It's 5.3*10^7. In Scientific Notation, you will be moving the decimal place until you have a number between 1 and 10. Then you add a the power of ten to show how many places you moved. For example, in Scientific Notation 52,314 with be moved left to get 5.2314*10^4. The decimal can be moved in either or direction depending on the problem. Hope this helps, have a nice day!
What is the simplified expression for 3 power 3 multiplied by 3 power 3 over 3 power 4? 30 31 32 34
Answer:
The simplest form of the expression is 3² ⇒ 3rd answer
Step-by-step explanation:
- The expression is 3 power 3 multiplied by 3 power 3 over 3 power 4
∵ 3 power 3 = 3³
∵ multiplied by 3 power 3 = × 3³
∵ over 3 power 4 = ÷ [tex]3^{4}[/tex]
- Lets write all of them in one expression
∴ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- All the numbers in the expression is 3 to the power
∴ The expression have the same base 3
- Remember: if we have numbers of same base multiplied then we
add their powers and if divided then we subtract their powers
[tex]\frac{a^{m}*a^{n}}{a^{q}}=a^{m+n-q}[/tex]
- Lets use this rule to simplify the expression
∵ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- Use the rule of the same base above
∴ [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex] = [tex]3^{3+3-4}=3^{6-4}=3^{2}[/tex]
∴ The simplest form of the expression is 3²
Answer:
3 to the 2nd power.
Step-by-step explanation:
Michelle is a server in a restaurant. On a weekend night, Michelle earned $4 an hour and $65 in tips She made a total of $93 Write and solve an equation to determine how many hours she worked
Answer:worked 7 hours
Step-by-step explanation:
93 - 65 = 28
28/4 = 7 hours
Michelle worked for 7 hours on the weekend night based on the equation 4h + $65 = $93, where h represents the number of hours worked.
How many hours she worked?Let's denote the number of hours Michelle worked as "h". She earned $4 per hour for her work, so the total amount she earned from her hourly wage is 4h. Additionally, she earned $65 in tips.
So, the total amount she made can be represented by the equation:
Total earnings = Hourly wage + Tips
$93 = 4h + $65
Now, we can solve for the number of hours Michelle worked:
4h + $65 = $93
Subtract $65 from both sides:
4h = $93 - $65
4h = $28
Now, divide both sides by 4 to solve for "h":
h = $28 / 4
h = 7
Michelle worked for 7 hours on that weekend night.
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50pts!! Which expression is equivalent to the polynomial given below? 54x+30
A.) 9(5x+5)
B.) 6(9x+30)
C.) 6(9x+5)
D.) 6(9x+4)
Answer:
6(9x+5)
Step-by-step explanation:
6*9x = 54x
6*5 = 30
The expression should be 6(9x+5)
Given information;The equation is 54x + 30
Calculation of an expression:A polynomial represents an expression that comprises of indeterminates and coefficients, which includes only the operations of addition, subtraction, multiplication, and a non-negative integer.
So,
= 54x + 30
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Rectangle GHIJ inscribed in a circle, GK⊥JH, GK = 6cm, m∠GHJ = 15°. Find the radius of the circle. pls help !!
Final answer:
To find the radius of the circle, we can use the properties of a right triangle to solve for GH. GH is approximately 10.39cm.
Explanation:
To find the radius of the circle, we can start by observing that the angle GHJ is 15°, and the side GK is 6cm. Since GK is a radius of the circle and it is perpendicular to JH, we can conclude that JH is a diameter of the circle. So, the length of JH is twice the length of GK, which is 12cm.
Now, we can use the properties of a right triangle to find the radius of the circle. We have a right triangle GHJ, where GH is the radius of the circle and JH is the hypotenuse. Using the Pythagorean theorem, we can solve for GH:
GH^2 + GK^2 = JH^2
GH^2 + 6^2 = 12^2
GH^2 + 36 = 144
GH^2 = 108
GH = sqrt(108)
GH ≈ 10.39cm
The radius of the circle is approximately 10.39cm.
Which expression should replace the word numerator in the work shown
B: x-5 is expression should replace the word “numerator” .
If you solve using the equation for the constant of proportionality, y/x = k, with k=4/5 and y = 2/3, what is the value of x?
A. X = -2/15
B. X = 8/15
C. X = 5/6
D. X = 1 1/5
[tex]\bf \cfrac{y}{x}=k\qquad \begin{cases} k=\frac{4}{5}\\ y=\frac{2}{3} \end{cases}\implies \cfrac{~~\frac{2}{3}~~}{x}=\cfrac{4}{5}\implies \cfrac{2}{3}(5)=4x\implies \cfrac{10}{3}=4x \\\\\\ \cfrac{10}{12}=x\implies \cfrac{5}{6}=x[/tex]
In this problem, we solve for 'x' in the equation for constant of proportionality, 'y/x = k', given that 'y' is 2/3 and 'k' is 4/5. Substituting these values in the equation and solving for 'x' gives the result 5/6.
Explanation:The question refers to the concept of the constant of proportionality which is a key topic in mathematics. We have an equation, y/x = k, where k is the constant of proportionality. Here, we have been given that y = 2/3 and k = 4/5. If we substitute these values into the equation, we will be able to solve for x.
To solve for x, we rearrange the equation by multiplying both sides by x and then dividing by k. This leaves us with an equation in terms of x: x = y/k. Substituting the given values, we get x = (2/3) / (4/5) = 5/6. So, the correct answer according to the provided options is C. X = 5/6.
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Which property of real numbers is shown below?
-6+6=0
associative property of addition
commutative property of addition
identity property of addition
inverse property of addition
O
Answer:
The inverse property of addition.
Step-by-step explanation:
The number 6 is added to its inverse -6.
The property of real numbers (-6) + 6 = 0 will be Inverse property of addition. Then the correct option is D.
What are the properties of the Addition?Any of the many numerical laws governing how values are added.
Some Addition properties are as follows:
Associative property of addition – The total is unchanged when the order of the sub-blocks is changed.
For example, (2 + 3) + 4 = 2 + (3 + 4)
Commutative property of addition – No matter how the addends are arranged, the result remains constant.
For example, 4 + 2 = 2 + 4
Identity property of addition – The integer is that summation of 0 and that value.
For example, 0 + 4 = 4
Inverse property of addition – Zero is the result of adding any integer to its inverse.
For example, a + (-a) = 4
The property of real numbers -6+6=0 will be Inverse property of addition.
Then the correct option is D.
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The following expression models the total cost of the field trip ,where x represents the number of students 80r What does the constant term in the above expression represents?
Answer:
no of students by cost per student?
Answer:The cost of the if 0 students signed up
Step-by-step explanation:I got the answer right :)
Meg dilated triangle W by a factor less than 1. Then she performed other transformations that were not dilations to create similar triangle W′.
Which could be the vertices of triangle W?
A. X(–2, 2), Y(–10, 2), Z(–6, 10)
B. X(2, 2), Y(4, 2), Z(3, 4)
C. X(0, 2), Y(4, 2), Z(2, –6)
D. X(2, 2), Y(2, 6), Z(4, 6)
Answer:
A. X(–2, 2), Y(–10, 2), Z(–6, 10)
Step-by-step explanation:
This looks a bit tough, but knowing that scale factors less than 1 are ½, ¼, etcetera, I come to this answer, also knowing that in the end, they must have an unproportional relationship.
I hope this is correct, and as always, I am joyous to assist anyone at anytime.
How many standard deviations from the mean is considered unusual? Why?
Answer:
It depends on how the data are distributed.
Step-by-step explanation:
If the data follow a normal (Gaussian) distribution, which is the most common, then 2 deviations from the mean is considered unusual because less than 4.55% of the data are in this situation.
Higher Order Thinking Suppose that solving
a system of equations algebraically gives the
following result: 0 = 0
What does this mean graphically?
Answer:
It means it's an infinite solution.
Is that what you meant? I apologize if it wasnt.
Since the system of equations algebraically gives this result: 0 = 0, graphically it means it has infinitely many solution.
What are infinitely many solutions?In Mathematics and Geometry, an equation is said to have an infinitely many solution (infinite number of solutions) when the left hand side and right hand side of the equation are the same or equal.
By critically observing the solution to the system of equations, we can reasonably infer and logically deduce that it has infinitely many solution (infinite number of solutions).
In conclusion, every point located on the graph of this line would satisfy the equation as shown in the image attached below.
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A function that has y-values with more than one corresponding x-value is
called a:
Answer:
Im not sure what the answers are on your test but its usually called a domain.
-
-
-
Let me know what the possible answers are if it is a multiple choice question!
Step-by-step explanation:
Answer: many-to-one function
Step-by-step explanation:
A florist can make a grand arrangement in 18 minutes or a simple arrangement in 10 minutes. The florist makes at least twice as many of the simple arrangements as the grand arrangements. The florist can work only 40 hours per week .The profit on the simple arrangements is $10 and. the profit on the grand arrangements is $25. hind the number and type of arrangements that the florist should produce to maximize profit.
Answer:
See explanation
Step-by-step explanation:
Let x be the number of simple arrangements and y be the number of grand arrangements.
1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so
[tex]x\ge 2y[/tex]
2. A florist can make a grand arrangement in 18 minutes [tex]=\dfrac{3}{10}[/tex] hour, then he can make y arrangements in [tex]\dfrac{3}{10}y[/tex] hours.
A florist can make a simple arrangement in 10 minutes [tex]=\dfrac{1}{6}[/tex] hour, so he can make x arrangements in [tex]\dfrac{1}{6}x[/tex] hours.
The florist can work only 40 hours per week, then
[tex]\dfrac{3}{10}y+\dfrac{1}{6}x\le 40[/tex]
3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.
The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.
Total profit: $(10x+25y)
Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines [tex]x=2y[/tex] and [tex]\dfrac{3}{10}y+\dfrac{1}{6}x=40[/tex]
But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is
[tex]\$(10\cdot 126+25\cdot 63)=\$2,835[/tex]
To maximize profit, the florist should produce 1 grand arrangement and 2 simple arrangements. The maximum profit is $45.
Explanation:To maximize profit, the florist should produce a combination of grand and simple arrangements. Let's assume the florist makes x grand arrangements and at least twice as many simple arrangements, which would be 2x or more. Given that the florist can work only a total of 40 hours per week, we can set up the following equation:
18x + 10(2x) ≤ 40
Now, we solve for x to find the number of grand arrangements.
Simplifying the equation, we have 18x + 20x ≤ 40
Combining like terms, we get 38x ≤ 40
Dividing both sides by 38, we find that x ≤ 1.05
Since we can't have a fraction of an arrangement, the florist should produce 1 grand arrangement. From the given information, we know that the florist must produce at least twice as many simple arrangements as grand arrangements. Therefore, the florist should produce at least 2 * 1 = 2 simple arrangements.
The florist's maximum profit can be calculated by multiplying the profit per arrangement by the number of corresponding arrangements.
The profit for the grand arrangement is $25, so the total grand arrangement profit is 1 * $25 = $25. The profit for the simple arrangement is $10, so the total simple arrangement profit is 2 * $10 = $20. Therefore, the maximum profit is $25 + $20 = $45.
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Karina has determined that the weight of a newborn elephant increases at a rate of 6% per week for the first 14 weeks. She
needs to determine how much weight a baby elephant will gain on the 14th week if it weighs 92 lbs. at birth. Write the explicit
formula of the geometric sequence that could be used to model this scenario.
This is an exponential growth problem.
The formula is y = a(1+r)^x
Y would be the final answer
a is the starting value
r is the percent of growth
x is the amount of time ( number of weeks)
The equation is:
y(x) = 92(1.06)^x
For 14 weeks replace x with 14:
y(14) = 92(1.06)^14 = 208 pounds.
Answer: W(n) = 92lb*1.06^n
and W(14) = 92lb*1.06^14 = 208lb
Step-by-step explanation:
We know that at the beginning the baby elephant weighs 92Lbs, and for each week it augments by a 6% (or 0.06 in decimals)
Then, at the end of the first week, the weight is:
92lb*1.06 = 97.52lb
at the end of the second week:
(92lb*1.06)*1.06 = 103.37lb
and so on, so you can see that the pattern is:
W(n) = 92lb*1.06^n
where n is the number of weeks after the birth
W(0) = 92lb
W(1) = 97.52lb
...
And we want to know the weight at the end of the 14th week, so we must find:
W(14) = 92lb*1.06^14 = 208lb
The angles X degree and (90-x degree) are
Answer:
Complementary angles
Step-by-step explanation:
Complementary angles sum to 90°, that is
x + 90 - x = 90°
Thus x and (90 - x) are complementary angles
To avoid a service fee, your checking account balance must be at least $500 at the end of each month. Your current balance is $529.57. You use your debit card to spend $126.08. What possible amounts can you deposit into your account by the end of the month to avoid paying the service fee?
Answer:
$96.51
Step-by-step explanation:
529.57 - 126.08 = 403.49
500 - 403.49 = 96.51
The possible amount you deposit into your account by the ed of the month to avoid paying the service fee would be $96.51
Answer:
$96.51
Step-by-step explanation:
Follow the steps to find the quotient. Please help !
Answer:
41
Step-by-step explanation:
1. Look at the first digit and ask yourself: is this divisible by 8? (3 is not so you look at the next one)
2. 8 goes into 32 evenly 4 times (put 4 at the top)
3. Subtract 42
4. Drag down the 8
5. Does 8 go into 8? (Yes!)
6. Put one at the top and subtract to get zero
7. Answer is at the top: 41
Answer:
Nothing goes into 3
8 goes into 32 four times (8 times 4= 32) so that means you'd put 4 on top of 2
then you bring down the 8 and 8 goes into 8 once. (8 times 1= 8) so you'd put 1 on top of 8.
Now down below you'd put 32 below 32 since you subtract it.
I'm not sure what the 3 bottom ones are.
I think you'd put 8 in the first boxes then 0 cause 8=8 = 0.
good luck <3
answer is 41 <3
PLEASE HELP!!!!!
the volume of a barrel of sand is 18 cubic feet. how many barrels of sand will be needed to fill a container with a volume of 2 cubic yards
The container with a volume of 2 cubic yards, which is equivalent to 54 cubic feet, would require 3 barrels of sand to fill it up, as the volume of each barrel is 18 cubic feet.
Explanation:To find out how many barrels of sand will be needed to fill a container with a volume of 2 cubic yards, we first need to convert cubic yards to cubic feet, as the measurement of the barrel volume is given in cubic feet. Since 1 cubic yard is equivalent to 27 cubic feet, 2 cubic yards will be 2 * 27 = 54 cubic feet.
Next, we divide the volume of the container by the volume of one barrel of sand. Hence, the number of barrels needed = 54 cubic feet / 18 cubic feet per barrel = 3 barrels.
So, it will take 3 barrels of sand to fill a container with a volume of 2 cubic yards.
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Please need help on this
Answer:
there is an 88% chance it will land on teal, because if you do 16/18, you get 0.8 repeating. then, you multiply by 100 and get 88%
2 intersecting lines are shown. A line with points M, H, K intersects a line with points J, H, L at point H. 4 angles are created. Clockwise, from the top, the angles are blank, (x + 15) degrees, blank, (2 x minus 20) degrees.
What is mAngleMHJ?
35°
50°
72.5°
92.5°
Answer:
m∠MHJ = 50°
========================
Step-by-step explanation:
Best explanation is as shown in the attached figure.
As shown in the figure:
x + 15 = 2x - 20 ⇒ vertex angles are congruent
solve for x ⇒ ∴ x = 35°
So, ∠MHJ = 2x - 20 = 2*35 - 20 = 50°
========================================
The measure of all angles will be:
∠MHJ = 2X - 20° = 2 * 35 - 20 = 50°
∠JHK = 180° - ∠MHJ = 180 - 50 = 130°
∠KHL = X + 15° = 35° + 15° = 50°
∠LHM = ∠JHK = 130°
Answer:
B 50 degrees
Step-by-step explanation:
given matrix A is 2x3 matrix, matrix C is a 2x1 matrix and A x B = C. what are the demensions of matrix B?
The dimensions of matrix B must be 3x1 to satisfy the given matrix multiplication where a 2x3 matrix A is multiplied by B to result in a 2x1 matrix C.
The student is asking about the dimensions of a matrix B that when multiplied by a given 2x3 matrix A, results in a 2x1 matrix C. In matrix multiplication, the product of an mxn matrix A and an nxp matrix B yields an mxp matrix C. The resulting matrix, C, has the same number of rows as the first matrix (A) and the same number of columns as the second matrix (B). Additionally, the number of columns in the first matrix must match the number of rows in the second matrix. Therefore, since matrix A has 3 columns, matrix B must have 3 rows for the multiplication to be defined. And since matrix C has 1 column, matrix B must have 1 column as well. So, the dimensions of matrix B are 3x1.
How to write 12,430,000 in expanded form?
Use the order of operations to evaluate the expression below.
15- [14 = (15-8) + 13 - 14 - 10
The method to solve the expression is given.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
The given expression,
15- [14 = (15-8) + 13 - 14 - 10
First, we solve the parenthesis.
15-14 = 7 + 13 - 14 -10
Now, adding the terms.
15-14 = 21 - 24
Subtracting the terms.
1 = -3
Which is contradiction.
Therefore, the expression is wrong.
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Which of the following is equivalent to the complex number i^{34}
Choose 1 answer:
(Choice A) 1
(Choice B) i
(Choice C) -1
(Choice D) -i
Answer:
Choice C, -1
Step-by-step explanation:
The trick here is to look at this as a pattern.
[tex]\sqrt{-1}[/tex] is i to the 1st power.
[tex]-1[/tex] is i to the 2nd power.
[tex]-\sqrt{-1}[/tex] is i to the 3rd power.
[tex]1[/tex] is i to the 4th power.
So what we do to solve something like this is divide the power by 4, and see how far away the number is from the pattern.
In other words, we divide, and our remainder is how many powers to count up to (a remainder of 0 is the 4th power).
So 34/4 = 8 with a remainder of 2. Therefore, it's i to the 2nd power, which is -1.
The present value of a house is $242.000. The value of the house increases at the rate of
every year. A function is shown below
10%) = 242.000(1.047
What does f(x)represent?
Answer: The future value of the house after x years
Step-by-step explanation:
Write a word problem with the information below.
89 x 2 = 178
178 + 89 = 267
Both doctors saw 267 patients altogether.
Answer:
there were 2 doctors. first doctor saw 89 patient. Second doctor saw the twice of first doctor. calculate how much patient did second doctor saw
Callie and Madison went to buy concert tickets for themselves and their five friends. The
tickets for the closest section were $45 each, and $30 for each ticket in the other section. They
ended up spending a total of $210. How many tickets of each type did they buy?
Answer:
They bought 0 ticket of closest section and 7 tickets of other section
Step-by-step explanation:
- Callie and Madison went to buy concert tickets for themselves and
their five friends
- That mean they are 7
- Tickets for the closest section were $45 each
- Tickets for other section were $30 each
- They ended up spending a total of $210
- Assume that they buy x tickets for closest section and y tickets for
the other section
∵ They want 7 tickets
∴ x + y = 7 ⇒ (1)
∵ The cost of the closest section ticket was $45
∵ The cost of the other section ticket was $30
∵ They spent $210 on them
∴ 45x + 30y = 210
- All terms have common factor 15, then divide them by 15
∴ 3x + 2y = 14 ⇒ (2)
* Now we have a system of equations to solve
- Multiply equation (1) by -2 to eliminate y
∴ -2x - 2y = -14 ⇒ (3)
- Add equations (2) and (3)
∴ x = 0
- substitute the value of x in equation (1) to find y
∴ 0 + y = 7
∴ y = 7
∵ x represents the number of tickets of the closest section and y
represents the number of tickets in the other section
∴ They bought 0 ticket of closest section and 7 tickets of other
section
Solve for x: 4 over 5 x + 4 over 3 = 2x x = Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar. (2 points)
Answer:
(5 + √115)/15 or (5 - √115)/15
Step-by-step explanation:
4/5x+4/3 = 2x
Multiply each term by the least common multiple of the denominators (15x)
12 + 20x = 30x²
Move all the terms to the left-hand side.
-30x² + 20x + 12 = 0
Multiply each term by -1
30x² - 20x - 12 = 0
Remove the common factor (2)
15x² - 10x - 6 = 0
Solve by using the quadratic formula
a = 15, b = -10, c = -6
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\= \frac{-(-10)\pm\sqrt{(-10)^2-4(15)(-6)}}{2(15)}\\\\= \frac{10\pm\sqrt{100 + 360}}{30}\\\\= \frac{10\pm\sqrt{460}}{30}\\\\= \frac{10\pm\sqrt{4\times115}}{30}\\\\= \frac{10\pm2\sqrt{115}}{30}\\\\= \mathbf{\frac{5\pm\sqrt{115}}{15}}[/tex]
x = (5 + √115)/15 or x = (5 - √115)/15
Garland put 2b+ 3 dollars in the bank in the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week he doubled what was in the bank. If he now has $477 in Thebes bank, how much did he put in the bank the first week?
Calcular el volumen en m3 de la esfera en el que el área de uno de sus círculos maximos es 36pim2
Answer:
The volume of the sphere is [tex]V=288\pi\ m^3[/tex]
Step-by-step explanation:
The question in English is
Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2
we know that
The radius of the maximum circle in the sphere is equal to the radius of the sphere
Step 1
Find the radius of the maximum circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=36\pi\ m^2[/tex]
substitute and solve for r
[tex]36\pi=\pi r^{2}[/tex]
Simplify
[tex]36=r^{2}[/tex]
take the square root both sides
[tex]r=6\ m[/tex]
Step 2
Find the volume of the sphere
The volume of the sphere is
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
substitute the value of r
[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]
[tex]V=288\pi\ m^3[/tex]