The number 77.31 x 10^4 in scientific notation is 7.731 x 10 ^ 5. To achieve this, the decimal place was moved to the left and the power of 10 increased accordingly.
Explanation:To express the number 77.31 x 10^4 in scientific notation, we need to adjust it to fit the format 'a x 10^n', where 1 ≤ |a| < 10 and n is an integer. So, the main step is to transfer the decimal place in '77.31' to after the first digit, followed by multiplying by an appropriate power of 10.
Firstly, rewrite 77.31 as 7.731 by moving the decimal place one place to the left. Now, since our original number was multiplied by 10^4, this needs to be amended by 1 place for the movement of the decimal point. This results in 10^5, since you are now multiplying by 10 one more time than before.
Combining these, the given number is represented in scientific notation as 7.731 x 10 ^ 5.
Learn more about Scientific Notation here:https://brainly.com/question/2005529
#SPJ3
One student rewrote the expression 17 x 102 as 17 parentheses 100 + 2 parentheses then 2 simplified to get the expression 1700 + 34. B what property of a number does this demonstrate
The expression demonstrates distributive property.
Explanation:
The given expression is [tex]17 \times 102[/tex]
Thus, solving the expression results in [tex]1734[/tex]
One student rewrote this expression as [tex]17(100+2)[/tex]
Then, simplified the expression as
[tex]1700+34[/tex]
Thus, [tex]17(100+2)=1700+34[/tex]
The expression demonstrates distributive property and the property can be generally written as
[tex]$a(b+c)=a b+a c$[/tex]
The given expression [tex]17(100+2)[/tex] is of the form [tex]$a(b+c)$[/tex]
Hence, The expression demonstrates distributive property.
To save for a new car, Trafton invested $7,000 in a savings account that earns 6.5% interest, compounded continuously. After four years, he wants to buy a used car for $10,000. How much money will he need to pay in addition to what is in his savings account? (Round your answer to the nearest cent.)
Answer:
Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Initial deposit = $ 7,000
Annual interest = 6.5% = 0.065 compounded continuously
Time of the investment = 4 years
Price of the used car Trafton wants to buy = $ 10,000
2. How much money will he need to pay in addition to what is in his savings account?
1. For answering the question, let's calculate how much money Trafton has in his savings account after 4 years, this way:
FV = PV * e ^ (i * t)
Where,
FV = Future value of the initial deposit after t time
PV = Initial deposit
e = Euler's number (2.7183)
i = 0.065 compounded continuously
t = 4 years
Replacing with the real values, we have:
FV = 7,000 * 2.7183^(0.065 * 4)
FV = 7,000 * 1.30 (Rounding to the nearest hundredth)
FV = $ 9,100
Now, we can elaborate how much money will Trafton need to pay in addition, as follows:
Money in addition = Price of the used car Trafton wants to buy - Future Value of the savings account after 4 years
Money in addition = 10,000 - 9,100
Money in addition = $ 900
Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.
Which one of the following words means most nearly the opposite of RANDOM? (remember,opposite)
Answer:
predictable
Step-by-step explanation:
the opposite of random is predictable
The opposite of 'random' would be a word like 'ordered' or 'systematic', which suggest a set plan or sequence, contrasting with the concept of randomness.
Explanation:The opposite of the word 'random' would be a term that denotes a sense of order, structure, or predictability. In this context, one example of a word that is the opposite of 'random' is 'ordered' or 'systematic'. These words suggest that things are arranged or occur according to a set plan or sequence, thereby contrasting with the concept of 'random', which indicates a lack of any discernible order or pattern.
Learn more about Antonyms here:https://brainly.com/question/1984692
#SPJ2
Please help..can't figure it out!
Answer:
B) y = x + 2 and y = -x - 4
Step-by-step explanation:
The equation of a line is represented with y = mx + b.
"x" and "y", when substituted, tell you if a point (x, y) is on the line.
"m" is slope, and tells if it goes up (positive slope) or down (negative)
"b" is the y-intercept, when the line hits the y-axis.
In the graph, we have two lines. One goes upwards (read from left to right), and the other goes downwards.
The graph that goes upwards hits the y-axis at positive "2".
The graph that goes downwards hits the y-axis at (negative) "-4".
Since the choices only have positive 1 or negative 1 as the slope, we only have to worry if it goes up or down.
Take the key information, slope and y-intercept, to write the equations.
"upwards slope, y-axis at 2"
y = x + 2
"downwards slope, y-axis at -4"
y = -x - 4
Choose the missing exponent to create a polynomial: 3x^4+4x^2-9x^-?+2
?=Missing Value
A) 2
B) 3
C) -9
D) 7
E) 4
Answer:
C) -9
Step-by-step explanation:
Exponents in a polynomial must be positive integers. Since your ? has a minus sign in front, its value must be negative. The only such choice is C.
what is 0.8888(non terminal) as a fraction?
Hmmm.... do you mean 0.8888...... or just 0.8888.
If you mean point eight repeating the fraction equivalent is just 8/9.
what are the three first terms of 8-n
Step-by-step explanation:
First term : 8 - 0 = 8
second term: 8 - 1 = 7
third term : 8 - 2 = 6
How many solutions does an equation have when the variable adds out and the final sentence is true?
Answer:
Infinitely many solutions
Step-by-step explanation:
If we have a system of equation like:
2x+y=4
6x+3y=12
If we make y the subject in the first equation and substitute into the second equation, we get:
6x+3(4-2x)=12
We expand to get:
6x+12-6x=12
6x-6x+12=12
Now the variable adds out to give:
12=12
This statement is true so the equation has infinitely many solution.
Answer:
infinite solutionsExplanation:
When the variable adds out means that after all the simplifications, at the end, it will not appear in the final sentence or expression.
Then, if the final sentence is true, and not variable appears, but only constants, the sentence is always true, no matter what value the variable takes.
That means that you can put any value for the variable in the original equation and the equation will be true; hence there are infinite solutions.
This is an example:
1. Equation:
3x + 5+ x² = 2 - ( - 4x - x²) + (3 - x)2. Remove the parenthesis:
3x + 5+ x² = 2 + 4x + x² + 3 - x3. Add like terms on the right side and transpose the variables to the left side:
3x + 5 + x² = 5 + 3x + x²3x + x² - 3x -x² + 5 = 54. Combine like terms on the left side:
5 = 5Thus, the variable added out and the final sentence is true. Hence, this equation has infinite solutions, which you can prove substituting the variable with any value.
What is the reference angle for 120°? A. 30° B. 45° C. 60° D. 120° E. 240°
Answer:
C
Step-by-step explanation:
120° is an angle in the second quadrant.
The reference angle is the related acute angle in the first quadrant, that is
reference angle = 180° - 120° = 60° → C
Answer:
C
Step-by-step explanation:
Add...- 3+(-3) =
Thank youuuu!!!!
Answer:
the answer is 0
Step-by-step explanation:
well - 3 plus 3 would just by 0 because if the number with the negative is the biggest then the answer is negative but if the positive number is the biggest then the answer would be positive because there is not a bigger number it would be 0 because 3 and -3 have pretty much the same value other then them being negative and positive
In a certain card game, for every 4 44 blue cards, there are 3 33 yellow cards. There are a total of 84 8484 blue and yellow cards in the game. How many blue cards are in the game?
The total number of blue cards in the game = 48
Step-by-step explanation:
Total number of blue and yellow cards = 84
let the blue card denote B and yellow card as Y
B = 4
Y = 3
Total number of cards in one round = 7
number of rounds possible = total number of cards / number of cards in one round
= 84/7
= 12
number of blue cards = 12 x 4
= 48
The total number of blue cards in the game = 48
Answer:
48
Step-by-step explanation:
Determine whether the statement is true or false.
Let A = {1, 3, 5, 7}
B = {5, 6, 7, 8}
C = {5, 8}
D = {2, 5, 8}
U = {1, 2, 3, 4, 5, 6, 7, 8}
Answer: I think it's True :)
Answer:
I feel like it true. Happy yo help!!!
Step-by-step explanation:
Question 6 of 10
2 Points
The solution set of an equation of a circle is all of the points that lie in the
circle
O
A
True
O
B. False
SUBMIT
It is true that the solution set of an equation of a circle is all of the points that lie in the circle
How to determine the true statement?The equation of a circle is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where:
Center = (a,b)
Radius = r
The points are represented by (x,y)
The (x,y) can take any value as long as it makes the equation (x - a)^2 + (y - b)^2 = r^2 to be true
Hence, it is true that the solution set of an equation of a circle is all of the points that lie in the circle
Read more about circle equations at:
https://brainly.com/question/1559324
#SPJ1
Answer:
False
Step-by-step explanation:
a preschool has a student to teacher ratio of 5:2. The total number of students and teachers was 56 last year and is 70 this year. How many students and teachers were there for each of these two years?
Answer:
Step-by-step explanation:
student teacher ratio of 5:2....added = 7
so students make up 5/7 of the total people and teachers make up 2/7 of the total people.
Last year.....56 people
students : 5/7 * 56 = 280/7 = 40 students
teachers : 2/7 * 56 = 112/7 = 16 teachers
this year....70 total people
students : 5/7 * 70 = 350/7 = 50 students
teachers : 2/7 * 70 = 140/7 = 20 teachers
Final answer:
To find the number of students and teachers based on their ratio and total count, we applied the ratio of 5:2 to the total counts of 56 and 70 for the last year and this year, respectively. This calculation revealed there were 40 students and 16 teachers last year, and 50 students and 20 teachers this year.
Explanation:
The student has asked about finding the number of students and teachers at a preschool in two different years based on a given student-to-teacher ratio and the total count of students and teachers for those years.
Step-by-Step Solution:
First, understand the ratio of students to teachers is 5:2. This means for every 5 students, there are 2 teachers.
To solve for last year, we have a total of 56 individuals (students and teachers). Let's represent students as 5x and teachers as 2x, given their ratio. Therefore, 5x + 2x = 56, solving this gives us x = 8. This means there were 40 students (5*8) and 16 teachers (2*8) last year.
For this year, we have a total of 70 individuals. Using the same method, 5x + 2x = 70, we find that x = 10. This means there are 50 students (5*10) and 20 teachers (2*10) this year.
By understanding and applying the concept of ratios, we were able to find the number of students and teachers for both years.
Solve the following expression. 36 - {-49 + (32.9) ] =
Answer:
52.1
Step-by-step explanation:
The given expression is 36 - [-49 + 32.9]
First we have to simplify the numbers which are in parenthesis.
= 36 -(-16.1)
Here -(-16.1) = + 16.1
So, we get
= 36 + 16.1
= 52.1
The answer is 52.1
(SAT Prep) In △ABC, AB = BC = 20, DE ≈ 9.28. Approximate BD.
The measure of BD ≈ 5.36
Step-by-step explanation:
The side BC = BD+DE+EC.The measure of BC = 20 and DE ≈ 9.28The angles ∠BD and ∠EC are both equal to 15°If the angles are same, then their sides are equal.Let 'x' be the measure of BD and EC.
BC = x+9.28+x
20 = 9.28 + 2x
2x = 20-9.28
x = 10.72/2
x = 5.36 (approx.)
∴ The measure of BD ≈ 5.36
A container is filled with 100 grams of bird feed that is 80% seed. How many grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed?
Thank you!
Answer:
43.65 grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed
Step-by-step explanation:
Let us assume the total capacity of the container = m grams
Here, given: 80% of m = 100 grams
[tex]\implies \frac{80}{100} \times m = 100\\\implies m = \frac{100 \times 100}{80} = 125[/tex]
or, the TOTAL CAPACITY of container = 125 grams
Now, the container already has 5 % seeds.
Calculating 5% of the capacity, we get:
[tex]\implies \frac{5}{100} \times 125 = 6.25[/tex]
So, the container already has 6.25 grams.
Now, the total filling of the container should be 40%.
Calculating 40% of the capacity, we get:
[tex]\implies \frac{40}{100} \times 125 = 50[/tex]
So, the weight of seeds that NEEDS To be in total = 50 grams.
Also, it already has 6.35 grams.
So, the weight of seeds to be added = 50 grams - 6.35 grams
= 43.65 grams
Hence, 43.65 grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed.
43.75 grams of bird feed containing 5% seed must be added to get bird feed that is 40% seed
PercentagePercentage is a number or ratio that can be expressed as a fraction of 100.
Let the total mass of the container = x
Therefore,
80% of x = 100g of bird feed
80 / 100 × x = 100
80x = 10000
x = 10000 / 80
x = 125 grams
Therefore, 5% volume will be as follows;
5 / 100 × 125 = 625 / 100 = 6.25 gramsTherefore, 40% volume is as follows:
40 / 100 × 125 = 5000 / 100 = 50 gramsFinally, the weight to be added to make the bird feed 40% seed is as follows;
50 - 6.25 = 43.75 gramslearn more on percentage here: https://brainly.com/question/1691136
A fair coin is tossed in the air 50 times. It landed on tail 24 times. What is the experiment probability that the coin will NOT land on talis
Answer:50/50
Step-by-step explanation:
It’s a 50/50 chance because there is only two sides to a coin
What is the image point of (3,7) after translation right 5units and up 1 unit
Answer:
(8,8)
Step-by-step explanation:
The image point of (3,7) after translation 5 units to the right and 1 unit up is (8,8).
Explanation:Translation of a point in a coordinate plane involves moving the point to a new location without changing its orientation or size.
To find the image of a point (3,7) after a translation of 5 units to the right and 1 unit up, we simply add the translation amounts to the original coordinates.
For a rightward movement, we add 5 to the x-coordinate, and for an upward movement, we add 1 to the y-coordinate.
Therefore, the new position of the point after translation will be:
New x-coordinate = Original x-coordinate + Rightward translation = 3 + 5 = 8New y-coordinate = Original y-coordinate + Upward translation = 7 + 1 = 8So, the image point after the translation is (8,8).
Find the equation of a line that is perpendicular to y=−12x−1 and passes through the point (3,2).
Answer:
y = (1/12)*x + 7/4
Step-by-step explanation:
y=−12x−1
Perpendicular line:
y = a*x + b
y = (1/12)*x + b
2 = (1/12) * 3 + b
2 = (3/12) + b
2 = 1/4 + b
2 - 1/4 = b
7/4 = b
Perpendicular line:
y = (1/12)*x + 7/4
rewrite equation without fractions, do not use decimals in the answer.
7/9x +2 = 5/6
Answer:
Step-by-step explanation:
7/9x + 2 = 5/6.....multiply by the common denominator of 18
14x + 36 = 15 <=== re-written without fractions
14x = 15 - 36
14x = -21
x = -21/14
x = - 3/2...(or - 1 1/2)...ur solution
To rewrite the equation 7/9x + 2 = 5/6 without fractions, we multiply every term by the least common denominator (18) to get 14x + 36 = 15. Subtracting 36 from both sides and solving for x results in x = -21/14.
Explanation:In order to rewrite the equation without fractions, we can eliminate the fractions by finding the least common denominator (LCD) and multiplying every term in the equation by it.
The original equation is 7/9x + 2 = 5/6. The least common denominator for 9 and 6 is 18.Multiply each part of the equation by 18: 7/9x * 18 + 2 * 18 = 5/6 * 18. This simplifies to 14x + 36 = 15.Finally, subtract 36 from both sides to solve for x: 14x = 15 - 36, so x = -21/14.Learn more about Rewrite Equation here:https://brainly.com/question/31910848
#SPJ2
Chau's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Chau $5.50 per pound, and type B coffee costs $4.20 per pound. This month, Chau made 143 pounds of the blend, for a total cost of $677.30. How many pounds of type B coffee did he use?
84 pounds of Type B coffee is used
Solution:
Let "x" be the pounds of type A coffee
Let "y" be the pounds of type B coffee
Cost per pound of type A = $ 5.50
Cost per pound of Type B = $ 4.20
This month, Chau made 143 pounds of the blend
x + y = 143
x = 143 - y -------- eqn 1
For a total cost of $677.30. Thus we frame a equation as:
pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30
[tex]x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2[/tex]
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
[tex]5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84[/tex]
Thus 84 pounds of Type B coffee is used
To determine how many pounds of type B coffee were used in Chau's coffee blend, we set up a system of equations based on the total weight and total cost of the blend. By substituting one equation into the other, we can solve for the quantity of type B coffee.
Calculating the Blend of Coffee:
To solve the problem, let's use a system of equations to determine how many pounds of type B coffee Chau used in his coffee blend. We have two unknowns here: the amount of type A coffee (let's call it A) and the amount of type B coffee (let's call it B). The total weight of the coffee blend is given as 143 pounds, and the total cost of the blend is $677.30.
The first equation comes from the total weight of the blend:
A + B = 143
The second equation comes from the total cost:
5.50A + 4.20B = 677.30
We can use either substitution or elimination to solve this system. If we solve the first equation for A (i.e., A = 143 - B) and substitute it into the second equation, we get:
5.50(143 - B) + 4.20B = 677.30
After simplifying, we can solve for B to find out how many pounds of type B coffee were used.
Convert z = 9cos200° + 9isin200° from polar form to rectangular form.
-8.46 - 3.08i
-2.09 – 6.84i
8.46 + 3.08i
2.09 + 6.84i
Answer:
z = -8.46 - 3.08i.
Step-by-step explanation:
cos 200 = -0.93969 so 9 * cos 200 = -8.46 to the nearest hundredth.
sin 200 = -0.3420 so 9 * sin 200 = -3.08 to nearest hundredth.
Khybar Inc. manufactures dental X-ray machines. The company can sell an X-ray machine which cost $508.17 to produce for
$1.295.75. Each of the company's two salespeople ears a different commission per sale, as shown in the table below.
Salesperson
Greg
Colleen
Commission/Sale
$243.15
$288.75
Last year, Greg sold 11 fewer X-ray machines than Colleen did. Khybar Inc.'s total expenses last year, not counting
production costs or commissions, came to $79,558.59. If Khybar Inc. broke even, how many X-ray machines were sold last
year in total?
The answer is B (153) on Edge.
The X-ray machines were sold last year in total is 157.
What is Commission?A commission is a sum of money that a salesperson receives for each transaction they make. If a salesman is compensated on commission, their pay is based on how much they sell. Salespeople are paid only on commission.
We have,
The company can sell an x-ray machine which cost $508.17 to produce for $1.295.75.
So, the number of x-ray machines that were sold last year by Khybar inc.
= 79558.59/508.17
= 156.5
= 157
Learn more about Commission here:
https://brainly.com/question/27635932
#SPJ7
A gain of 56 points in a game as an integer
Answer:
+56
Step-by-step explanation:
The value of a boat is $53,650. It loses 14% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
Answer:
1.17
Step-by-step explanation:
this is because first you would do 14÷12 as 14 is yearly and you want to find the monthly percentage this gives you 1.1666666667. then the next step is to round it so you would round 1.1666666667 to 1.17 for hundredth of a percent
14÷12=1.1666666667
round 1.1666666667 to 1.17
hoped this helped
The perimeter of a rectangle is 34 units. Its width is 6.5, point
Answer:
Length = 10.5units,Area = 68.25 unit²
Step-by-step explanation:
Perimeter =34 units
Width =6.5 units
Perimeter = l+l+w+w
Where l= length and w= width
34 = l + l + 6.5+ 6.5
34.= 2l + 13
Subtract 13 from both sides
2l = 34 - 13
2l = 21
Divide both sides by 2
L= 21/2
Length = 10.5units
If we are to find the area.
Area = length x width
Area = 10.5 × 6.5
Area = 68.25 unit²
I hope this was helpful, please mark as brainliest
What is the answer to 5(a-b)?
Answer:
5xA-5xB
Step-by-step explanation:
Answer: 5a-5b
Step-by-step explanation: Distribute the 5 and carry the negative sign over
Janice is babysitting this summer she already has $35 in her account before she
begins babysitting. If she makes $25 each week, how much does she have after 3
weeks?
Answer:
$110
Step-by-step explanation:
35+25(3)
what is the orthocenter of a triangle on (-2,5), (6,5), and (4,-1)
Answer:
(4,3)
Step-by-step explanation:
The orthocenter of a triangle is the point of intersection of the altitudes of the triangle .
The vertices are:
A(-2,5), B(6,5), and C(4,-1)
Slope of (6,5), and (4,-1) is
[tex]m = \frac{5 - - 1}{6 - 4} = 3[/tex]
Slope of altitude through A is
[tex] - \frac{1}{3} [/tex]
The equation of the altitude through A is
[tex]y - 5 = - \frac{1}{3} (x - - 2)[/tex]
[tex]y = - \frac{1}{3} x + \frac{13}{3} [/tex]
The slope of A(-2,5), B(6,5) is zero because it is a horizontal line.
The equation of altitude through (4,-1) will be the vertical line x=4.
This implies that,
[tex]y = - \frac{4}{3} + \frac{13}{3} = 3[/tex]
Hence the orthocenter is (4,3)