Answer:
16984
Step-by-step explanation:
Given
[tex]a = 16000[/tex] ---- Initial
[tex]r = 1\%[/tex] --- rate
Required
Determine the population after 6 years
To do this, we make use of the following exponential function
[tex]f(x) = a(r+1)^x[/tex]
Substitute values for a and r
[tex]f(x) = 16000(1\%+1)^x[/tex]
Express 1% and decimal
[tex]f(x) = 16000(0.01+1)^x[/tex]
[tex]f(x) = 16000(1.01)^x[/tex]
The population after 6 years is:
Substitute 6 for years
[tex]f(6) = 16000(1.01)^6[/tex]
[tex]f(6) = 16984.3224096[/tex]
[tex]f(6) = 16984[/tex] -- approximated
here is my algebra 13 homework, can someone please help me quick!
The decreasing interval of function is (-∞ , 0) .
The decreasing interval in the function is said to be when the value of the derivative f' (x) ≤ 0 .
Decreasing interval is when f(x) is decreasing as x is increasing.
Here the graph is of a parabola the equation of a upper parabola is
f(x) = x²
Now doing derivation of the parabola equation, we get
f'(x) = 2x
As for decreasing interval we will put
f'(x) ≤ 0
Putting the value of f'(x) in the equation
2x ≤ 0
x ≤ 0
Decreasing interval (-∞ , 0)
To know more about decreasing interval click here :
https://brainly.com/question/29197921
#SPJ1
PLEASE HELP
Triangle ABC is similar to triangle XYZ.
Solve for p.
Answer:
Step-by-step explanation:
65 POINTS!!!!!! PLEASE ANSWER QUICK
The probabilities are: 1a) P(A) = 12, 1b)P(B) = 1.055 + 1,160 = 1,161.055 . 1c) P(A and B) = P(AB) = 1.055
How to find the probabilitiesP(A) = 12
P(B) = 1.055 + 1,160 = 1,161.055
P(A and B) = P(AB) = 1.055
To determine if the events A and B are independent, we need to check if P(A and B) = P(A) * P(B).
P(A) * P(B) = 12 * 1,161.055 = 13,932.66
Since P(AB) = 1.055 is not equal to P(A) * P(B) = 13,932.66, the events A and B are not independent.
P(A | B) = P(AB) / P(B) = 1.055 / 1,161.055 ≈ 0.0009098
To convert this probability to a percentage, we multiply by 100:
Percentage chance = P(A | B) * 100 ≈ 0.0009098 * 100 ≈ 0.091%
Therefore, the company should report a percentage chance of approximately 0.091% to the person as an estimate of their risk of developing the disease based on the study.
The reasoning behind this estimation is that among those who have the genetic variation (B), the probability of having the disease (A) is approximately 0.0009098, which corresponds to 0.091% when expressed as a percentage.
Learn more about probabibilty at https://brainly.com/question/13604758
#SPJ1
what is the area,in square centimeters
Answer:
11.9 sq cm, answer choice C.
Step-by-step explanation:
Area of a parallelogram = base x height.
The base is 4.25 cm, and the height is 2.8 cm. The other measurement is not needed.
area = 4.25 x 2.8 = 11.9 sq cm, answer choice C.
Evaluate
--(5-1)(5²).
Answer:
100
Step-by-step explanation:
You want the value of --(5-1)(5²).
Minus signsThe even number of leading minus signs cancel each other, so the effect is as if there were no leading minus signs.
--(5 -1)(5²)
= --(4)(25)
= --(100)
= -(-100)
= 100
__
Additional comment
As always, the value of a numeric expression can be found using a calculator.
<95141404393>
A top travels 8 centimeters each time it is spun. if it is spun 7 times what distance does it travel?
If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.
How the total distance is determined:The total distance is determined by multiplication of the distance traveled per spin and the number of spins.
Multiplication involves the multiplicand, the multiplier, and the product.
The traveling distance per spun = 8 centimeters
The number of spinning of the top = 7 times
The total distance = 56 centimeters (8 x 7)
Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.
Learn more about multiplication at https://brainly.com/question/4721701.
#SPJ1
On the first day of the month, Sandra starts to read a 420-page book. She is determined to read 30
pages each night. The function P (d) = 420-30d specifies the number of pages P remaining
after Sandra does her reading on day d of the month.
Which equation offers a solution giving the day of the month Sandra finishes, and what day of the
month is that?
OP(d)=0; day 21
OP(d)-30; day 21
OP(d) = 420; day 21
OP(d) = 420; day 14
OP(d) = 0; day 14
OP (d)-30; day 14
Answer:
P(d) = 0; 14 days
Step-by-step explanation:
First part of answer: Setting P(d) = 0 would allow us to find the day Sandra finishes since P represents the pages remaining the book will be finished when there are 0 pages left to read.
Second part of answer: We can solve the equation P(d) = 0 = 420 - 30d to see how it would take 14 days to finish the book and have 0 pages left to read:
Step 1: Subtract 420 from both sides:
(0 = 420 - 30d) - 420
-420 = -30d
Step 2: Divide both sides by -3 to solve for d:
(-420 = -30d) / -30
14 = d
What are the first two steps in solving the radical equation below?
√x+1-4 = 8
A. Square both sides and then subtract 1 from both sides.
B. Add 4 to both sides and then subtract 1 from both sides.
C. Square both sides and then add 4 to both sides.
D. Add 4 to both sides and then square both sides.
SUBMIT
The first two steps in solving the radical equation, √x+1-4 = 8 is D. Add 4 to both sides and then square both sides.
How do we solve the radical equation?We can solve the radical equation by adding 4 to both sides and then squaring both sides.
Given equation: √x+1 - 4 = 8.
The First step: add 4 to both sides of the equation:
√x+1 - 4 + 4 = 8 + 4
Simplifying the equation:
√x+1 = 12
The Second step: square both sides of the equation to eliminate the square root:
(√x+1)² = 12²
Squaring both sides gives:
x + 1 = 144
Finally, subtract 1 from both sides to isolate x:
x + 1 - 1 = 144 - 1
x = 143
So, adding 4 to both sides and then squaring both sides are the first two steps in solving the equation.
Learn more about radical equation at brainly.com/question/31941585
#SPJ1
The diagram shows a right-angled triangle.
24 cm
18 cm
_Not to scale
Calculate the value oft. Give your answer correct to 1 decimal place.
Answer:
can i have a photo, please?
Step-by-step explanation:
Directions: For A and B, use the given rules to write the first five terms in each
sequence. Then, use the terms to create ordered pairs for each numerical pattern.
A. Rule 1: Add 3 starting from 13.
Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9.
Sequence 2
Sequence 1
B. Rule 1: Multiply by 3, then add 2, starting from 1.
Rule 2: Multiply by 2, then add 3, starting from 6.
Sequence 1
Sequence 2
Ordered Pair
Ordered Pair
OFFERING 50 POINTS
In solving the sequence using the provided rules, we have:
A) Sequence 1: 13, 16, 19, 22, 25.
Sequence 2: 15, 13, 11, 9, 7.
Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B) Sequence 1: 1, 5, 17, 53, 159.
Sequence 2: 6, 15, 33, 69, 141.
Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (159, 141).
How to solve the sequence?Using the given rules, we can solve the sequence as follows:
A. Rule 1: Add 3 starting from 13
The first five terms in Sequence 1 would be:
13, 13 +3 = 16, 16 +3 = 19, 19 + 3 = 22, 22 + 3 = 25.
13, 16, 19, 22, 25
Using Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9
The first five terms in Sequence 2 would be:
25 - 2(5) = 25 - 10 = 15
25 - 2(6) = 25 - 12 = 13
25 - 2(7) = 25 - 14 = 11
25 - 2(8) = 25 - 16 = 9
25 - 2(9) = 25 - 18 = 7
The ordered pairs for each numerical pattern would be:
(13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B. Rule 1: Multiply by 3, then add 2, starting from 1
The first five terms in Sequence 1:
1, (1 * 3) + 2 = 5, (5 * 3) + 2 = 17, (17 * 3) + 2 = 53, (53 * 3) + 2 = 159
Using Rule 2: Multiply by 2, then add 3, starting from 6
The first five terms in Sequence 2:
6, (6 * 2) + 3 = 15, (15 * 2) + 3 = 33, (33 * 2) + 3 = 69, (69 * 2) + 3 = 141
The ordered pairs for each numerical pattern would be:
(1, 6), (5, 15), (17, 33), (53, 69), (159, 141)
Learn more about sequence at brainly.com/question/28369191
#SPJ1
100 Points! Geometry question. Identify the similar triangles. Then find each measure. Photo attached. Please show as much work as possible. Thank you!
The similar triangles for this problem are given as follows:
RST and VUT.
Then the measure VT is given as follows:
VT = 5.4 units.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Hence the similar triangles for this problem are given as follows:
RST and VUT.
The proportional relationship for the side lengths is given as follows:
6/14 = (x + 2)/(4x - 1).
Applying cross multiplication, the value of x is obtained as follows:
14(x + 2) = 6(4x - 1)
14x + 28 = 24x - 6
10x = 3.4
x = 3.4.
Then the length VT is given as follows:
VT = 3.4 + 2
VT = 5.4 units.
More can be learned about similar triangles at brainly.com/question/14285697
#SPJ1
Hi can someone who is great at math please help me with these math questions. I'm struggling with them!!
1) The value of x = 12°
2) For any real value of n, y = n and x = (3/2)n
And the measure of angle B is 68°
3) The measure of angle A is 26° and the measure of angle B is 154°
4) The coordinates of vertex D(4, 0)
1)
We know that a linear pair of angles always add up to 180°
168° + x° = 180°
x = 180° - 168°
x = 12°
2)
Here, in parallelogram ABCD, the measure of angle A = 112°
We know that the opposite angles of a parallelogram are equal.
So, m∠C = 112°
Let measure of angle B and D is p degrees.
∠A + ∠B + ∠C + ∠D = 360°
2p + 2(112) = 360°
p = (360 - 224)/2
p = 68°
so, the measure of angle B is 68°
The opposite sides of a parallelogram are equal.
So, side AD = side BC
(2x + 4) = (3y + 4)
2x = 3y
x = (3/2)y
For any real value of n,
y = n
then x = (3/2)n
3)
Consider parallelogram ABCD.
Let us assume that one of the interior angle measures x and then other interior angle be y.
x is 50 degrees more than 4 times the measure of y
x = 4y + 50
We know that the sum of two interior angles (non-opposite) is 180°
⇒ x + y = 180°
⇒ 4y + 50 + y = 180°
⇒ 5y = 130°
⇒ y = 26°
And the value of x would be,
x = 4(26) + 50
x = 154°
So, the measure of angle A is 26° and the measure of angle B is 154°
4)
Let the fourth vertex be D(a,b)
Since ABCD is a parallelogram, the diagonals bisect each other.
coordinates of midpoint of AC = coordinates of midpoint of BD
By midpoint formula,
((1 + 6)/2, (2 + 4)/2) = ((3 + a)/2 , (6 + b)/2)
comparing x and y coordinates,
(3 + a)/2 = (1 + 6)/2
3 + a = 7
a = 4
(6 + b)/2 = (2 + 4)/2
6 + b = 6
b = 0
So, the coordinates of vertex D(4, 0)
Learn more about the parallelogram here:
https://brainly.com/question/7720055
#SPJ1
What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4,-3)?
y + 3 = -4(x + 4)
y + 3 =(x+4)
Y + 3 = ¹/(x+4)
y + 3 = 4(x + 4)
An equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4,-3) is: C. y + 3 = 1/4(x + 4) .
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-3 - 1)/(0 + 1)
Slope (m) = -4
m₁ × m₂ = -1
-4 × m₂ = -1
m₂ = -1/-4
Slope, m₂ = 1/4
At data point (-4, -3) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 3 = 1/4(x + 4)
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A cone with a height of 50 meters has a volume of 5,400π meters cubed. What is the radius of the cone?
The radius of the cone with the given volume which is is terms of π would be = 18m
How to calculate the radius of a cone?To determine the radius of the cone, the formula that should be used in the formula for the volume of cone which would be given below;
Volume of cone =1/3πr²h
where;
radius = ?
volume = 5,400π
height = 50m
That is;
5,400π = 1/3×π×r²×50
make r² the subject of formula;
r² = 5400π×3/50π
= 108×3
= 324
r = √324
= 18
Learn more about volume here:
https://brainly.com/question/28795033
#SPJ1
If your heart beats 48 times in 40 seconds, which proportion could be used to make the best estimate for the number of beats in 60 seconds? A. 48/40 = 60/x B. 40/60 = 48/x C. 48/40 = 60/x D. 48/60 = 40/x
Given statement solution :- The correct proportion to make the best estimate for the number of beats in 60 seconds is:
A. 48/40 = 60/x
To make the best estimate for the number of beats in 60 seconds, we need to find the proportion that relates the beats per second in the given scenario to the desired duration of 60 seconds.
Let's set up the proportion using the given information:
Heart beats per second (beats/sec) = 48 beats / 40 seconds
We want to find the number of beats in 60 seconds (x beats / 60 seconds).
The correct proportion would be:
48 beats / 40 seconds = x beats / 60 seconds
Therefore, the correct proportion to make the best estimate for the number of beats in 60 seconds is:
A. 48/40 = 60/x
For such more questions on Heart Beats Estimation
https://brainly.com/question/22323579
#SPJ11
Pls can someone help me?
I’m pretty sure the value of a->60
b-> 110
c->80
What do i write for the reasons of them tho? Pls help! thanks
The values of the angles a, b and c are 60°, 110° and 80° respectively.
Given is a figure we need to find the measure of the angles given,
a, b, c.
So,
70° + 50° + a = 180° [making linear pair angles]
120° + a = 180°
a = 60°
50° + a = b [corresponding angles between parallel lines]
b = 50° + 60°
b = 110°
a + 40° + ∠HFE = 180° [angle sum property of a triangle]
60° + 40° + ∠HFE = 180°
∠HFE = 80°
∠HFE = c [alternate angles between parallel lines]
c = 80°
Hence the values of the angles a, b and c are 60°, 110° and 80° respectively.
Learn more about angles between parallel lines click;
https://brainly.com/question/30445886
#SPJ1
The dot plot displays data from 14 random samples, each consisting of 30 middle school students. Each dot represents the mean number of sports played per year by students in the sample.
Which number best represents the mean number of sports played by middle school students? Write your answer as a decimal to the nearest tenth.
__ sports
Part B
Find and interpret the variability in the distribution. Round the MAD to the nearest hundredth.
The MAD is about_____ sport(s). The majority of the sample means are within ______ sport(s) of the mean. This means our estimate is likely not far off from the true mean.
The best representation of the mean number of sports played by middle school students is 2.75 sports and the MAD is about 0.84 sports.
To find the best representation of the mean number of sports played by middle school students, we need to calculate the median of the given data.
The median represents the central tendency of the data and is less affected by extreme values.
Arranging the means of the samples in ascending order, we have:
1, 1, 2, 2.5, 3, 3, 3.5, 4
Since there are eight values, the median will be the average of the fourth and fifth values:
(2.5 + 3) / 2 = 2.75
Variability in the Distribution
Summing up the absolute deviations:
1.75 + 1.75 + 0.75 + 0.25 + 0.25 + 0.25 + 0.75 + 1.25 = 6.75
To find the MAD, we divide the sum of the absolute deviations by the total number of data points:
MAD = 6.75 / 8 = 0.84
Therefore, the MAD is about 0.84 sports.
To learn more on Mean click:
https://brainly.com/question/31101410
#SPJ1
Find the area of the shaded region. Round to the nearest tenth if necessary.
A. 332.1 cm
B. 210 cm
C. 201.3 cm
D. 205.8 cm
The area of the shaded region, obtained by finding the area of the composite figure is the difference between the area of the square and the area of the triangle and semicircle composite figure.
5. The area of the shaded region is about 205.8 cm squared. The correct option is therefore;
D. 205.8 cm squared
What is a composite figure?A composite figure is a figure that is composed two or more regular figures.
The area of the shaded region can be found by considering the unshaded region as a composite figure consisting of a triangle and a semicircle.
The area of the unshaded semicircle = π × 24²/8 = 72·π
The area of the triangular part of the unshaded region = (1/2) × 24 × 12 = 144
Area of the square = 24 × 24 = 576
Therefore, the area of shaded region = 576 - (72·π + 144) ≈ 205.8
The area of the shaded region ≈ 205.8 cm squared
Learn more on the area of composite figures here: https://brainly.com/question/29077084
#SPJ1
I need the steps for this one
Answer:
[tex]-61[/tex]
Step-by-step explanation:
[tex]\mathrm{We\ have\ f(}x)=-3x^2-2x+4\\\mathrm{Put}\ x=-5,\\\mathrm{f}(-5)=-3(-5)^2-2(-5)+4=-3(25)+10+4=-75+10+4=-61[/tex]
The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menus to complete the proof. b Click the arrows to choose an answer from each menu. The expression Choose.. represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
The expression 2ab + [tex]c^2[/tex] represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
The equivalent expression [tex]a^2 +b^2+2ab[/tex] use the length of the figure to represent the area.
[tex]2ab +c^2=a^2+b^2+2ab[/tex]
Subtracting 2ab from both sides
[tex]c^2=a^2+b^2[/tex]
Figure of a square with some shaded triangles.
Area of the triangle formula is 1/2 times base times height
base =a and height =a
Area of one triangle = 1/2ab
There are 4 shaded triangles
Area of 4 shaded triangles = 4 x 1/2ab
Area of the square = side times side
Now we find the area of outer square. side length is a+b
Area of outside square = (a + b)(a + b) = [tex](a+b)^2[/tex] = [tex]a^2 +b^2+2ab[/tex]
Using the length of the figure to represent the area.
Thus, now set both the areas equal to each other.
For more details regarding area, visit:
https://brainly.com/question/30307509
#SPJ1
Your question seems incomplete, the probable complete question is
Which shows all the exact solutions of 2sec²x-tan^x=-1? Give your answer in radians.
0+
O +k and+k
0+ -2k* and 5+2K*
3
7%
5+28
4
○ 주 +2kx3+2kx +2kx, and 7+2kx
+kr2+ks 4*k* and 5+k
47
+ K
Kx
Answer:
Step-by-step explanation:
The exact solutions for the equation 2sec²x - tan²x = -1 in radians are:
x = π/4 + πk, where k is an integer
x = 3π/4 + πk, where k is an integer
These solutions represent all the values of x that satisfy the given equation.
14. All of the following are advantages of a 401(k), EXCEPT... *
1 point
A.You don't pay taxes on your investments' growth each year
b.You can invest your 401(k) into a wider variety of asset types than you can with
an IRA
c.Your employer may match some of your 401(k) contributions
d.You can contribute more money into a 401(k) than into an IRA
Except You can invest your 401(k) into a wider variety of asset types than you can with an IRA. All are the advantages. Option B
A) You don't pay taxes on your investments' growth each year: One of the main advantages of a 401(k) plan is the tax advantage it provides.
Contributions to a traditional 401(k) are made on a pre-tax basis, meaning that the money you contribute is not subject to income tax. Additionally, the growth of investments within the 401(k) account is tax-deferred until you make withdrawals in retirement.
C) Your employer may match some of your 401(k) contributions: Many employers offer a matching contribution to their employees' 401(k) plans. This means that for every dollar you contribute to your 401(k), your employer will contribute a certain percentage, up to a specified limit.
D) You can contribute more money into a 401(k) than into an IRA: 401(k) plans generally allow for higher contribution limits compared to Individual Retirement Accounts (IRAs).
In 2021, the annual contribution limit for a 401(k) is $19,500 (with an additional $6,500 catch-up contribution for individuals aged 50 or older).
In contrast, the annual contribution limit for an IRA is $6,000 (with an additional $1,000 catch-up contribution for individuals aged 50 or older). The higher contribution limits of a 401(k) allow individuals to save more for retirement on a tax-advantaged basis.
In summary, the correct answer is B. The ability to invest in a wider variety of asset types is not an advantage of a 401(k) plan. However, the other options listed (A, C, and D) are all advantages of a 401(k) plan.
For more such questions on invest visit:
https://brainly.com/question/29227456
#SPJ11
the coldest temperature ever recorded on earth was -89.2
The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.
What was the coldest temperature recorded ?The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.
This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.
Find out more on temperature at https://brainly.com/question/30554883
#SPJ1
It is given that f(x) =1/x³, for x > 0. Show that f is a decreasing function.
The function f(x) = 1/x³ is indeed a decreasing function for x > 0.
To show that the function f(x) = 1/x³ is a decreasing function, we need to demonstrate that the derivative of f(x) is negative for all x > 0.
Let's calculate the derivative of f(x) with respect to x:
f'(x) = d/dx (1/x³)
Using the power rule for differentiation, we can rewrite the expression as:
[tex]f'(x) = (-3) / x^{(3+1)[/tex]
Simplifying further, we have:
f'(x) = -3 / x⁴
Now, to show that f(x) is decreasing, we need to prove that f'(x) < 0 for all x > 0.
Substituting x = 1 in f'(x), we get:
f'(1) = -3 / 1⁴ = -3
Since -3 is negative, we can conclude that f'(x) < 0 for all x > 0.
For similar question on function.
https://brainly.com/question/10439235
#SPJ11
Please help. Any unnecessary answers will be reported.
You are in a competition that involves building card towers. The quickest person to reach 100 stories wins the competition. After reaching 5 stories of cards as shown in the picture below, you needed to use 40 cards.
How many cards will be necessary to build , in a similar way, a tower with 100 stories? Make sure you include work.
The 10,100 cards will be necessary to build a 100-story card tower.
To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:
Triangular number = (n * (n + 1)) / 2
In this case, n represents the number of stories in the tower (100). Plug in the value for n:
Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050
Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:
Total cards = 5,050 * 2
Total cards = 10,100
To learn more about : cards
https://brainly.com/question/28714039
#SPJ11
Directions: Complete the table below.
Scientific Notation
5.397 x 10^2
Convert it to Standard Notation
The standard notation for the given scientific notation[tex]5.397 * 10^2[/tex] is 539.7
How to convert to standard notationTo convert the given scientific notation [tex]5.397 * 10^2[/tex]to standard notation, you simply need to multiply the coefficient (5.397) by the power of [tex]10 (10^2).[/tex]
The power of 10 indicates how many places the decimal point should be moved to the right. In this case, [tex]10^2[/tex] means moving the decimal point two places to the right.
Multiplying the coefficient 5.397 by
[tex]10^2[/tex]
gives us:
[tex]5.397 \times 10^2 = 5.397 \times \ 100 = 539.7[/tex]
Therefore, the standard notation for the given scientific notation 5.397 x [tex]10^2[/tex] is 539.7.
Learn more about standard notation at https://brainly.com/question/19169731
#SPJ1
Can a triangle be formed with side lengths 4,8,11? Explain
No because 11-8<4
Yes because 11-4<8
No because 4+8>11
Yes because 4+8>11
What’s the answers to this?
The vector representing the radius at the given position is -13i - j - 5k.
The magnitude of the radius vector is 13.96 units.
What is the vector representing the radius?
The vector representing the radius at the given position is calculated as follows;
center of the sphere = (11, 5, 2)
The point of the radius = ( -2, 4, -3 )
The radius vector = ( - 2 - 11) , ( 4 - 5), ( -3 - 2)
r = ( -13, - 1, - 5)
r = -13i - j - 5k
The magnitude of the radius vector is calculated as follows;
| r | = √ x² + y² + z²
where;
x, y, z are the various component of the radius| r | = √[ ( -13²) + ( -1)² + ( -5 )² ]
| r | = √ ( 169 + 1 + 25 )
| r | = √ ( 195 )
| r | = 13.96 units
Learn more about magnitude of vectors here: https://brainly.com/question/3184914
#SPJ1
The number 1.3 is both a(n) __________ and a(n) __________ number.
The number 1.3 is both a rational and an irrational number.
What is the number 1.3?The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.
The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.
So we can conclude that the number 1.3 is both rational and irrational number.
Learn more about rational numbers here: https://brainly.com/question/19079438
#SPJ1
What is the definition of postulate? A. an assumption, presumed to be true, that is used as the basis for a logical argument B. a statement that has been shown to be false by logical argument C. a statement that has been shown to be true by logical argument D. a statement, known to be false, that is used as the basis for a logical argument
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
We have,
A postulate is a statement or proposition that is accepted as true without proof.
It is an assumption or starting point in a logical argument that is considered to be self-evident or evident based on previous experience or observation.
In mathematics,
Postulates are used to define the basic concepts and axioms that form the foundation of a particular system of thought.
They are often used as the starting point for deriving other mathematical concepts and theorems.
Postulates are also known as axioms or assumptions.
Thus,
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
Learn more about postulates here:
https://brainly.com/question/11872456
#SPJ1