The amount of interest that Laura will be paid in the first 5 years is $600.
How much interest will Laura be paid in the first 5 years?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given that;
Principal P = $3,000Interest rate r = 4% = 4/100 = 0.04Elapsed time t = 5 yearsInterest I = ?Plug the given values into the above formula and solve for interest I.
I = P × r × t
I = $3,000 × 0.04 × 5
I = $3,000 × 0.2
I = $600
Therefore, the amount of interest payable is $600.
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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)
Amount of water in a pool
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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The DNA molecule comes in the form of a double helix, meaning two helices that wrap around one another. Suppose a single one of the helices has a radius of 7 A (1 angstrom = 10-8 cm) and one full turn of the helix has a height of 33 A. Find the paremetrization r(t) of the helix. r(t) = (7 cos(t), a,b) (Use symbolic notation and fractions where needed.) a = b= Find the arc length L of one full turn of the helix.
The parameterization of the helix is:
[tex]r(t) = (7 cos(t), 7 sin(t), 33/(2*\pi ) * t)[/tex] & the arc length of one full turn of the helix is approximately 147.26 Å
where t is the parameter that varies from 0 to [tex]2\pi[/tex]
In this parameterization, the first two coordinates give the coordinates of a point on a circle of radius 7 that lies in the plane perpendicular to the helix axis, while the third coordinate gives the height of the point along the axis.
To find the arc length L of one full turn of the helix, we use the arc length formula:
[tex]L = ∫_0^(2π) ||r'(t)|| dt[/tex]
where r'(t) is the derivative of r(t) with respect to t, and || || denotes the Euclidean norm.
We have:
[tex]r'(t) = (-7 sin(t), 7 cos(t), 33/(2*pi))and||r'(t)|| = √[(-7 sin(t))^2 + (7 cos(t))^2 + (33/(2pi))^2] = 7√(2 + (33/(2pi))^2)So, we get:L = ∫_0^(2π) 7√(2 + (33/(2pi))^2) dt = 7√(2 + (33/(2pi))^2) * ∫_0^(2π) dt = 14π√(2 + (33/(2*pi))^2)[/tex]
(Note: the symbol "Å" represents angstrom, which is [tex]10^(-10)[/tex] meters, and it is used to express atomic distances.)
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Point A is located at (-3, 7) on a
coordinate plane. Which point is located
8 units from Point A?
A. (-3, 8)
B. (8,7)
C. (−3, 1)
D. (-3,-1)
A point that is located 8 units from Point A include the following: D. (-3,-1).
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the coordinate of point A vertically downward by 8 units, the coordinates of the image of point A' include the following:
(x, y) → (x, y - 8)
Coordinate of point A = (-3, 7) → Coordinate of point A' (-3, 7 - 8) = (-3, -1)
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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.
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:
Yellow cab charges 1.75 flat rate in in addition to $0.75per mile. Leo has no more than $20 to spend on a ride. How many miles can Leo travel without exceeding his limit?
Show steps
Answer:
Step-by-step explanation:
Set x miles Leo can travel, and his cost have to be no more than $20, so
1.75+0.75x =20
0.75x = 20-1.75
0.75x = 18.25
x = 18.25/0.75 = 24.333 miles
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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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
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:
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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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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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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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.
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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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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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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Question Write an equation that you can use to find the value of x . Perimeter of square: 30 m
An equation that helped to find the value of x is 30 = 4x.
The value of x is 7.5mm.
What is the perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
A shape is a square.
And perimeter of the square is 30 mm.
And we know that the sides of the square are equal.
So, the perimeter of the square = 4 x The length of one side.
Substituting all the given values,
we get,
30 = 4x
x = 30/4
x = 7.5 mm
Therefore, x = 7.5 mm.
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HELP ME PLEASE ANYONE I NEED HELPP
Step-by-step explanation:
I don't know car stuff, but that looks like its asking you to use the formula:
F1 x r1 = F2 x r2
Therefore, it will be:
175N x 200mm = 160N x 20mm
I hope this helps :)
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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which is greater 4/7 ×1/4 or 4/7×1/6
Answer:4/7*1/4
trust me >:)
17.) passes through X(1,-4), parallel to YZ with Y(5, 2) and Z(-3,-5) helppp please
The equation of the line parallel to the line passing through the points Y(5, 2) and Z(-3,-5) will be y = 7/8x + 4.5.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line is passes through X(1,-4), parallel to YZ with Y(5, 2) and Z(-3,-5).
The equation of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -5 - 2 ) / ( -5 - 3 )
Slope = 7 / 8
The equation will be written as:-
y = 7/8x + c
The slope of the two parallel lines will be the same. The y-intercept of the parallel lines will be,
y = 7/8x + c
1 = (7/8 x -4 ) + c
c = 4.5
The equation will be:-
y = 7 / 8x + 4.5
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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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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.
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
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.
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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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]
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.