The scientific notation for the mass of 49,000 molecules of oxygen is 4.9 × 10⁴ grams.
How do you define the scientific notation?To transform numbers into scientific notation, use the following rule: In scientific notation, the exponent equals the number of times the decimal point must always be shifted to produce a number between 1 and 10.
The proper scientific notation format is an x 10∧b, where an is a number or decimal number with an absolute value greater or equal to one and less than ten, or 1 |a| 10.Scientific notation is a method of writing extremely large or extremely small numbers in a way that makes them easier to read as well as work with. A number formed by multiplying a number greater or equal to one but less than ten by an integral power of ten.For the given value;
= 49,000 grams
write the number such that only one digit is left to the left of decimal of the number and the remaining digits to the write are written to the power of 10
= 4.9000 × 10⁴
This could be written as;
= 4.9 × 10⁴.
Therefore, the value of the mass of 49,000 oxygen molecules in the form of scientific notation is 4.9 × 10⁴ grams.
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Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards
long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
11 inches : ? yards
The scale used by Wyatt is; 11 inches : 4 yards.
What is defined by the term scale factor?The Scale Factor is utilised to scale forms in various dimensions. The scale factor is a measurement for figures with similar appearances but distinct scales or measures. Assume two circles appear similar but have different radii.The scale factor specifies how much larger or smaller a figure is than the earlier figure.Now, for the given values in question.
For the area of picnic is 84 yards.= long.
The length in the drawing is 31 inches.
Let the scale for yards is 'x'.
Then;
231 inches: 84 yards = 11 inches: x yards
Write in the fraction form,
231/84= 11/x
Cross multiplying;
x = (11×84)/231
x = 4
Thus, scale becomes; 11 inches : 4 yards.
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the international shark attack file recorded the number of shark attacks between 1837 and 2016 for 8 different u.s. states.
what is the mean number of shark attacks over these states?
4,8, 5, 13,3,4, 1, 10
The mean of the data given 4, 8,5, 13, 3, 4, 1, 10 shows number of shark attacks over 8 different states is 6.
As given,
Number of different states 'n'= 8
Number of sharks attacks for 8 different states
[tex]x_{i}[/tex] = 4, 8,5, 13, 3, 4, 1, 10
Mean = [tex]\frac{\sum x_{i} }{n}[/tex]
= (4+ 8+ 5 + 13 + 3 + 4 + 1 + 10) /8
=48 /8
=6
Therefore, the mean of the data given 4, 8,5, 13, 3, 4, 1, 10 shows number of shark attacks over 8 different states is 6.
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Answer: 16.0 is the correct answer
Step-by-step explanation:
Pls help i will give brainly
Answer:
B. y = -1/4x + 2
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So slope is -1/4
Using m = -1/4, y =4, x = -8
y = mx + b
4 = -1/4(-8) + b
4 = 2 + b
b = 2
so y = -1/4x + 2
Create a Box and Whisker Plot using the following data: 13, 16,
17, 19, 23, 24, 25, 27, 30, 32, 35. What is the median of the set
of data?
24 is the median number because it is found to be at the Middle of all digits
Rearrange the formula to make x the subject y=4(x-1)
By rearranging the formula using algebraic operations, the value of x is [tex]\frac{y}{4}[/tex] - 1.
What is an Algebraic Expression?When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
To find the value of x, use the same operations on both sides of the equation.
For making x the subject
Divide by 4 on both sides
[tex]\frac{y}{4}[/tex] = (x-1)
On both sides of the equation, add 1.
[tex]\frac{y}{4}[/tex] - 1 = x
As a result, by rearranging the equations, the value of x is [tex]\frac{y}{4}[/tex] - 1.
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Write an expression that represents the total owed for 4 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $35?
Answer:
4c + 35
Step-by-step explanation:
What every the monthly amount is (c) you would multiply that by 4 to find the cost for 4 months and then you have to add in the one time cost of 35
A school has 360 students, 4/9 of whom are boys. How many of the students are boys? How many are girls?
Answer:
There are 160 boys and 200 girls
Step-by-step explanation:
its a proportion
Ken alone takes x days to finish a project
Anson alone takes 3 days more than Ken
alone to finish the project. If they together
take 2 days to finish the project, find the
value of x.
Fice card are dealt fom a deck. what is the probability of getting any two distinct face values occuring axactly twice?
The likelihood of any two different face values occurring exactly twice is 0.0475.
Describe probability using an example?
The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.An event's probability grows with its likelihood of happening. Tossing a fair (impartial) coin provides a simple illustration.Two pairs
two pairs = 13C2 *4C2 * 4C2 * 11C1 * 4C1 = 123552
P( two pairs) = 123552/2598960 = 0.0475
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The complete question is -
In a poker game, five cards are dealt at random from an ordinary deck of 52 playing cards. Find the probability of gettingtwo pairs (any two distinct face values occurring exactly twice)
factor the expressions:
1234567890123456789012345678901234567890
You have one box that is 1 3 11 feet tall and a second box that is 1.27 feet tall. Write the decimal expansion for 1 3 11. If you stack the boxes, about how tall will the stack be?
Answer:
Step-by-step explanation:
A loaf of bread 9 in. long is cut into slices 3/8 in. thick.
Answer:
32
Step-by-step explanation:
There is nothing this but the answer is 32.
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 2), (negative 1, 4), (1, 1), (1, 3), (2, negative 3).
Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?
We need to remove either (1, 4) or (1, 1) to create a function.
How to alter a relation in order to obtain a function
Relations are formed by two sets, an input set known as domain and an output set known as range and relationships between these sets. A relation is a function if and only if each element from domain is related to only one element of the range. Mathematically speaking, we must satisfy the following proposition:
x → f(x), x → f'(x) ⇒ f(x) = f'(x)
Based on this definition, there are two possibilities to create a function:
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1,3 is the answer I believe. :)
Segment AC has a length of 60. Find the following values.
DG = 60
Therefore,[tex]4x - 3 + 2x + 21 = 60[/tex]
→[tex]6x+18 = 60 \\ 6x = 60 - 18[/tex]
→[tex]6x = 42[/tex]
Divide both sides by 6
→[tex]x = 7[/tex]
DO =[tex]4x - 3 [/tex]
→[tex]4(7) - 3 \\ 28 - 3[/tex]
DO [tex]= 25[/tex]
OG [tex]= 2x + 21[/tex]
→[tex]2(7) + 21 \\ 14 +21[/tex]
OG [tex]= 35[/tex]
Therefore:
[tex]x = 7[/tex]
[tex]DO = 25 ft[/tex]
[tex]OG = 35 ft[/tex]
I hope this helpsPlease help thank youuu
Answer:
f(-7) = -15
g(-3) = 27
Step-by-step explanation:
We see that the functions defined are:
f(x) = 2x - 1
AND
g(x) = 2x^2 - 3x
This problem asks to find f(-7) and g(-3). To find this, we have to plug the respective numbers into the respective functions.
f(-7) = 2 (-7) - 1
f(-7) = - 14 - 1
f(-7) = -15
g(-3) = 2(-3^2) - 3(-3)
g(-3) = 2(9) + 9
g(-3) = 18+9
g(-3) = 27
FINAL ANSWER: f(-7) = -15, g(-3) = 27
How much of a(n) 70% orange juice drink must be mixed with 18 gallons of a 30% orange juice drink to obtain a mixture
that is 50% orange juice?
Answer:
18 gallons
Step-by-step explanation:
Start with x gallons of 70% juice and 18 gallons of 30% juice.
Result: x + 18 gallons of 50% juice
0.7x + 0.3 × 18 = (x + 18)(0.5)
0.7x + 5.4 = 0.5x + 9
0.2x = 3.6
x = 18
Answer: 18 gallons
4a + 2b - 12ax + 15b = -40x - 52. What is a and b
Answer:
a = 10/3 and b = -196/51.
Step-by-step explanation:
4a + 2b - 12ax + 15b = -40x - 52
Equating coefficients of x:
-12ax = -40x
-12a = -40
a = 40/12
= 10/3.
Equating constants:
4a + 2b + 15b = -52
4a + 17b = -52
Substituting a = 10/3:
40/3 + 17b = -52
17b = -52 - 40/3
b = (-52 - 40/3) / 17
= (-156/ 3 - 40/3) / 17
= -196 / 51
use mathematical symbols to write 3 different expressions to represent three groups of five
The different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3
How to write different expressions to represent three groups of five?The mathematical statement is given as:
three groups of five
The statement three groups of five means
Three multiplied by 5
i.e. 3 * 5
This can also be written as
5 + 5 + 5
Also, it can be expressed as
3 + 3 + 3 + 3 + 3
Hence, the different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3
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What should be added to -7/12 to get 9/16
Answer:
1/48 should be added.
Step-by-step explanation:
If you add 9/16 to -7/12 you will get -1/48. Then do -7/12 + 1/48 and it will give you 9/16.
During a cake-eating contest, Dave ate three and a half pizza and Daisy
ate two-thirds of a pizza. How many pizzas did they eat altogether?
HELP EXPLAIN STEP BY STEP!
Answer:
4 1/6
Step-by-step explanation:
Dave eats 3 3/6
Daisy eats 4/6
Together they eat 3 1/6
First you have to make it to a common denominator for Dave and Daisy. then you add the fractions.
4 full pizzas plus 1/6 of a pizza
i.e. 4 full pizzas plus one extra slice
======================================================
Explanation:
1/2 = 3/6
2/3 = 4/6
The fractions add to 1/2 + 2/3 = 3/6 + 4/6 = 7/6 = 1 & 1/6
That first "1" is the carry and it adds to the 3 whole pizzas Dave ate. So we have 3+1 = 4 full pizzas consumed, plus an additional 1/6 of a pizza.
This gives the mixed number 4 & 1/6
Check out the diagram below. I show Dave's slices in blue, and Daisy's slices in pink for the first two rows. The third row is the combination of those slices to get 4 full pizzas and 1 extra slice (to represent that extra 1/6). Let me know if you have questions about the diagram, or the steps in general.
Are -345° and 2185° co-terminal?
Answer:
No
Step-by-step explanation:
You want to know if angles -345° and 2185° are coterminal.
Coterminal anglesAngles are co-terminal when their terminal sides are coincident. Each angle will have the same measure modulo 360°.
-345° / 360° = -1 remainder 15°
2185° / 360° = 6 remainder 25°
These angles have different values, modulo 360°, so are not co-terminal.
The brady family received 31 31 pieces of mail on april 22. the mail consisted of bills, letters, magazines, and ads. how many bills did they receive if they received the same number of bills as magazines, five more ads than letters, and three more letters than magazines?
The number of bills received by brady family are 781.
What is Linear equation in one variable?A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable with the form an x + b = 0 are solved utilizing basic algebraic operations.
Let x equal the number of letters obtained,
(x - 3) equal the number of bills obtained,
(x + 5) equal the number of advertisements received, and also
the number of magazines did receive is also given (x - 3).
The following equation can be derived:
x + (x - 3) + (x + 5) + (x - 3) = 3131
4x - 1 = 3131
4x = 3132
x = 784
Thus, number of bills received are-
(x - 3) = 784 - 3
number of bills received = 781.
Therefore, the number of bills obtained by brady family are 781.
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mina's explanation: i counted up from 15.75 to 176.3 to find the difference. i underlined each number i added on each line.
160.55 is the difference. i underlined each number i added on each line.
What is an linear equation in math?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The two numbers are 15.75 and 176.3
First we will compare the numbers.
1. A=176.3
2. B=15.75
one's place of A is greater than once place of B.
tens place of A is greater than tens place of B.
Hundred place of A is greater than hundred place of B.
So, A>B
So we will subtract 15.75 from 176.3.
176.30 -15.75=
176.30 ----A
- 1 5.75 ----B
Hundreths place of A - Hundreths place of B = 0-5=10-5=5
Tenth place of A - Tenth place of B =12-7=5
ones place of A - ones place of B=5-5=0
Tens place of A - Tens place of B =7-1=6
So the solution is 160.55
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a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge.
Shelly Lemony obtains a small business equipment loan for $120,000. Her down payment is 20% and the APR is 8% for 12 months.
a) Shelly Lemony's down payment is $24,000.
b) The loan amount is $96,000.
c) The monthly payment is $8,350.89.
d) The finance charge is $4,210.68.
What is the down payment?The down payment represents the initial up-front partial payment for the purchase of the equipment on loan.
The down payment reduces the cost of the equipment to the loan amount. Finance companies demand a down payment to ascertain the buyer's willingness and ability to proceed with the loan arrangement.
It is a sign of commitment to meet the loan contract obligations.
Data and Calculations:Monthly Pay: $8,350.89
Total Loan Amount = $96,000.00
Upfront Payment $24,000.00
Equipment loan = $120,000
Number of periods = 12 months
APR = 8%
Total of 12 Loan Payments = $100,210.68
Total Loan Interest = $4,210.68
Total Cost (price, interest, tax, fees) = $124,210.68
Thus, Shelly will make a down payment of $24,000 or 20% of the equipment loan.
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Consuelo is buying flavored coffee and plain coffee. the total amount of money she spends on coffee is t = 5.50p + 7f, where p represents the cost of a package of flavored coffee.
Answer is
(a) She can buy 7 packages of plain coffee or 5 packages of coffee.
(b) f = [tex]\frac{T- 5.50 p}{7}[/tex]
(c) she can buy 3 packages of flavoured coffee
(a) she spent on coffee is $ 40
amount of money she spends on coffee is 5.50
then, packages of plain coffee = [tex]\frac{40}{5.50}[/tex] ≈ 7.2
so she buy 7 packages of plain coffee.
she spent on coffee is $ 40 and amount spends on flavoured coffee is 7
then , packages of flavoured coffee = [tex]\frac{40}{7}[/tex] ≈ 5.7
so she can buy 5 packages of flavoured coffee.
(b)According to question ,
T = 5.50 + 7f
so 7f = T - 5.50
then , f = [tex]\frac{T - 5.50}{7}[/tex]
(c) we get the value of f = [tex]\frac{T - 5.50}{7}[/tex]
given that , f is equal to 3
then, f = [tex]\frac{T - 5.50}{7}[/tex]
= [tex]\frac{T - 5.50}{7}[/tex]×3
we get = [tex]\frac{T - 16.5}{7}[/tex]
when T is equal to 40
then , f = [tex]\frac{40 - 16.5}{7}[/tex] ≈ 3.35
so she can buy 3 packages of flavoured coffee.
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Given last periods forecast of 65, and last periods demand of 62, what is the simple exponential smoothing forecast with an alpha of. 4 for the next period?.
The exponential smoothing forecast for next period is 63.2.
What is exponential smoothing?A time series forecasting technique called exponential smoothing can be expanded to support data with a systematic trend or seasonal component.
Now,
Given:
Last period forecast = 65Last period demand = 62α = 0.4To find: Simple exponential smoothing forecast with α = 0.4 for next period.
Finding:
Now, by the concept of exponential smoothing, forecast for next period will be given by:
Ft + 1 = α Dt + (1 - α)F,
where,
Ft+1 = the next forecast,
α = weighing factor,
Dt = actual value for this period,
F = forecast value for the current period,
Substituting the values in the above expression:
=> Ft + 1 = 0.4 (65) + (1 - 0.4) 62
=> Ft + 1 = 26 + 37.2
=> Ft + 1 = 63.2
Hence the exponential smoothing forecast for next period is 63.2.
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The functions are defined:
f(x) = -2x
g(x) = 2x + 5
h(x) = x² + 3x-10
Calculate the indicated function values.
ƒ(6²)
The indicated function value is f(6²) = -72
How to calculate the indicated function values?The function definitions are given as
f(x) = -2x
g(x) = 2x+ 5
h(x) = x^2 + 3x - 10
The function f(6²) means that x = 6² in f(x)
So, we have
f(6²) = -2(6²)
Evaluate
f(6²) = -72
Hence, the indicated function value is f(6²) = -72
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Solve
each of the following equations. Show its solution set on a number line. Check a
your answers.
|5x |=3
Find the rate of change for each set of ordered pairs. What is
the average rate of change of all the sets?
(2,3.5), (6,5.5)
(-1,0), (0, 3)
(3,-3), (4,4)
Write your answer to the average rate of change as a fraction,
a/b.
Enter the answer
SCRATCHPAD
Check it
Improve this question
The rate of change for each set of ordered pairs is:
a. 1/2
b. 3
c. 7
How to Find the Average Rate of Change?The average rate of change = change in y / change in x.
Average rate of change for (2,3.5), (6,5.5):
Average rate of change = (5.5 - 3.5)/(6 - 2) = 2/4 = 1/2
Average rate of change for (-1,0), (0, 3):
Average rate of change = (3 - 0)/(0 - (-1)) = 3/1 = 3
Average rate of change for (3,-3), (4,4):
Average rate of change = (4 -(-3))/(4 - 3) = 7/1 = 7
Therefore, the rate of change for each set of ordered pairs is:
a. 1/2
b. 3
c. 7
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The formula for the area of a trapezoid is given. Solve this equation for h, height. a=H(B1+B2)/2
The solution of the equation for h is H = 2a/(B1 + B2)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to solve the equation for h?The equation is given as
a=H(B1 + B2)/2
The above means that the variable h is represented by the variable H
Multiply both sides of the equation by 2
So, we have
2a = H(B1 + B2)
Divide both sides of the equation by (B1 + B2)
H = 2a/(B1 + B2)
Hence, the solution of the equation for h is H = 2a/(B1 + B2)
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