Answer:
Step-by-step explanation:
If we represent the first number as "x", then the second number can be represented as "2x-3".
For example, if the first number is 5, then the second number would be 2(5)-3 = 7.
Alternatively, if the first number is 10, then the second number would be 2(10)-3 = 17.
In general, we can say that the second number is equal to twice the first number minus 3.
A 500-gallon tank initially contains 200 gallons of brine containing 90 pounds of dissolved salt. Brine containing 3 pounds of salt per gallon flows into the tank at the rate of 4 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 1 gallon per minute. Set up a differential equation for the amount of salt A(t) in the tank at time t.
How much salt is in the tank when it is full?
The differential equation for the amount of salt A(t) in the tank at time t is 12 - A(t)/(200 + 3t) and the amount of salt in the tank when it is full is 290.72 pounds.
To set up a differential equation for the amount of salt A(t) in the tank at time t, we need to determine how the amount of salt changes over time. The rate of change of the amount of salt in the tank is determined by the difference between the rate at which salt flows into the tank and the rate at which salt flows out of the tank.
Since the incoming brine contains 3 pounds of salt per gallon, the rate at which salt flows into the tank is 3 pounds per gallon times 4 gallons per minute, or 12 pounds per minute. Since the mixture flows out of the tank at a rate of 1 gallon per minute, the rate at which salt flows out of the tank is A(t)/V(t), where V(t) is the volume of the mixture in the tank at time t.
Since the volume of the mixture in the tank at time t is the sum of the initial volume and the volume of incoming brine minus the volume of outgoing mixture, we have:
V(t) = 200 + 4t - t = 200 + 3t
Therefore, the rate at which salt flows out of the tank is A(t)/(200 + 3t) pounds per minute. Thus, the differential equation for the amount of salt A(t) in the tank at time t is:
dA/dt = 12 - A(t)/(200 + 3t)
To find the amount of salt in the tank when it is full, we need to find the time t when the tank is full. The tank is full when its volume is 500 gallons, so we have:
200 + 4t - t = 500
Simplifying this equation, we get:
3t = 300
t = 100
Therefore, the tank is full after 100 minutes. To find the amount of salt in the tank when it is full, we can solve the differential equation for A(t) using an appropriate initial condition (i.e., the amount of salt in the tank at t=0):
dA/dt = 12 - A(t)/(200 + 3t)
A(0) = 90
Solving this differential equation, we get:
A(t) = 360 - 270e^(-t/300)
Therefore, the amount of salt in the tank when it is full (i.e., after 100 minutes) is:
A(100) = 360 - 270e^(-1/3)
which is approximately 290.72 pounds.
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A deck of cards contains RED cards numbered 1,2,3,4,5 and BLUE cards numbered 1,2,3,4. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 5 is one of the outcomes in which of the following events? Select all correct answers.
The probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)
What is probability?Probability in mathematics is the process of finding chances of an event to happen.
Given that, a deck of card have,
Red cards = 1,2,3
Blue cards =1,2,3,4,5,6
Pr(R) = Drawing a red card = 3/9 = 1/3
Pr(B) = Drawing a blue card = 6/9 = 2/3
Pr(E) = Drawing an even card = 4/9
Pr(O) = Drawing an odd number card = 5/9
Probability of drawing the red 5 = P(red 5) = 1/9
From the options, we have :-
(A) R or O = Pr(R) + Pr(O) = 1/3 + 1/9 = 8/9 ≠ 1/9
(B) B and O = Pr(B) × Pr(O) = 2/3 × 5/9 = 10/21 ≠ 1/9
(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27 ≠ 1/9
(E) R'. E' = 1-Pr(R)-1-Pr(E) = 1-1/3 =2/3- 1-4/9 =5/9
= 2/3-5/9
= 1/9
Hence, the probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)
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Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.
After she rolls it 2,000 times, she finds that she rolled the number 2 a total of 187 times. Which of the following is true?
A. Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times.
B. Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability.
C. We cannot draw any conclusions from Joan's experience with this die because there is only a very weak link between the relative frequency of an event and the theoretical probability.
D. We cannot draw any conclusions from Joan's experience with this die without also knowing how many times the other numbers appeared.
The true statement is that Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times. The answer is A.
The theoretical probability of rolling a 2 on a fair four-sided die is 1/4 or 0.25. If Joan rolled the die 2,000 times, we would expect her to roll a 2 approximately 500 times (0.25 x 2,000 = 500).
However, she only rolled a 2 187 times. The relative frequency of rolling a 2 is 187/2,000, which is 0.0935 or 9.35%. This is quite different from the expected theoretical probability of 25%, which suggests that the die may not be fair.
Joan's experience provides evidence that the die may not be fair. The relative frequency of rolling a 2 is significantly lower than the theoretical probability, indicating that the die may be biased.
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you have a toonie, a loonie, and three quarters. Hiw many different sums of money can you make?
The given sum of money in cents as 375 cents.
What is money?Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.
Given that, person has a toonie, a loonie, and three quarters.
1 Toonie = 2 dollars
1 Loonie = 1 dollar
3 quarters = 0.75 dollars
So, sum of money = 2+1+0.75
= 3.75 dollars
1 Toonie = 200 cents
1 Loonie = 100 cents
3 quarters = 75 cents
Sum of money = 200+100+75
= 375 cents
1 Toonie = 8 quarters
1 Loonie = 4 quarters
So, in quarters = 8+4+3
= 15 quarters
Therefore, the given sum of money in cents as 375 cents.
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Please Explain as well
Given f (x)=25-x² and g(x)=2x-9, determine the simplified form of the composite function f (g(x))?
Answer:
Step-by-step explanation:
[tex]25-(2x-9)^{2}[/tex]=[tex](25-2x+9)(25+2x-9)=(34-2x)(16+2x)=4(17-x)(8+x)[/tex]
The coordinate grid below shows the graph of supply and demand functions for the sales of a certain video game. For the functions, x
represents the number of video games sold, in thousands of units, and y
represents the price, in dollars, of each game.
The equilibrium point for the supply and demand functions can be found by locating the point where the two functions are equal. Which of these appears to be the number of video games, in thousands, that must be sold to achieve equilibrium?
6
90
8
14
Answer:
(c) 8
Step-by-step explanation:
You want the x-coordinate of the point where the lines on the graph cross.
Equilibrium pointThe equilibrium point, as the problem statement tells you, is the point where the two lines have the same x- and y-values. That is the point where the lines cross.
The problem statement also tells you that the x-coordinate represent the number of games, in thousands, that will be sold at the price represented by the y-coordinate. By asking for the number of games sold, the question is asking for the x-coordinate of the point where the lines cross.
The lines cross at a grid intersection that is 4 squares right of the y-axis. The label 10 on the 5th square tells you that each square represents 2 (thousands). Hence the x-coordinate of the equilibrium point is ...
8 . . . . . (thousands of games sold)
A colored spinner with eight equal sections is given.
spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow
Using the fair spinner, determine P(less than 4) when the spinner is spun once.
0.125
0.25
0.375
0.5
The Probability (less than 4) when the spinner is spun once is 0.5, the correct option is D.
How to find the geometric probability?When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:
E = favorable event
S = total sample space
Then:
P(E) = [tex]\dfrac{A(E)}{A(S)}[/tex]
where A(E) is the area/volume/length for event E, and similar for A(S).
Given that;
Spinner is divide in eight sections that has 3blue, 1 red, 2 purple, 2 yellow
Now,
The coloured spinner is divided into = 8 colour sections
The P event;
=4/8
=1/2
=0.5
Therefore the probability of event will be 0.5.
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1. Find the 15th term in the sequence if a1= 3 and d= 4
2. Find Sn for the arithmetic series where a1= 5, an= 119, n= 20
3. Find Sn for the arithmetic series where a1= 12, d= 6, n= 15
4. Find the 6th term in the geometric sequence where a1= 2, a6= 64, r= 2
5. Find Sn for the geometric series where a1= 2 , r= 4, n= 6
Using the formula, we can conclude that the 15th term in the following sequence is 59.
What is Arithmetic Sequence?A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.
The common difference in that mathematical progression is the constant difference.
n: The method for determining the nth term is used to locate a particular term in an arithmetic series.
Step 1:
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.
So, the formula is:
an = a + (n – 1)d
Now, insert the values as follows:
an = a + (n – 1)d
a15 = 3 + (15 – 1)4
a15 = 3 + (14)4
a15 = 3 + 56
a15 = 59
Therefore, using the formula, we can conclude that the 15th term in the following sequence is 59.
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Correct question:
Find the 15th term in the sequence if a1= 3 and d= 4
Let A = {H, T}, B = {1, 2, 3, 4, 5}, and C = {red, green, blue}. Find the number indicated. HINT [See Example 5.]
n(B × C)
There are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.
Describe Cartesian Product?In mathematics, the Cartesian product is a binary operation that takes two sets and forms a set consisting of all possible ordered pairs of elements from the two sets. The resulting set is often denoted by A × B, where A and B are the two original sets.
Formally, if A and B are two sets, the Cartesian product A × B is defined as:
A × B = {(a, b) : a ∈ A and b ∈ B}
This means that the Cartesian product contains all possible ordered pairs (a, b) where a is an element of A and b is an element of B. For example, if A = {1, 2} and B = {x, y}, then A × B would be {(1, x), (1, y), (2, x), (2, y)}.
The Cartesian product B × C is the set of all ordered pairs (b, c) where b is an element of B and c is an element of C. Since B has 5 elements and C has 3 elements, there are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.
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a bicycle was bought for R1489 and sold at a profit of R387. what was the selling price of the bicycle?
The selling price of the bicycle is equal to R1,102.
What is profit?In Mathematics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.
Mathematically, the amount of profit made from selling a bicycle can be calculated by using the following function:
Profit made = Cost price - Selling price
Making selling price the subject of formula, we have:
Selling price = Cost price - Profit made
Selling price = R1489 - R387.
Selling price = R1,102.
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Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)
(a) 71st
(b) 29th
(c) 76th
(d) 24th
(e) 7th
You may need to use the appropriate table in the Appendix of Tables to answer this question.
(a) 0.52, (b) -0.54, (c) 0.68, (d) -0.71, (e) -1.44 - Percentiles for standard normal distribution using z-table.
(a) To find the 71st percentile, we search for the z-score that relates to a combined area of 0.71 to one side of the mean. From the standard typical circulation table, we find that the nearest z-scores are 0.67 and 0.72, with relating areas of 0.7486 and 0.7642, individually. To interject, we utilize the equation:
z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))
where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.71). Connecting the qualities, we get:
z = 0.67 + (0.72 - 0.67) * ((0.71 - 0.7486)/(0.7642 - 0.7486)) = 0.52
Consequently, the 71st percentile is z = 0.52.
(b) To find the 29th percentile, we search for the z-score that compares to a combined area of 0.29 to one side of the mean. From the standard ordinary conveyance table, we find that the nearest z-scores are - 0.53 and - 0.52, with relating areas of 0.2981 and 0.3050, individually. To add, we utilize the recipe:
z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))
where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.29). Connecting the qualities, we get:
z = - 0.53 + (- 0.52 - (- 0.53)) * ((0.29 - 0.2981)/(0.3050 - 0.2981)) = - 0.54
Consequently, the 29th percentile is z = - 0.54.
(c) To find the 76th percentile, we search for the z-score that relates to an aggregate area of 0.76 to one side of the mean. From the standard ordinary appropriation table, we find that the nearest z-scores are 0.73 and 0.77, with relating areas of 0.7673 and 0.7794, separately. To interject, we utilize the equation:
z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))
where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.76). Connecting the qualities, we get:
z = 0.73 + (0.77 - 0.73) * ((0.76 - 0.7673)/(0.7794 - 0.7673)) = 0.68
Consequently, the 76th percentile is z = 0.68.
(d) The 24th percentile compares to a z-score of - 0.71, meaning 24% of the standard ordinary conveyance misleads its left.
(e) The seventh percentile relates to a z-score of - 1.44, meaning 7% of the standard typical conveyance misleads its left.
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Nicole has two bags of coins. The first bag contains 5 silver dollars, 4 quarters, and 6 dimes. The second bag contains 2 silver dollars, 3 quarters, and 2 dimes. Nicole is going to let her little brother, Jacob, randomly select and keep 1 coin from each bag. What is the probability that Jacob will choose a silver dollar from each bag?
First, we need to find the probability of Jacob choosing a silver dollar from the first bag and a silver dollar from the second bag.
The probability of choosing a silver dollar from the first bag is 5/15 = 1/3 since there are 5 silver dollars out of a total of 15 coins in the bag.
The probability of choosing a silver dollar from the second bag is 2/7 since there are 2 silver dollars out of a total of 7 coins in the bag.
To find the probability of both events happening (Jacob choosing a silver dollar from each bag), we multiply the probabilities:
(1/3) x (2/7) = 2/21
Therefore, the probability that Jacob will choose a silver dollar from each bag is 2/21.
Amount of water in a pool
A certain city logged 128 days of precipitation for 1990, and 137 days of precipitation for 2002. Assuming a linear trend over this time frame, calculate the average rate of change in the annual number of days of precipitation for this city.
Answer:
Step-by-step explanation:
a) the probability of having exactly 10 days of precipitation in the month of April
Answer:
3/4
Step-by-step explanation:
All of the following statements are true about brake drum inside diameter measurements with a brake drum micrometer EXCEPT:A. The drum should be cleaned before measuring the diameter.B. If the drum diameter is less than specified, replace the drum.C. The diameter should be measured at two locations around the drum.D. The drum diameter variation should not exceed 0.035 in (0.009 mm).
The statement that is NOT true about brake drum inside diameter measurements with a brake drum micrometer is B.
If the drum diameter is less than specified, replace the drum. In fact, if the drum diameter is less than the minimum specified limit, the drum can be machined to a larger diameter to restore its proper dimension. This will depend on the manufacturer's recommendations, and the minimum thickness limits of the drum should also be checked to ensure it is within safe tolerances.
The other statements are true: A. The drum should be cleaned before measuring the diameter, to avoid errors due to dirt or rust. C. The diameter should be measured at two locations around the drum, usually at the top and bottom of the friction surface, to check for taper or out-of-roundness. D. The drum diameter variation should not exceed 0.035 in (0.009 mm), to ensure proper brake function and minimize vibration or noise.
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A local high school has 1400 students; 800 of whom are girls, 300 of the students are seniors; of which 200 are girls. If we chose a student
at random, what is the probability that we would choose a girl or a senior?
Step 1: List the events.
Event A: Choosing student who is a girl
Event B:
Choosing a student.
Step 2: Decide if the events are mutually exclusive or not.
The events are not mutually exclusive because one student can
Step 3: Write the correct equation and solve for the probability.
The events are not mutually exclusive, so we should use the equation P(A or B) = P(A) + P(B) - P(A and B) = because
P(A and B) 0.
How many total students attend the school?
+
800
1400
1400
P(G or S)=P(G) + P(S) - P(G and S)
200
P(G or S)=
300/1400
1400
46
3
students
* be a girl and a senior at the same time.
P(G or S) 14 I
P(G or S)=2
The probability of choosing a student who is a girl or a senior is. This means that 9 out of ever
or both.
students is a girl, a senior,
Event A: Choosing a student who is a girl
Event B: Choosing a student who is a senior
Therefore, the events are not mutually exclusive because one student can be a girl and a senior at the same time.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to happen.
The correct equation is:
P (G or S) = P(G) + P(S) - P(G and S)
= 800/1400 + 300/1400 - 200/1400
= 900/1400
= 9/14
This means that 9 out of 19 students is either a girl or a senior.
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Which function represents exponential growth?
A) y = 8x
B) y = 0.5x^2
C) y = 3(1.5)^x
D) y = -3(0.5)^x
A function that represents exponential growth include the following: C) y = 3(1.5)^x.
How to determine an exponential growth rate?Mathematically, an equation which can be used to model an exponential growth rate is given by this mathematical expression:
A(t) = P(1 + r)^{t}
Where:
A(t) represents the future value.P represents the initial value.r represents the rate of change or growth rate.T represents the time.Based on the exponential functions provided above, we can reasonably infer and logically deduce that the required exponential growth rate function is given by;
y = 3(1.5)^x
1 + r = 1.5
r = 1.5 - 1
Rate of change, r = 0.5.
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The table shows the median individual income for the citizens of a particular town since 2005. Find the average rate
of change from 2010 to 2020.
The average rate of change from 2020 to 2010 of the median individual income is 157.
What is average rate of change?The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.
The average rate of change is given by the formula:
R = f(b) - f(a) / (b - a)
where, f(b) and f(a) are values of the function at b and a respectively.
Here, the value of the functions are:
f(b) = 31675
f(a) =30105
b = 2020
a = 2010
Substituting the values in the equation we have:
R = (31675 - 30105)/ (2020 - 2010)
R = 1570/10 = 157
Hence, the average rate of change from 2020 to 2010 of the median individual income is 157.
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Answer: 158
Step-by-step explanation: The average rate of change from 2020 to 2010 of the median individual income is 157.
What is average rate of change?
The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.
The average rate of change is given by the formula:
R = f(b) - f(a) / (b - a)
where, f(b) and f(a) are values of the function at b and a respectively.
Here, the value of the functions are:
f(b) = 31675
f(a) =30105
b = 2020
a = 2010
Substituting the values in the equation we have:
R = (31675 - 30105)/ (2020 - 2010)
R = 1570/10 = 157
A high school student became dehydrated while recuperating from a virus. In the hospital he was given 120 cc of glucose intravenously at a drip rate of 1.02 cc per minute.
a. Make a table comparing the elapsed time with the amount of glucose given to the patient by calculating how much glucose is left in the bag over time. Use g for the number of ccs of glucose left in the bag and t for time in minutes.
NOTE: The x-axis is usually used to represent time.
b. Write an equation describing the relationship between the elapsed time and the amount of glucose remaining in bag.
c. Draw a graph. Discuss the meaning of the t-intercept and the g-intercept in this real-world situation.
d. What information from the table in part (a) and the graph in part (b) might be valuable to the doctor?
The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t
What is an equation ?
In mathematics, an equation is a statement that shows the equality between two expressions containing variables. It is typically written as a combination of numbers, variables, and mathematical symbols, such as addition, subtraction, multiplication, and division.
Here is a table comparing the elapsed time with the amount of glucose given to the patient:
Time (minutes) Glucose remaining in bag (cc)
0 120
1 119.98
2 119.96
3 119.94
4 119.92
... ...
t 120 - 1.02t
The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t
where g represents the amount of glucose remaining in the bag in cc and t represents the elapsed time in minutes.
Hence, The equation describing the relationship between the elapsed time and the amount of glucose remaining in the bag is: g = 120 - 1.02t
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When I combine 2x and - 10x what should I get?
Answer:
-8x
Step-by-step explanation:
when you combine 2x and -10x,
2x - 10x = -8x
This means that the expression 2x and -10x are combined to form the expression -8x.
25 points and will make the brainiest. Please answer each question as soon as possible. Thank you.
The sets of the domain and range of the relation are X = {- 4, - 3, 1, 0} and Y = {- 4, - 1, 0, 3, 4}.
How to determine the domain and range of a relation
In this problem we find a graphic representation of a relation, that is, a construction formed by two sets and its relationships. There is an input set called domain and an output set called range. Domain is represented by all values along the horizontal axis (x-axis) and range is represented by all values along the vertical axis (y-axis).
The points seen in the graph are now listed: (x₁, y₁) = (- 4, 0), (x₂, y₂) = (- 3, - 1), (x₃, y₃) = (1, - 4), (x₄, y₄) = (1, 4) and (x₅, y₅) = (0, 3). The set of the domain is {- 4, - 3, 1, 0} and the set of the range is {- 4, - 1, 0, 3, 4}.
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Simplify the expression: 4p + 2 (5p - 4)
Answer:
14p - 8Step-by-step explanation:
4p + 2 (5p - 4)
Expand:-
4p + 10p - 8Combine like terms (4p + 10p = 14p) :-
14p - 8-Hope this helps! :)
Answer:
2(7p-4)
Step-by-step explanation:
which is greater 4/7 ×1/4 or 4/7×1/6
Answer:4/7*1/4
trust me >:)
help i don't understand my math
Answer:
cant help if there is nothing to answer bud/gal.
Step-by-step explanation:
cant help if there is nothing to answer bud/gal.
Rhonda has a USB drive that can hold
8
,
000
,
000
,
000
B
8,000,000,000 B8, comma, 000, comma, 000, comma, 000, start text, space, B, end text.
Choose the best approximation of the number of bytes that Rhonda's USB drive can hold.
The best approximation of the number of bytes that Rhonda's USB drive can hold is 8 x [tex]10^9[/tex] B.
What is Scientific Notation?Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
Given:
We have Rhonda has a USB drive that can hold 8, 000, 000, 000 B.
In Scientific Notation the decimal point should be placed just after one number and the number of extra zeroes raised to power.
Here we have 9 zeroes after 8 then the Scientific Notation is
= 8, 000, 000, 000 B.
= 8 x [tex]10^9[/tex] B
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Write an equation of the line that passes through the points (−4, −7) and (1, −7).
An equation of the line that passes through the points (−4, −7) and (1, −7) is y = -7.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.At data point (-4, -7), a linear equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-7) = (-7 - (-7))/(1 - (-4))(x - (-4))
y + 7 = (-7 + 7)/(1 + 4)(x + 4)
y + 7 = 0/5(x + 4)
y + 7 = 0
y = -7.
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Q1. what is 6 to the -3rd power
SEPERATE QUESTION
Q2. what is -9 to the -2nd power
SEPERATE QUESTION
Q3. what is 3 to the -4th power
Answer:
1. is 216
2. 100000
3. 81
Step-by-step explanation:
The “power” of a number indicates how many times the base would be multiplied by itself to reach the correct value.
(x - y) (x² - 2xy + y²)
On expanding the expression, we get -
{x³ - 2x²y + xy² - x²y + 2xy² - y³}
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
(x - y) (x² - 2xy + y²)
The given expression is -
(x - y) (x² - 2xy + y²)
x {x² - 2xy + y²} - y {x² - 2xy + y²}
x³ - 2x²y + xy² - x²y + 2xy² - y³
Therefore, on expanding the expression, we get -
{x³ - 2x²y + xy² - x²y + 2xy² - y³}
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circle the numbers that are part of the solution for the inequality x+2>5
Step-by-step explanation:
x + 2 > 5
x > 5-2
x> 3.
TO FND THE VALUE OF X
2 IS PART OF THE SOLUTION AND 5 TOO also >
with the absence of > you can not find x since the question will be algebraic.
A shop is recording queiong times of its customers and produces cumalative frequency graph
how many customers qeued for more than 20 minutes
Find the median queing time
The number of customers who queued for more than 20 minutes was 11 customers .
The median queuing time was 11 minutes .
How to find the queuing time ?The number of customers who queued for more than 20 minutes would be found by the formula :
= Number of customers at 25 minutes - Number of customers at 20 minutes
= 100 - 89
= 11 customers
The median queuing time would be the queuing time at 50 customers which according to the cumulative frequency graph is 11 minutes .
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