side lengths are proportional.2. The pairs of polygons are not similar, as the side lengths are not proportional, as the ratio of 6 and 9 is different of the ratio of 3 and 4.For item 3, the side lengths are proportional, hence:
x/2.6 = 8/4
x/2.6 = 2
x = 2 x 2.6
x = 5.2.
Same as item 4, hence:
x/10 = 9.6/6
x/10 = 1.6
x = 16.
For item 5, considering the equivalent side lengths, we have that:
AB/8 = 12/16
AB/8 = 3/4
AB = 24/4
AB = 6.
The perimeter of the yellow tile is of 240 cm in item 6, as the ratio between the side lengths is of 3, hence the ratio of the perimeters will also be of 3, then:
3 x 80 cm = 240 cm.
For item 7, we have that:
DF/3.4 = 2.25/9
DF = 3 x 2.25/9
DF = 0.75.
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Principal Interest Rate Time Simple Interest
$12,000 4.25% 5 years
The value of Simple interest for the given data comes as $2550.
Given,
The Principal amount is equal to 12,000 dollars.
The Rate of Interest is stated at 4.25%.
The Total time period given for the question is 5 years.
Let the principal amount be considered as (P), the Rate of Interest per annum be (R), the Time period is (T), and Simple Interest is (S.I).
So, according to the given question,
P = $12,000
R = 4.25%
T = 5 years
We know, Simple interest can be calculated by multiplying the Principal amount with the Rate of Interest as well as the Time period.
If we write it mathematically, the formula will be,
S.I = PRT/100
=> S.I = (12,000* 4.25* 5)/100
=> S.I = (2,55,000)/100
=> S.I = $2550.
Hence, the value of Simple Interest will be 2550 dollars.
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I need help like asap !!!
only numbers and decimal points
Answer:
a = 6.63 cm
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (12)² = a² + (10)²
→ 144 = a² + 100
→ a² = 144 - 100
→ a = √44
→ [ a = 6.63 cm ]
Hence, value of a is 6.63 cm.
−12+(−20)
Enter your answer in the box.
Answer:-32
Step-by-step explanation:
-12+(-20)
-12-20
-32
Answer: -32
Step-by-step explanation:
−12+(−20)=
-12 - 20= ==> adding a negative number is equal to subtracting by the positive version of that number. ?-20=?+(-20)
-(12+20)=-32
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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-2(7+3m) +6m>3 (3m-5)
Answer:
1/9 > m
Step-by-step explanation:
-2(7+3m)+6m>3(3m-5)
Distribute.
-14-6m+6m>9m-15
Combine like terms.
-14>9m-15
1>9m
Get m to be alone.
1/9>m
-2(7+3m) + 6m > 3(3m-5)
-2(3m+7) + 6m > 3(3m-5)
The final answer is m < 1/9
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a change in the unit of measurement of the dependent variable in a model does not lead to a change in:
Throughput is often a dependent variable with "bits per second" as its unit.
what is unit and measurment?
Standards are provided by units of measurement so that all of our measurements' numbers correspond to the same item. A physical quantity is described using numbers as part of the measurement procedure. We can gauge an object's size, warmth, weight, and a number of other characteristics.The metre, for instance, is a common unit for measuring length. Before 1982, the measurement of a meter was the separation of two markings on a unique metal rod.At that time, describing anything as having a length of two meters meant that it was exactly twice as long as the rod that served as the standard for measuring distance. Scientists now use the speed of light to define the meter.Different units were employed in many nations in the past.learn more about units and measurment click here:
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16-2t=5t+9 One solution was found : t = 1 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
Answer
Step-by-step explaination:
This is an algebraic equation. We have to solve it like this......
16-2t=5t+9
-5-2t=-16+9
-7t=-7
Ans: -7t=-7
[24+9-(5x3)+10]÷2
what is the value of the following the expression
Answer:
14
Step-by-step explanation:
[tex](33 - (15) + 10) \div 2 \\ 33 - 15 + 10 \div 2 \\ 18 + 10 \div 2 \\ 28 \div 2 \\ = 14[/tex]
Answer:14
Step-by-step explanation:1/2 (24+9- 5 x 3 + 10
83.978, 78.934, 84.765 Underline the thousandths digit in each number
help meee pleaseeee
Answer:
83.978 the thousandth digit is 3, 78.934 the thousandth digit is 8,84.765 the thousandth digit is 4
Answer:
Step-by-step explanation:
Ok:
1. Identify the thousandths digit
The numbers to the left of the decimal point are the ones and hundreds digits
The first number to the right of the point is the tenths digits
The second to the right of point i s the Hundreths
The third number to the right of point is the thounsandths which is what we are looking for!
2. Apply to problem!
1. 83.978 : Thousandths digit is 8
2. 78.934 : Thousandths digit is 4
3. 84.765 : Thousandths digit it 5
Extra tips and tricks writing as fractions!Ps: Some are not simplified!
1. 83.978= 83 978/1000 as fraction
2. 78.932= 78 932/1000 as fraction
3. 84.765= 84 765/1000 as fraction
1. Find the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10).
Hint: Use quadratic regression to find the standard form.
The standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile travelling under the pull of gravity will travel along a curve similar to this one.For parabolas that open either up or down, the standard form equation is y = ax² + bx + cThe equation of parabola in standard form is y = ax² + bx + c
We have given the points,
(1, 0), (2, -3), and (3,-10)
Let's put each point in parabola equation and form three equation as,
Equation for point (1, 0)
0 = a * (1)² + b * 1 + c
a + b + c = 0 --------------------eq(i)
Now, equation for point(2, -3)
-3 = a * (2)² + b * 2 + c
4a + 2b + c = -3 --------------------eq(ii)
And, equation for point (3, -10)
-10 = a * (3)² + b * 3 + c
9a + 3b + c = -10 ---------------------eq(iii)
Now, we have three equation let's put them together
a + b + c = 0 --------------------eq(i)
4a + 2b + c = -3 --------------------eq(ii)
9a + 3b + c = -10 ---------------------eq(iii)
Now, form equation which is of two variable.
For that, we take first two equation and subtract eq(ii) from eq(i)
4a+2b+c = -3
a + b + c = 0
- - - -
------------------------
3a + b = -3 ---------------eq(a)
Now, subtract eq(iii) from eq(ii)
9a + 3b + c = -10
4a + 2b + c = -3
- - - -
------------------------
5a + b = -7 ------------------eq(b)
Now, we get eq(a) and eq(b) consist of two variable.
3a + b = -3 ---------------eq(a)
5a + b = -7 ----------------eq(b)
Now, solve this equation simultaneously and find the value of a and b.
3a + b = -3
5a + b = -7
- - -
----------------
-2a = 4
a = -2
put a = -2 in eq(a) to find b
3a + b = -3
⇒3 * -2 + b = -3
⇒-6 + b = -3
⇒b = 3
We get the values of a and b. And, left with value of c for that just put the a and b value in eq(i) and find c
a + b + c = 0
-2 + 3 + c = 0
c = -1
Now, we get all the necessary values for equation.
Next, just put a, b and c values in parabola equation.
y = ax² + bx + c
y = -2x² + 3x - 1
Hence, the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
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Dividing the polynomial P(x) by x + 2 yields a quotient Q(x) and a remainder of 8. If Q(2) = 5, find P(-2) and p(2)
================================================
Explanation:
Part A) Find P(-2)
We'll divide P(x) over (x+2) to get a quotient Q(x) and remainder 8 like so
P(x)/(x+2) = quotient + remainder/(x+2)
P(x)/(x+2) = Q(x) + 8/(x+2)
When multiplying both sides by (x+2), it clears out the fractions and we're left with this
P(x) = (x+2)*Q(x) + 8
From here, plug in x = -2 and simplify
P(x) = (x+2)*Q(x) + 8
P(-2) = (-2+2)*Q(-2) + 8
P(-2) = (0)*Q(-2) + 8
P(-2) = 0 + 8
P(-2) = 8
Luckily we don't need the value of Q(-2) since it cancels out with the zero.
-----------------------------------
Part B) Find P(2)
This time we'll plug in x = 2 and we'll get...
P(x) = (x+2)*Q(x) + 8
P(2) = (2+2)*Q(2) + 8
P(2) = 4*Q(2) + 8
P(2) = 4*5 + 8
P(2) = 20+8
P(2) = 28