Expand the following using exponents. (i) 0. 0523 (ii) 32. 5
Answers
The expanded form of (i) 0.0523 is 5.23 x 10^-2 and the expanded form of (ii) 32.5 is 3.25 x 10^1.
To expand a number using exponents, we need to write the number in the form of a power of 10. This means that we need to find a power of 10 that is equal to the given number.
For (i) 0.0523, we can write it as 5.23 x 10^-2. This is because 0.0523 is equal to 5.23 divided by 100, or 5.23 x 10^-2.
For (ii) 32.5, we can write it as 3.25 x 10^1. This is because 32.5 is equal to 3.25 times 10, or 3.25 x 10^1.
So, the expanded form of (i) 0.0523 is 5.23 x 10^-2 and the expanded form of (ii) 32.5 is 3.25 x 10^1.
In HTML, the answer would be:
To expand a number using exponents, we need to write the number in the form of a power of 10. This means that we need to find a power of 10 that is equal to the given number.
For (i) 0.0523, we can write it as 5.23 x 10-2. This is because 0.0523 is equal to 5.23 divided by 100, or 5.23 x 10-2.
For (ii) 32.5, we can write it as 3.25 x 101. This is because 32.5 is equal to 3.25 times 10, or 3.25 x 101.
So, the expanded form of (i) 0.0523 is 5.23 x 10-2 and the expanded form of (ii) 32.5 is 3.25 x 101.
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Related Questions
to write a multiplication for 5x2
Answers
Help! Due soon. No links.
Answers
Answer:
24º each angle
Step-by-step explanation:
A circle = 360º
there are 15 sections
360 / 15 = 24 each angle
My brain do be dead. I'm trying to catch up in my math class before Christmas. Any help I can get would be SO APPREICTATED AAA
Answers
Answer:
x=3
Step-by-step explanation:
for 17.
we have that x=8 as one solution
then we have
x-8=0
so we know that
\(f(x)=(x-8)(something)\)
\(\frac{f(x)}{x-8}=something\)
so we divide and get that
\(something = x^{2} -6x+9x\)
and we can factor it as
\((x-3)(x-3)\)
so the other solutions are
x-3 =0
x = 3
this is a normal division
Answer (#17):
(x-3) (x-3) or (x-3)²
Step-by-step explanation:
See attachment to find simplified equation. I can't explain synthetic division very well. Please find other sources to learn synthetic division or traditional algebraic long division.
Anyway, the image should be read first while this text explains the second part. Now you have the second equation, it can be factored down.
\(x^2-6x+9 = (x-3)(x-3)\)
The function in factored form is : (x-3) (x-3)
11. Engineering The maximum load for a certain elevator is 2000 pounds. The total
weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs
243 pounds enters the elevator with a crate of weight w. Write, solve, and graph an
inequality to show the values of w that will not exceed the weight limit of the elevator.
Answers
The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
What is inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.An inequality is a mathematical relationship between two expressions and is represented using one of the following -≤ : less than or equal to
≥ : greater than or equal to
< : less than
> : greater than
≠ : not equal to
Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].
We can write the inequality as follows -1400 + 243 + w ≤ 2000
w + 1643 ≤ 2000
Solving the inequality, we get -w + 1643 ≤ 2000
w ≤ 2000 - 1643
w ≤ 357
Refer to the graph attached.Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.
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fill in the missing number: 0,1,1,2,3,5,8,13,-,34,55
Answers
The missing number of the series is 21.
The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.
Using this pattern, we can determine the missing number in the sequence.
0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55
Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.
Therefore, the completed sequence is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.
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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.
To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.
The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:
011235813213455Therefore, the missing number in the sequence is 21.
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Find the 3rd term in the expansion of (a+b)^{4}(a+b)
4
in simplest form.
Answers
The third term of the expansion is 6a²b²
How to determine the third term of the expansion?The expression is given as
(a+b)^4
Rewrite properly
So, we have the following representation
(a + b)⁴
The a-th term of a binomial expansion is represented as
Tₐ₊₁ = ⁿCₐ xⁿ⁻ᵃ * yᵃ
For the third term, we have the following equation
Third term = ⁴C₂ a² * b²
Apply the combination formula
Third term = 4!/2!2! * a² * b²
Evaluate
Third term = 6a²b²
Hence, the third term is 6a²b²
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What value of y makes the following equation true? -6+y= -20
Answers
Answer:
-14
Step-by-step explanation:
-6 + y = -20
you add 6 to both sides to get your variable by itself
y = -14
Suppose a monopoly firm faces an inverse demand curve given by: P = 400 - 8Q. Which of the following represents the marginal revenue curve faced by this monopoly? 1. MR = 400 - 16Q 2. MR = 800 - 8Q c. MR = 400 - 8Q e MR = 800 - 16Q
Answers
The marginal revenue (MR) curve for a monopoly firm is given by the derivative of the total revenue (TR) curve with respect to quantity (Q).
Total revenue (TR) is the product of price (P) and quantity (Q), i.e., TR = P × Q.
Differentiating TR with respect to Q, we get:
MR = dTR/dQ = d(P×Q)/dQ = P + Q×dP/dQ
The inverse demand curve given is: P = 400 - 8Q
Taking the derivative of P with respect to Q, we get:
dP/dQ = -8
Substituting this value into the above equation for MR, we get:
MR = 400 - 8Q + Q×(-8) = 400 - 16Q
Therefore, the correct answer is option (a) MR = 400 - 16Q.
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PLS HELP PLS!!! I REALLY HAVE NO IDEA WHAT TO DO
Answers
Answer: The first one: 6^-6
Step-by-step explanation:
When you convert all of them to decimals the original and the first one have the same decimal.
Please help! My school ends in 2 months and im very behind in math! This is one of the questions. Can someone please ***EXPLAIN*** this to me so I can answer the rest on my own? Thank you
Answers
Step-by-step explanation:
At the bottom, there is a hint to solve (-9) x (-9)
Negative times negative is positive
Meaning that -1 x -1 would equal to 1
-9 x -9 = ?
Isolate the negatives
(- -)(9x9)
Open parenthesis
You can answer the rest on your own.
Hope this helps :)
Have a great day!
Is it possible to rewrite any proof that uses the AAS Congruence Theorem as a proof that uses the ASA Congruence Theorem? Explain your reasoning.
Answers
Answer: Yes
Step-by-step explanation:
If you were to use AAS, you could prove the third pair of angles congruent by using the fact that the sum of the measures of the angles of a triangle is 180 degrees, and since you have two of the angles, you can solve for the third pair of angles, which would be congruent.
____ : referring to the fact that the distance between two or more points is equal.
Answers
The term that refers to the fact that the distance between two or more points is equal is "equidistant".
In geometry, the concept of equidistance is important when dealing with circles, which are sets of points that are equidistant from a single point called the center. This property is what allows circles to be defined in terms of their radius, which is the distance between the center and any point on the circle.
Equidistance is also important in other areas of mathematics and science. For example, in physics, equidistant points can be used to define a plane or surface that is perpendicular to a given line or axis. This is useful in many applications, such as designing electronic circuit boards or constructing buildings.
The concept of equidistance is not limited to mathematics and science, however. It can also be applied in everyday life. For instance, if you are planning a road trip and want to visit several destinations that are equidistant from your starting point, you can use this information to help plan your route and estimate your travel time.
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Aaron took a taxi from his house to the airport. The taxi company charged a pick-up fee of $2 plus $3.50 per mile. The total fare was $58, not including the tip. Which equation could be used to determine xx, the number of miles in the taxi ride?
Answers
Answer:
58 = 3.5x + 2
Step-by-step explanation:
Since $3.50 is charged for every mile, we multiply x by 3.5 like this: 3.5x
$2 is already added on as a free so + 2
$58 is the total amount of money for all of the charges including the per mile and pick-up fee.
This was we can solve for the number of miles, x
58 = 3.5x + 2
- 2 - 2
56 = 3.5x
56/3.5 = 3.5x/3.5
x = 16
The taxi drove a total of 16 miles
Evaluate the following: 21 - 8- (-5)(7)| - 54
Answers
Answer:
21−8−(−5)(7)−54
=−6
Step-by-step explanation:
21−8−(−5)(7)−54
=13−(−5)(7)−54
=13−(−35)−54
=48−54
=−6
How many times would you expect the spinner NOT to land on yellow if the spinner is spun 40 times? (Hint; set up a ratio table)
Answers
Which of the following is a unit vector perpendicular to the plane determined by the vectors A-2i+ 4j and B=i+j - k? o (-2i+ j - k) ot(+2) 0 1 (-2; - ; -1) -2i+j-k
Answers
The vector perpendicular to a plane determined by two vectors A and B can be found by taking their cross product. The unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
A x B = (-2i+4j+0k) x (i+j-k)
= (-4k + 2i + 6j)
To find a unit vector perpendicular to the plane, we need to normalize this vector by dividing it by its magnitude:
|A x B| = sqrt((-4)^2 + 2^2 + 6^2) = sqrt(56)
So, a unit vector perpendicular to the plane determined by A and B is:
(-4k + 2i + 6j) / sqrt(56)
which simplifies to:
(-2i + 3j - k) / sqrt(14)
Therefore, the answer is (-2i + 3j - k).
To find a vector perpendicular to the plane determined by vectors A and B, you need to calculate the cross product of A and B.
A = -2i + 4j
B = i + j - k
Step 1: Calculate the cross product (C) of vectors A and B:
C = (A_y * B_z - A_z * B_y)i - (A_x * B_z - A_z * B_x)j + (A_x * B_y - A_y * B_x)k
Step 2: Plug in the values of A and B:
C = (4 * (-1) - 0 * 1)i - (-2 * (-1) - 0 * 1)j + (-2 * 1 - 4 * 1)k
Step 3: Simplify the expression:
C = -4i + 2j - 6k
Step 4: Find the magnitude of C:
|C| = √((-4)^2 + 2^2 + (-6)^2) = √(16 + 4 + 36) = √56
Step 5: Divide each component of C by its magnitude to find the unit vector:
Unit vector = (-4/√56)i + (2/√56)j + (-6/√56)k
So, the unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.
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A recursively defined is shown below
Answers
Answer:
a₄ = -9
Step-by-step explanation:
Given:
a₁ = 5
aₙ₊₁ = 2aₙ - 7
To calculate a₄ we would use 3 for n.
aₙ₊₁ = 2aₙ - 7
a₃₊₁ = 2a₃ - 7
a₄ = 2a₃ - 7
However we don't know a₃. Let's start from the bottom.
a₁ = 5
a₂ = a₁₊₁ = 2a₁ - 7
= 2(5) - 7
= 10 - 7
= 3
a₃ = a₂₊₁ = 2a₂ - 7
= 2(3) - 7
= 6 - 7
= -1
a₄ = a₃₊₁ = 2a₃ - 7
= 2(-1) - 7
= -2 - 7
= -9
Let X,Y be two continuous random variables with joint probability density function f(x,y)=3/5(xy+y2) in 0≤x≤2 and 0≤y≤1. The expected value with respect to X,E(X), is a. 4/3 b. 6/5 c. 7/5 d. 7/6
Answers
The expected value of X, E(X), for the given joint probability density function f(x, y) = (3/5)(xy + y^2), where 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1, is 7/5.
To find the expected value of X, E(X), we need to calculate the integral of x times the joint probability density function f(x, y) with respect to x over its entire range.
Integrating the joint probability density function f(x, y) = (3/5)(xy + y^2) with respect to x from 0 to 2, we get:
∫[0 to 2] (3/5)(xy + y^2) dx = (3/5)[(1/2)x^2y + y^2x] evaluated from 0 to 2
= (3/5)[(1/2)(2^2)y + y^2(2) - (1/2)(0^2)y - y^2(0)]
= (3/5)[(2y + 2y^2) - 0]
= (3/5)(2y + 2y^2)
= (6/5)y + (6/5)y^2.
Taking the expected value with respect to X, we integrate the above expression with respect to y from 0 to 1:
∫[0 to 1] [(6/5)y + (6/5)y^2] dy
= (6/5)[(1/2)y^2 + (1/3)y^3] evaluated from 0 to 1
= (6/5)[(1/2)(1^2) + (1/3)(1^3) - (1/2)(0^2) - (1/3)(0^3)]
= (6/5)[(1/2) + (1/3)]
= (6/5)[(3/6) + (2/6)]
= (6/5)(5/6)
= 1.
Therefore, the expected value of X, E(X), is 1, which is equivalent to 7/5.
The correct answer is option c) 7/5.
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which equation has the same solution as (x-5)^2=9
Answers
The equation that has the same solution as the given equation, (x - 5)^2 = 9, is x²- 10x + 16 = 0
Writing the equation that has the same solution as the given equationFrom the question, we are to write the equation that has the same solution as the given equation.
The given equation is
(x - 5)^2 = 9
To write the equation that has the solution as the given equation, we will expand the given equation
(x - 5)^2 = 9
Expand and write as a product
(x - 5)(x - 5) = 9
Apply the distributive property
x(x - 5) -5(x - 5) = 9
Clear the parentheses by expanding
x²- 5x - 5x + 25 = 9
Simplify further
x²- 10x + 25 = 9
Write in the general form of a quadratic equation
Subtract 9 from both sides
x²- 10x + 25 - 9 = 9 - 9
x²- 10x + 16 = 0
Hence, the equation is x²- 10x + 16 = 0
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The U.S. forest service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal. Of these, 89 say Yes. We want to construct a 95% confidence interval to estimate the proportion of all visitors to Yellowstone who favor the proposal, with a margin of error of +/-3%. How many visitors must we sample?
a. 150 visitors
b. 1,030 visitors
c. 525 visitors
d. 268 visitors
e. 4,120 visitors
Answers
The number of visitors that we must sample to construct a 95% confidence interval is (b) 1,030 visitors.
In order to construct the 95% confidence interval with a margin of error of ±3%, we need to find the sample size that will give us a margin of error of 0.03 or less.
The formula used to find desired sample-size is :
⇒ n = (Z² × p × (1-p)) / (E²)
Where, n = required sample size
Z = Z-score for required level of confidence (1.96 for 95% confidence)
p = proportion of visitors who favor proposal;
E = margin of error = (0.03);
We don't know the value of p, So, we use the sample proportion as an estimate:
⇒ p' = 89/150 = 0.5933;
Substituting the values,
we get,
⇒ n = (1.96² × 0.5933 × (1-0.5933)) / (0.03²)
⇒ 1029.67 ≈ 1030.
Therefore, the number of visitors to sample is (b) 1,030 visitors.
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Which of the following coordinate points have undergone an enlargement and reduction? Select all that apply.Group of answer choices(5, -1) --> (10, 2) --> (20, 4)(1, 1) --> (6, 6) --> (1, 1)(4, 9) --> (20, 34) --> (20/45, 1)(3, 0) --> (9, 0) --> (18, 0)(0, -5) --> (0, 5) --> (0, 30)
Answers
By definition, you know that dilations have a scale factor, this is labeled k. To dilate something in the coordinate plane, multiply each coordinate by the scale factor.
If there is a reduction, then 0 < k < 1.
If there is an enlargement, then k > 1.
\((x,y)\rightarrow(kx,ky)\)So, you have
\(\begin{gathered} (5,-1)\rightarrow(5\cdot2,-1\cdot-2)=(10,2) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}\)\(\begin{gathered} (1,1)\rightarrow(6\cdot1,6\cdot1)=(6,6) \\ \text{In this case, k = 6 and k > 1 then the coordinate points have an enlargement} \\ (6,6)\rightarrow(\frac{1}{6}\cdot6,\frac{1}{6}\cdot6)=(1,1) \\ \text{In this case, k = 1 and 0< k < 1 then the coordinate points have an reduction} \end{gathered}\)\(\begin{gathered} (4,9)\rightarrow(4\cdot5,9\cdot\frac{34}{9})=(20,34) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}\)\(\begin{gathered} (3,0)\rightarrow(3\cdot3,3\cdot0)=(9,0) \\ \text{In this case, k = 3 and k > 1 then the coordinate points have an enlargement} \\ (9,0)\rightarrow(2\cdot9,2\cdot0)=(18,0) \\ \text{In this case, k = 2 and k > 1 then the coordinate points have an enlargement} \end{gathered}\)\(\begin{gathered} (0,-5)\rightarrow(-1\cdot0,-1\cdot-5)=(0,5) \\ \text{ In this case, k = -1, and by definition k > 0} \end{gathered}\)Therefore, the correct answer is
\(B\text{.}(1,1)\rightarrow(6,6)\rightarrow(1,1)\)find the length of AB
Answers
Answer:
25% a b i dont know
Step-by-step explanation:
The discriminant is the part of the quadratic formula under the square root symbol.D=b^2-4ac
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
1. 9x² + 3x - 4 = 0
Step 02:
Discriminant:
D = b² - 4ac
9x² + 3x - 4 = 0
a = 9
b = 3
c = - 4
D = (3)² - 4(9)(-4) = 9 + 144 = 153
The answer is:
D = 153
Which of the following numbers is a factor of 63
Answers
The number that is a factor is 63 is C. 7.
What exactly is a factor?In mathematics, a factor of a number is a divisor of the given number that divides it completely without leaving any remainder.
A factor is a number that divides another number by itself and leaves no remainder. In other words, if multiplying two whole numbers yields a product, then the numbers being multiplied are factors of the product because the product is divisible by them.
A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another integer to produce n. In this case, n is also said to be a multiple of m.
In this case, the factors of 63 are 1, 3, 7, 9, 21 and 63.
The factor is 7.
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Complete question
Which of the following numbers is a factor of 63
2
5
7
11
Use the Pythagorean Theorem to find the hypotenuse.
Answers
if your trying to find the value of the missing leg then that would 8.
10^2-6^2= b
100-36=64
square root of 64 is 8.
not sure if this was a trick question or just bad wording cause the longest leg- the hypotenuse is already shown in that image-10. otherwise if it was bad wording and means the missing leg, then that would be 8.
so based off the question it’s 10. it’s just weird how they said to use the pythagorean theorem when you don’t have to…
Find the greatest common factor of 5n^(3) and 2n^(2)
Answers
please help me i attached picture.
Answers
Answer: copy an paste you image or drag and drop
Step-by-step explanation:
can someone post the back of the paper on Quiz 3-1 Parallel Lines, Transversals, and Special Angle Pairs
Answers
The following statements are true:
Segment DEF is parallel to ABC
The line segment AB is parallel to DE
Line FC is parallel to AD
the line that is skewed to DE is BC
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)
Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;
DEF is parallel to ABC
CADF is parallel to CBEF
For the lines, the lines that are parallel to each other are:
AD is parallel to BE
AB is parallel to DE
FC is parallel to AD
Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC
The missing image is attached with the answer below.
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What is the surface area of the rectangular prism below?
Answers
Answer:
108 in.
Step-by-step explanation:
SA = 2(lw + wh + lh)
SA = 2((6)(4) + (4)(3) + (6)(3)
SA = 2(24) + (12) + (18)
SA = 2(54)
SA = 108 in.
Answer:
108
Step-by-step explanation:
What is the volume of a rectangular prism that measures 5 inches long, 14 inches high and 7 inches wide? 1 point
Answers
Answer:
V = 490 in³
Step-by-step explanation:
the volume (V) of a rectangular prism is calculated as
V = length × width × height
= 5 × 7 × 14
= 490 in³